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IN THIS ISSUE

### Research Papers

J. Vib. Acoust. 2013;135(5):051001-051001-13. doi:10.1115/1.4024393.

It is difficult to use conventional nondestructive testing methods to detect damage, such as loosening of bolted connections, in a space frame structure due to the complexity of the structure and the nature of the possible damage. A vibration-based method that uses changes in the natural frequencies of a structure to detect the locations and extent of damage in it has the advantage of being able to detect various types of damage in the structure, including loosening of bolted connections. Since the vibration-based method is model-based, applying it to a space frame structure with L-shaped beams and bolted joints will face challenges ranging from the development of an accurate dynamic model of the structure to that of a robust damage detection algorithm for a severely underdetermined, nonlinear least-square problem under the effects of relatively large modeling error and measurement noise. With the development of modeling techniques for fillets in thin-walled beams (He and Zhu, 2009, “Modeling of Fillets in Thin-Walled Beams Using Shell/Plate and Beam Finite Elements,” ASME J. Vib. Acoust., 131 (5), p. 051002) and bolted joints (He and Zhu, 2011, “Finite Element Modeling of Structures With L-shaped Beams and Bolted Joints,” ASME J. Vib. Acoust., 131(1), p. 011010) by the authors, accurate physics-based models of space frame structures can be developed with a reasonable model size. A new damage detection algorithm that uses a trust-region search strategy combined with a logistic function transformation is developed to improve the robustness of the vibration-based damage detection method. The new algorithm can ensure global convergence of the iterations and minimize the effects of modeling error and measurement noise. The damage detection method developed is experimentally validated on an aluminum three-bay space frame structure with L-shaped beams and bolted joints. Three types of introduced damage, including joint damage, member damage, and boundary damage, were successfully detected. In the numerical simulation where there are no modeling error and measurement noise, the almost exact locations and extent of damage can be detected.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2013;135(5):051002-051002-12. doi:10.1115/1.4024509.

Many systems have, by their nature, a small damping and therefore they are potentially subjected to dangerous vibration phenomena. The aim of active vibration control is to contain this phenomenon, improve the dynamic performance of the system, and increase its fatigue strength. A way to reach this goal is to increase the system damping, preferably without changing its natural frequencies and vibration modes. In the past decades this has been achieved by developing the well-known independent modal space control (IMSC) technique. The paper describes a new approach to the synthesis of a modal controller to suppress vibrations in structures. It turns from the traditional formulation of the problem and it demonstrates how the performance of the controller can be evaluated through the analysis of the modal damping matrix of the controlled system. The ability to easily manage this information allows us to synthesize an efficient modal controller. Furthermore, it enables us to easily evaluate the stability of the control, the effects of spillover, and the consequent effectiveness in reducing vibration. Theoretical aspects are supported by experimental applications on a large flexible system.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2013;135(5):051003-051003-10. doi:10.1115/1.4023811.
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Vibration reduction in harmonically forced undamped systems is considered using a new vibration absorber setup. The vibration absorber is a platform that is connected to the ground by a spring and damper. The primary system is attached to the platform, and the optimal parameters of the latter are obtained with the aim of minimizing the peaks of the primary system frequency response function. The minimax problem is solved using a method based on invariant points of the objective function. For a given mass ratio of the system, the optimal tuning and damping ratios are determined separately. First, it is shown that the objective function passes through three invariant points, which are independent of the damping ratio. Two optimal tuning ratios are determined analytically such that two of the three invariant points are equally leveled. Then, the optimal damping ratio is obtained such that the peaks of the frequency response function are equally leveled. The optimal damping ratio is determined in a closed form, except for a small range of the mass ratio, where it is calculated numerically from two nonlinear equations. For a range of mass ratios, the optimal solution obtained is exact, because the two peaks coincide with the two equally leveled invariant points. For the remaining range, the optimal solution is semiexact. Unlike the case of the classical absorber setup, where the absorber performance increases with increasing mass ratios, it is shown that an optimal mass ratio exists for this setup, for which the absorber reaches its utmost performance. The objective function is shown in its optimal shape for a range of mass ratios, including its utmost shape associated with the optimal mass ratio of the setup.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2013;135(5):051004-051004-6. doi:10.1115/1.4024213.

Analytical and finite element models are developed for investigating the modal characteristics of a hyperelastic rubber latex membrane for micro air vehicle wings applications. A radially prestretched membrane specimen is attached to a thin, rigid circular ring and vibrated in vacuum and in air at atmospheric pressure. The natural frequencies of the membrane computed by analytical and finite element models are correlated well. The natural frequencies increase with mode and prestretch level of the membrane but decrease in air from those in vacuum due to the effect of added mass of air. The damping is low and has a very minimal effect on the frequencies but helps to reduce the amplitude of vibration. Aerodynamic pressure at different angles of attack and a freestream velocity is computed from the wind tunnel test data, and a finite element model is developed for investigating the effect of the aerodynamic pressure on the modal characteristics of the membrane. It is found that the effect of aerodynamic pressure on the natural frequencies of the membrane is not significant.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2013;135(5):051005-051005-11. doi:10.1115/1.4023913.
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This work provides an analytical solution for the nonlinear vibration of gear pairs that exhibit partial and total contact loss. Partial contact loss is where parts of contact lines lose contact although other parts remain in contact. The gear tooth surface modifications admit an arbitrary combination of profile and lead modifications. Modifications are a source of partial contact loss. The analysis also applies for total contact loss. Unlike models in the literature that are excited by static transmission error or time-varying mesh stiffness, the excitation and the nonlinearity are not a priori specified. Instead, the force-deflection function of the gear pair is provided by an independent source, such as a finite element model or Hertz contact formula. The manipulation of the single-degree-of-freedom oscillator equation of motion yields the excitation and the nonlinearity that arise from Fourier and Taylor series expansions of the force-deflection function. These expansions capture the essential contact behavior that includes tooth profile and lead modifications as well as the bending and shear flexibility of the gear teeth and gear blanks. The method of multiple scales gives the steady-state dynamic response in terms of a frequency-amplitude relation. Comparisons with gear vibration experiments and simulations from the literature that include spur and helical gears with tooth profile and lead modifications verify the method.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2013;135(5):051006-051006-13. doi:10.1115/1.4023998.

Characterizing dynamic characteristics of structures with uncertainty is an important task that provides critical predictive information for structural design, assessment, and control. In practical applications, sampling is the fundamental approach to uncertainty analysis but has to be conducted under various constraints. To address the frequently encountered data scarcity issue, in the present paper Gaussian processes are employed to predict and quantify structural dynamic responses, especially responses under uncertainty. A self-contained description of Gaussian processes is presented within the Bayesian framework with implementation details, and then a series of case studies are carried out using a cyclically symmetric structure that is highly sensitive to uncertainties. Structural frequency responses are predicted with data sparsely sampled within the full frequency range. Based on the inferred credible intervals, a measure is defined to quantify the potential risk of response maxima. Gaussian process emulation is proposed for Monte Carlo uncertainty analysis to reduce data acquisition costs. It is shown that Gaussian processes can be an efficient data-based tool for analyzing structural dynamic responses in the presence of uncertainty. Meanwhile, some technical challenges in the implementation of Gaussian processes are discussed.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2013;135(5):051007-051007-11. doi:10.1115/1.4024094.

It is recognized that unstable vibration occurs at a rotating speed above the major critical speed by a rotating-conducting-disk type magnetic damper, but not by a rotating-circular-magnet type magnetic damper. In addition, magnetic dampers generally have relatively poor damping performance. In the present work, two new rotating-circular-magnet type magnetic dampers, (which consist of a combined hollow cylinder magnet with alternating directional magnetic poles), are introduced and their design method is presented. Applying the modeling method that the authors have been studying, a prototype magnetic damper with a combined magnet is fabricated and the damping ratios from the analytical results agree well with those from the experimental results. Rotating tests are performed and it is confirmed that unstable vibration does not occur at a rotating speed of more than twice the major critical speed. Based on these findings, an optimally designed magnetic damper with a combined magnet is developed and a damping ratio of 0.25 (damping coefficient of 215 Ns/m) is achieved.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2013;135(5):051008-051008-10. doi:10.1115/1.4023990.

An analytical approach has been applied to obtain the solution of Navier's equation for a homogeneous, isotropic half-space under an inertial foundation subjected to a time-harmonic loading. Displacement potentials were used to change the Navier's equation to a system of wave-type equations. Calculus of variation was employed to demonstrate the contribution of the foundation's inertial effects as boundary conditions. Use of the Fourier transformation method for the system of Poisson-type equations and applying the boundary conditions yielded the transformed surface displacement field. Direct contour integration has been employed to achieve the surface waves. In order to clarify the foundation's inertial effects, related coefficients were defined and a parametric study was conducted. Final results revealed that increasing the mass per unit length of the foundation or the frequency of the applied harmonic load intensifies the inertial effect factors. On the other hand, an increase in strip width or Poisson's ratio would imply reduction in the inertial effect factors.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2013;135(5):051009-051009-10. doi:10.1115/1.4024377.

This paper aims to present a thorough investigation into the mechanics of a $C60$ fullerene oscillating within the center of a carbon nanotube bundle. To model this nanoscale oscillator, a continuum approximation is used along with a classical Lennard–Jones potential function. Accordingly, new semianalytical expressions are given in terms of single integrals to evaluate van der Waals potential energy and interaction force between the two nanostructures. Neglecting the frictional effects and using the actual van der Waals force distribution, the equation of motion is directly solved. Furthermore, a new semianalytical formula is derived from the energy equation to determine the precise oscillation frequency. This new frequency formula has the advantage of incorporating the effects of initial conditions and geometrical parameters. This enables us to conduct a comprehensive study of the effects of significant system parameters on the oscillatory behavior. Based upon this study, the variation of oscillation frequency with geometrical parameters (length of tubes or number of tubes in bundle) and initial energy (potential energy plus kinetic energy) is shown.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2013;135(5):051010-051010-13. doi:10.1115/1.4024216.

An optimization methodology to increase the noise transmission loss (TL) of damped sandwich structures is presented. The prediction of the TL uses a numerical tool based on a finite element formulation for the sandwich plate coupled to a boundary element method for the acoustic medium. This tool can be used for arbitrarily shaped three-layer sandwich plates with various boundary conditions and it is well adapted to parametric and optimization studies. First, a parametric study was conducted to choose the objective function, the constraints, and the pertinent design variables to use in the optimization problem which consist in reducing the sound power transmitted by a viscoelastically damped sandwich plate. Next, by constraining the acoustical behavior of the sandwich panel, the surface mass of the sandwich structure was minimized. It is shown that a significant reduction in the transmitted sound power can be achieved by selecting the appropriate geometric configuration and damping layer material.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2013;135(5):051011-051011-8. doi:10.1115/1.4023950.
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An energy harvester operating in the thickness-mode (TMH) or longitudinal-mode (LMH) consists of a piezoelectric element which is sandwiched between a proof mass and a base. The piezo-element is poled along a direction perpendicular to the electrodes. When the base is subjected to a sinusoidal excitation, along the poling direction, a relative motion is generated between the proof mass and the base producing mechanical strain in the piezoelectric element. The resulting strain is converted into electrical power by virtue of the direct piezoelectric effect. In this study, a shear-mode harvester (SMH) is considered as a viable alternative to the TMH and LMH to enhance the harvested output power. The enhancement is generated by capitalizing on the fact that the strain constant of the piezoelectric in shear is much higher than those due to thickness or longitudinal deflections. To achieve such an enhancement, the piezoelectric element is poled along a direction parallel to its electrodes and is sandwiched between a proof mass and oscillating base in a design similar to that of the TMH and the LMH. Sinusoidal excitation of the base, along the poling direction, makes the piezo-element experience mechanical shear strain which when converted into electrical power produces outputs that are larger than those of the TMH and the LMH. The theory governing the operation of this class of SMH is developed for simple resistive electrical loads. Numerical examples are presented to illustrate the optimal performance characteristics of the SMH in comparison with the TMH and LMH. The effect of the piezo-element material, excitation frequency and electrical load on the harvested power is presented. The obtained results demonstrate the feasibility of the SMH as a simple and effective means for enhancing the power output characteristics of conventional TMH and LMH.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2013;135(5):051012-051012-10. doi:10.1115/1.4023813.
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This work presents an effective method to identify the tip locations of an internal crack in cantilever plates based on a Kriging surrogate model. Samples of varying crack parameters (tip locations) and their corresponding root mean square (RMS) of random responses are used to construct the initial Kriging surrogate model. Moreover, the pseudo excitation method (PEM) is employed to speed up the spectral analysis. For identifying crack parameters based on the constructed Kriging model, a robust stochastic particle swarm optimization (SPSO) algorithm is adopted for enhancing the global searching ability. To improve the accuracy of the surrogate model without using extensive samples, a small number of samples are first used. Then an optimal point-adding process is carried out to reduce computational cost. Numerical studies of a cantilever plate with an internal crack are performed. The effectiveness and efficiency of this method are demonstrated by the identified results. The effect of initial sampling size on the precision of the identified results is also investigated.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2013;135(5):051013-051013-5. doi:10.1115/1.4023951.
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The transverse vibrations and stability of an axially moving sandwich beam are studied in this investigation. The face layers are assumed to be in the membrane state, which bears only axial loading but no bending. Only shear deformation is considered for the soft core layer. The governing partial equation is derived using Newton's second law and then transferred into a dimensionless form. The Galerkin method and the complex mode method are employed to study the natural frequencies. In comparison with the classical homogenous axially moving beam, the gyroscopic matrix is no longer skew-symmetric because of the introduction of the soft core. The critical speed for the divergence of the axially moving sandwich beam is analytically obtained. The contribution of the core layer shear modulus to the natural frequencies and critical speed is discussed.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2013;135(5):051014-051014-8. doi:10.1115/1.4023815.
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An enhanced multiple-input multiple-output (MIMO) filtered-x least mean square (FXLMS) algorithm using improved virtual secondary path is proposed as the basis for an active noise control (ANC) system for treating vehicle powertrain noise. This new algorithm is developed to overcome the limitation caused by the frequency-dependent property of the standard FXLMS algorithm and to reduce the variation of convergence speed inherent in multiple-channel cases, in order to improve the overall performance of the control system. In this study, the convergence property of the proposed algorithm is analyzed in the frequency domain in order to yield a better understanding of the physical meaning of the virtual secondary path. In practice, because of the arrangement and sensitivities of the actuators (speakers), transducers (microphones), and physical environment, the magnitude response of the main secondary paths can be very different from each other. This difference will cause difficulty in the overall convergence of the algorithm, which will result in minimal attenuation at some of the channels. The proposed channel equalized (CE) virtual secondary path algorithm is designed to tackle this difficulty by equalizing the mean magnitude level of the main secondary paths and by adjusting other secondary paths correspondingly to keep the coupling effects among the control channels unchanged. The performance of the proposed algorithm is validated by analyzing a two-input two-output active powertrain noise control system.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2013;135(5):051015-051015-9. doi:10.1115/1.4023952.

In this work, a semiactive electromagnetic vibration absorber has been developed based on a proposed electromagnetic stiffness adjustable spring model, which presents a new solution for adjusting stiffness in the field of vibration absorber devices. Simulation study on the electromagnetic spring has been performed to determine the structural parameter of the semiactive vibration absorber. An experimental rig is also built up to investigate its practical vibration control effectiveness. Firstly, the finite element model of the test bench is used to analyze its vibration characteristics. Then, the vibration reduction effect is predicted through the simulation analysis, from which the optimal control positions are found. Finally, the experimental studies are also conducted, and the results show that this semiactive electromagnetic vibration absorber has a frequency adjustment range from 21 Hz to 25 Hz, in which considerable vibration reduction from 5 dB to 10 dB can be achieved.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2013;135(5):051016-051016-6. doi:10.1115/1.4024208.

In the current study, the torsional vibration of carbon nanotubes is examined using the strain gradient theory and molecular dynamic simulations. The model developed based on this gradient theory enables us to interpret size effect through introducing material length scale parameters. The model accommodates the modified couple stress and classical models when two or all material length scale parameters are set to zero, respectively. Using Hamilton's principle, the governing equation and higher-order boundary conditions of carbon nanotubes are obtained. The generalized differential quadrature method is utilized to discretize the governing differential equation of the present model along with two boundary conditions. Then, molecular dynamic simulations are performed for a series of carbon nanotubes with different aspect ratios and boundary conditions, the results of which are matched with those of the present strain gradient model to extract the appropriate value of the length scale parameter. It is found that the present model with properly calibrated value of length scale parameter has a good capability to predict the torsional vibration behavior of carbon nanotubes.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2013;135(5):051017-051017-10. doi:10.1115/1.4023991.

The present study aims at the free vibration analysis of double tapered columns. Foundation is assumed to be elastic and the effects of self-weight and tip mass with significant moment of inertia are considered. The governing equation of motion is obtained using the Hamilton principle, based on both the Euler–Bernoulli and Timoshenko beam models. Applying the power series method of Frobenius, the base solutions of the governing equations are obtained in the form of a power series via general recursive relations. Applying the boundary conditions, the natural frequencies of the beam/column are obtained using both models. The obtained results are compared with literature and a very good agreement is achieved. Subsequently, comprehensive studies are performed to provide an insight into the variation of the natural frequencies and instability conditions of the beam with respect to the tip mass, self-weight, taper ratio, slenderness, and foundation stiffness and eventually some general conclusions are drawn.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2013;135(5):051018-051018-9. doi:10.1115/1.4024095.

This paper proposes a novel retrofittable approach for dual-functional energy-harvesting and robust vibration control by integrating the tuned mass damper (TMD) and electromagnetic shunted resonant damping. The viscous dissipative element between the TMD and primary system is replaced by an electromagnetic transducer shunted with a resonant RLC circuit. An efficient gradient based numeric method is presented for the parameter optimization in the control framework for vibration suppression and energy harvesting. A case study is performed based on the Taipei 101 TMD. It is found that by tuning the TMD resonance and circuit resonance close to that of the primary structure, the electromagnetic resonant-shunt TMD achieves the enhanced effectiveness and robustness of double-mass series TMDs, without suffering from the significantly amplified motion stroke. It is also observed that the parameters and performances optimized for vibration suppression are close to those optimized for energy harvesting, and the performance is not sensitive to the resistance of the charging circuit or electrical load.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2013;135(5):051019-051019-14. doi:10.1115/1.4023992.

In this study, the aeroelastic stability and response of an aircraft swept composite wing in subsonic compressible flow are investigated. The composite wing was modeled as an anisotropic thin-walled composite beam with the circumferentially asymmetric stiffness structural configuration to establish proper coupling between bending and torsion. Also, the structural model consists of a number of nonclassical effects, such as transverse shear, material anisotropy, warping inhibition, nonuniform torsional model, and rotary inertia. The finite state form of the unsteady aerodynamic loads have been modeled based on the indicial aerodynamic theory and strip theory in the subsonic compressible flow. Novel Mach dependent exponential approximations of the indicial aerodynamic functions have been developed. The extended Galerkin’s method was used to construct the mass, stiffness, and damping matrices of the nonconservative aeroelastic system. Eigen analysis of the system was performed to obtain the aeroelastic instability (divergence and flutter) boundaries. Also, solving the equations of motion in the time domain leads to the aeroelastic response of wing in different flight speeds. The obtained results are compared with the available results in the literature, which reveals an excellent agreement. The numerical results obtained in this article seek to clarify the effects of geometrical and material couplings and flight Mach number on the aeroelastic instability and response of composite wings in subsonic compressible flow.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2013;135(5):051020-051020-8. doi:10.1115/1.4024384.

This paper presents a modeling approach for estimating time varying loads acting on a component from experimental strain measurements. The strain response of an elastic vibrating system is written as a linear superposition of strain modes. Since the strain modes, as well as the normal displacement modes, are intrinsic dynamic characteristics of a component, the dynamic loads exciting a component are estimated by measuring induced strain fields. The accuracy of the estimated loads depends on a number of factors, such as the placement locations and orientations of the gauges on the instrumented structure, as well as the number of retained modes from strain modal analysis. A solution procedure based on the construction of D-optimal designs is implemented to determine the optimum locations and orientations of strain gauges such that the variance in load estimates is minimized. A numerical as well as an experimental validation of the proposed approach through two example problems is also presented.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2013;135(5):051021-051021-8. doi:10.1115/1.4023999.

A dynamic model of a pantograph-catenary system is established. In the model, motion of the pantograph is coupled with that of the catenary by friction. Stability of the pantograph-catenary system is studied using the finite element complex eigenvalue method. Numerical results show that there is a strong propensity of self-excited vibration of the pantograph-catenary system when the friction coefficient is greater than 0.1. The dynamic transient analysis results show that the self-excited vibration of the pantograph-catenary system can affect the contact condition between the pantograph and catenary. If the amplitude of the self-excited vibration is strong enough, the contact may even get lost. Parameter sensitivity analysis shows that the coefficient of friction, static lift force, pan-head suspension spring stiffness, tension of contact wire, and the spatial location of pantograph have important influences on the friction-induced, self-excited vibration of the pantograph-catenary system. Bringing the friction coefficient below a certain level and choosing a suitable static lift force can suppress or eliminate the contact loss between the pantograph and catenary.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2013;135(5):051022-051022-16. doi:10.1115/1.4023831.

This paper discusses the control of coupled bending and axial vibrations in L-shaped and portal planar frame structures. The controller is designed based on a wave standpoint, in which vibrations are described as waves traveling along uniform structural waveguides, and being reflected and transmitted at structural discontinuities. Active discontinuities are created using active control forces/moments both along structural elements and at structural joints to control vibration waves. The classical Euler–Bernoulli as well as the advanced Timoshenko bending theories are applied in modeling and controlling the flexural vibrations in planar frames. The axial vibrations are modeled using the elementary theory as it is typically valid for frequencies up to twice the cutoff frequency of Timoshenko bending waves. Results are compared between the two bending vibration theories. It is concluded that for relatively higher frequencies, typically when the transverse dimensions are not negligible with respect to the wavelength, the effects of rotary inertia and shear distortion must be taken into account for both vibration analysis and control design.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2013;135(5):051023-051023-11. doi:10.1115/1.4024609.

By using magnetorheological (MR) fluid as the lubricating oil in a traditional squeeze film damper (SFD), one can build a variable-damping SFD, thereby controlling the vibration of a rotor by controlling the magnetic field. This study aims to control the vibration of a flexible rotor system using a magnetorheological squeeze film damper (MR-SFD). In order to evaluate the performance of the damper, the Bingham plastic model is used for the MR fluid and the hydrodynamic equation of MR-SFD is presented. Usually, the numerical methods are necessary for solving this equation. These methods are too costly and time consuming, especially in the simulation of complex rotors and the implementation of model-based controllers. To fix this issue, an innovative estimated equation for pressure distribution in MR-SFD is presented in this paper. By integration of this explicit expression, the hydrodynamic forces of MR-SFD are easily calculated as an algebraic equation. It is shown that the pressure and forces, which are calculated from the introduced expression, are consistent with the corresponding results of the original equations. Furthermore, considering the structural and parametric uncertainties of the system, proportional-integral-furthermore controller (PID) and sliding mode controllers are chosen for reducing the vibration level of the flexible rotor system, which is modeled by the finite element method. The time and frequency responses of a flexible rotor in the presence of these controllers show a good performance in reducing vibration of the shaft's midpoint, although near the rotor's critical speed the results of the sliding mode controller (SMC) are better than the corresponding results of the PID controller. The last part of this article is devoted to an analysis of the system's uncertainties. The results of the open loop system indicate that changes in the stiffness coefficient of the elastic foundation and the temperature of the MR fluid (two uncertainties of the system) strongly affects the outputs while using the controllers well increases the robustness of the system. The obtained results indicate that both the PID and sliding mode controllers have good performance against the uncertainty of the stiffness coefficient, but for changes in the MR fluid's temperature, the SMC presents better outputs compared to the PID controller, especially for high rotational speeds.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2013;135(5):051024-051024-5. doi:10.1115/1.4024559.

The inverse method based on the numerical solution of Laplace's equation is introduced for the design of acoustic metamaterial devices. An arbitrary shaped acoustic concentrator and an external cloak are designed numerically and validated by full wave simulation. Besides, an acoustic reciprocal cloak and a field rotator are proposed. Compared with the analytical method, the inverse method is much more universal, and arbitrary shaped acoustic metamaterial devices can be flexibly designed without any knowledge of the transformation equations.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2013;135(5):051025-051025-13. doi:10.1115/1.4024215.

In this article, a dynamical model of the vibrations and acoustic radiation of a circular clamped plate excited by a voice coil and two annular piezoelectric patches is derived. This model is used to perform an optimization of the geometries with the objective to minimize the vibration of the plate along its second and third modes, so that the plate's radiation is equilibrated between its first and fourth eigenfrequencies. Experiments are then performed and show a good agreement with the model. Radiation of the designed system presents improvements when compared to a system when only a voice coil is used.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2013;135(5):051026-051026-17. doi:10.1115/1.4024610.

This paper reports a bearing fault detection method based on kurtosis-based adaptive bandstop filtering (KABS) and iterative autocorrelation (IAC). The interferences in the bearing signal can be removed by KABS filtering, whereas IAC is employed for noise reduction and signal enhancement. In the KABS method, two window-merging schemes are proposed to identify the frequency bands potentially containing interferences and to preserve those covering fault frequencies. Issues related to the selection of the number of autocorrection iterations are also discussed. The proposed method can be used for bearing fault detection in a low signal-to-noise ratio (SNR) and low signal-to-interference ratio (SIR) environment. The implementation of the proposed method does not require prior knowledge of the fault-excited resonant frequency. The performance of the proposed method has been examined by simulation analysis, with favorable comparisons to the Hilbert enveloping, energy operator, and spectrum kurtosis methods. Its effectiveness in bearing fault detection has also been demonstrated using experimental data.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2013;135(5):051027-051027-12. doi:10.1115/1.4024698.

In this study, a model for the analysis of the wave localization in a special kind of simply-supported beam bridge, namely, the periodic elevated railway (PER), is developed. For simplicity, each span of the PER is supposed to be composed of two longitudinal beams, a pier, and three linking springs. The standard linear solid model is employed to describe the damping of the materials of the piers and beams. Transfer matrix for each span of the PER undergoing in-plane vibration is derived, whereby the wave transfer matrix for each span is obtained. By means of the Wolf's algorithm and using the aforementioned wave transfer matrices, the localization factors accounting for wave localization in the PER are determined. With the proposed model, the influence of the disorder of the beam lengths on the wave localization in the PER is examined. Also, the interactive effect of the damping and the beam-length disorder on the wave localization in the PER is investigated. As a special case, the wave localization in a PER with rigid beam-beam-pier (BBP) junctions is also discussed in this study. Moreover, by the wave transfer matrix method, the wave localization and conversion phenomena in a finite disordered PER segment are investigated. Finally, the relation between the response of a finite disordered PER segment to external loadings and the degrees of the disorder of the PER segment is examined.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2013;135(5):051028-051028-7. doi:10.1115/1.4024217.

Recent works have studied ground resonance in helicopters under the aging or damage effects. Indeed, blade lead-lag stiffness may vary randomly with time and differ from blade to blade. The influence of stiffness dissimilarities between blades on the stability of the ground resonance phenomenon was determined through numerical investigations into the periodic equations of motion, treated using Floquet's theory. A stability chart highlights the appearance of new instability zones as a function of the perturbation introduced on the lead-lag stiffness of one blade. In order to validate the theoretical results, a new experimental setup was designed and developed. The ground resonance instabilities were investigated using different rotors and the boundaries of stability were determined. A good correlation between both theoretical and experimental results was obtained and the new instability zones, found in asymmetric rotors, were verified experimentally. The temporal responses of the measured signals highlighted the exponential divergence in the instability zones.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2013;135(5):051029-051029-9. doi:10.1115/1.4023820.

This paper proposes a simple expression for calculating the restoring and damping forces of an air spring equipped with a small pipe. Air springs are commonly used in railway vehicles, automobiles, and various vibration isolators. The air spring discussed in this study consists of two tanks connected by a long pipe. Using a pipe instead of an orifice enables flexibility in the arrangement of the two tanks. In addition, this makes it possible to manufacture a thin air spring. A vertical translational oscillating system, which consists of a single mass supported by this type of air spring, looks like a single-degree-of-freedom (SDOF) system. However, it may have two resonance points. In this paper, we propose a vibratory model of a system supported by the air spring. With the proposed model it is possible to correctly reproduce the two resonance points of a system consisting of a single mass supported by this type of air spring. In our analysis, assuming that the vibration amplitude is small and the flow through the pipe is laminar, we derive the spring constant and damping coefficient of an air spring subjected to a simple harmonic motion. Then, we calculate the frequency response curves for the system and compare the calculated results with the experimental values. According to the experiment, there is a remarkable amplitude dependency in this type of air spring, so the frequency response curves for the system change with the magnitude of the input amplitude. It becomes clear that the calculation results are in agreement with the limit case when the input amplitude approaches zero. We use a commercially available air spring in this experiment. Our study is useful in the design of thin air spring vibration isolators for isolating small vibrations.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2013;135(5):051032-051032-11. doi:10.1115/1.4024853.

To calculate the probability density function of the response of a random acoustic field, a change-of-variable perturbation stochastic finite element method (CVPSFEM), which integrates the perturbation stochastic finite element method (PSFEM) and the change-of-variable technique in a unified form, is proposed. In the proposed method, the response of a random acoustic field is approximated as a linear function of the random variables based on a first order stochastic perturbation analysis. According to the linear relationship between the response and the random variables, the formal expression of the probability density function of the response of a random acoustic field is obtained by the change-of-variable technique. The numerical examples on a two-dimensional (2D) acoustic tube and a three-dimensional (3D) acoustic cavity of an automobile cabin verify the accuracy and efficiency of the proposed method. Hence, the proposed method can be considered as an effective method to quantify the effects of the parametric randomness of a random acoustic field on the sound pressure response.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2013;135(5):051034-051034-13. doi:10.1115/1.4024794.

The present study focuses on the uncertainty quantification of an aeroelastic instability system. This is a classical dynamical system often used to model the flow induced oscillation of flexible structures such as turbine blades. It is relevant as a preliminary fluid-structure interaction model, successfully demonstrating the oscillation modes in blade rotor structures in attached flow conditions. The potential flow model used here is also significant because the modern turbine rotors are, in general, regulated in stall and pitch in order to avoid dynamic stall induced vibrations. Geometric nonlinearities are added to this model in order to consider the possibilities of large twisting of the blades. The resulting system shows Hopf and period-doubling bifurcations. Parametric uncertainties have been taken into account in order to consider modeling and measurement inaccuracies. A quadrature based spectral uncertainty tool called polynomial chaos expansion is used to quantify the propagation of uncertainty through the dynamical system of concern. The method is able to capture the bifurcations in the stochastic system with multiple uncertainties quite successfully. However, the periodic response realizations are prone to time degeneracy due to an increasing phase shifting between the realizations. In order to tackle the issue of degeneracy, a corrective algorithm using constant phase interpolation, which was developed earlier by one of the authors, is applied to the present aeroelastic problem. An interpolation of the oscillatory response is done at constant phases instead of constant time and that results in time independent accuracy levels.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2013;135(5):051035-051035-10. doi:10.1115/1.4024762.

In this paper, we make an attempt to describe the phenomenon of wave propagation when a disturbance is introduced in an electromechanical system having a lumped parameter representation. We initially discuss mechanical waves in homogeneous spring mass systems and then focus on electromechanical wave propagation in power systems. We primarily discuss ring and open end systems. Eigenvalue analysis of the system is done to find the behavior of the orthogonal modes as a function of time and space. We then derive an expression for velocity of propagation of the disturbance wave and the transport delay associated with it. Effects of system parameters, like generator inertia and transmission line resistance, are also discussed. Although the theory was developed considering homogeneous systems (identical values of inertia/mass, line parameters/spring constant, etc.), an implementation on a nonhomogeneous system is also presented in this paper. Numerical simulations were done and compared with the analytical results derived in this paper.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2013;135(5):051036-051036-10. doi:10.1115/1.4024557.

A spatial discretization and substructure method is developed to accurately calculate dynamic responses of one-dimensional structural systems, which consist of length-variant distributed-parameter components, such as strings, rods, and beams, and lumped-parameter components, such as point masses and rigid bodies. The dependent variable of a distributed-parameter component is decomposed into boundary-induced terms and internal terms. The boundary-induced terms are interpolated from boundary motions, and the internal terms are approximated by an expansion of trial functions that satisfy the corresponding homogeneous boundary conditions. All the matching conditions at the interfaces of the components are satisfied, and the expansions of the dependent variables of the distributed-parameter components absolutely and uniformly converge if the dependent variables are smooth enough. Spatial derivatives of the dependent variables, which are related to internal forces/moments of the distributed-parameter components, such as axial forces, bending moments, and shear forces, can be accurately calculated. Combining component equations that are derived from Lagrange's equations and geometric matching conditions that arise from continuity relations leads to a system of differential algebraic equations (DAEs). When the geometric matching conditions are linear, the DAEs can be transformed to a system of ordinary differential equations (ODEs), which can be solved by an ODE solver. The methodology is applied to several moving elevator cable-car systems in Part II of this work.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2013;135(5):051037-051037-21. doi:10.1115/1.4024558.

This paper uses the methodology developed in Part I of this work to study the longitudinal, transverse, and their coupled vibrations of moving elevator cable-car systems. A suspension cable is a one-dimensional length-variant distributed-parameter component. When there is only one suspension cable connected to the car, the car is modeled as a point mass. When there are multiple suspension cables, the car is modeled as a rigid body, and the rotation of the car is considered. There are complicated matching conditions between the cable and car, which cannot be satisfied in the classical assumed modes method but can be satisfied in the current method. Hence, not only the longitudinal and transverse displacements but also the internal forces/moment, such as the axial force, the bending moment, and the shear force, which are related to the spatial derivatives of the longitudinal and transverse displacements, are accurately calculated. The results from different choices of boundary motions and trial functions are essentially the same, and the convergence is much faster than that of the assumed modes method. The longitudinal-transverse coupled vibrations of a moving cable-car system are also studied using the current method, and the results are compared with those from the linear models. While the result from the linear model for the transverse vibration agrees well with that from the nonlinear coupled model, the axial force from the linear model can significantly differ from that from the nonlinear model when the car approaches the top of the hoistway.

Commentary by Dr. Valentin Fuster

### Research Paper

J. Vib. Acoust. 2013;135(5):051030-051030-9. doi:10.1115/1.4024760.
FREE TO VIEW

This paper is meant to model free vibration of a coupled rotor-bearing-housing system. In particular, the rotor is cyclic symmetric and spins at constant speed while the housing is stationary and flexible. The rotor and housing are assembled via multiple, linear, elastic bearings. A set of equations of motion is derived using component mode synthesis, in which the rotor and the housing each are treated as a component. The equations of motion take the form of ordinary differential equations with periodic coefficients. Analyses of the equations of motion indicate that instabilities could appear at certain spin speed in the form of combination resonances of the sum type. To demonstrate the validity of the formulation, two numerical examples are studied. For the first example, the spinning rotor is an axisymmetric disk, and the housing is a square plate with a central shaft. The rotor and the housing are connected via two linear elastic bearings. For the second example, the rotor is cyclic symmetric in the form of a disk with four evenly spaced radial slots. The housing and bearings remain the same. In both examples, instability appears as a combination resonance of the sum type between a rotor mode and an elastic housing mode. The cyclic symmetric rotor, however, has more instability zones. Finally, effects of damping are studied. Damping of the housing widens the instability zones, whereas the damping of the rotor does the opposite.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2013;135(5):051031-051031-13. doi:10.1115/1.4024845.
FREE TO VIEW

Nonlinear phenomena such as internal resonances have significant potential applications in micro electro mechanical systems (MEMS) for increasing the sensitivity of biological and chemical sensors and signal processing elements in circuits. While several theoretical systems are known which exhibit 1:2 or 1:3 internal resonances, designing systems that have the desired properties required for internal resonance and that are physically realizable as MEMS devices is a significant challenge. Traditionally, the design process for obtaining resonant structures exhibiting an internal resonance has relied heavily on the designer's prior knowledge and experience. However, with advances in computing power and topology optimization techniques, it should be possible to synthesize structures with the required nonlinear properties (such as having modal interactions) computationally. In this work, a preliminary work on computer based synthesis of structures consisting of beams for desired internal resonance is presented. The linear structural design is accomplished by a Finite Element Method (FEM) formulation implemented in Matlab to start with a base structure and iteratively modify it to obtain a structure with the desired properties. Possible design criteria are having the first two natural frequencies of the structure in some required ratio (such as 1:2 or 1:3). Once a topology of the structure is achieved that meets the desired criterion, the linear mode shapes of the structure can be extracted from the finite element analysis, and a more complete Lagrangian formulation of the nonlinear elastic structure can be used to develop a nonlinear two-mode model of the structure. The reduced-order model is expected to capture the appropriate resonant dynamics associated with modal interactions between the two modes. The nonlinear response of the structure can be obtained by application of perturbation methods such as averaging on the two-mode model. Many candidate structures are synthesized that meet the desired modal frequency criterion and their nonlinear responses are compared.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2013;135(5):051033-051033-10. doi:10.1115/1.4024765.
FREE TO VIEW

A new model for a gas-filled encapsulated thermal-acoustic transducer, which uses newly devised carbon nanotube (CNT) thin film is developed and the exact and approximate solutions are derived. A comparison between theoretical prediction and experimental data is presented and excellent agreement is reported. The frequency response for this acoustic transducer is investigated and the acoustic response of as a function of window–thin-film distance of the encapsulated transducer is discussed. An optimal distance between window and thin film is successfully derived and used in some practical examples. Resonance takes place for a suitable input frequency, and thus such transducers can be used to either generate acoustic waves of specific frequency or to filter specific resonant frequencies from a wide spectrum of signals. This kind of transducer can be immersed in different liquid media. A gaseous medium shows better performance at lower frequency while it is otherwise for a liquid medium. The conclusions derived in this work could be regarded as effective guidelines and information for enhancing thermal-acoustics efficiency conversion, as well as for the optimal design of a thermal-acoustic transducer.

Commentary by Dr. Valentin Fuster

### Technical Briefs

J. Vib. Acoust. 2013;135(5):054501-054501-5. doi:10.1115/1.4024209.

The interaction of vibratory traveling waves in rotating and stationary axisymmetric components is examined. In the most general case, a resonance can occur when the wave propagation speed in a first structure is equal in magnitude and direction to the rotational velocity of an adjacent structure. When a backward wave in a rotor appears stationary, a major resonance, as discussed in Wilfred Campbell's classic paper (Campbell, W., 1924, “The Protection of Steam Turbine Disc Wheels from Axial Vibrations,” Trans ASME, 46, pp. 31–160), results. A related resonance has been observed when the wave propagation speed in the stator is equal to the physical speed of the adjacent rotor. A third mechanism is derived for resonance between a wave in rotor 1 and a co- or counter-rotating rotor 2. Description of a component test which demonstrated this final phenomenon is provided.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2013;135(5):054502-054502-5. doi:10.1115/1.4024761.

In gas turbine applications, forced vibrations of turbine blades under resonant—or nearly resonant—conditions are undesirable. Usually in airfoil design procedures, at least the first three blade modes are required to be free of excitation in the operating speed range. However, not uncommonly, a blade may experience resonance at other higher natural frequencies. In an attempt to avoid resonant oscillations, the structural frequencies are tuned away from the excitation frequencies by changing the geometry of the blade. The typical iterative design process—of adding and removing material through restacking the airfoil sections—is laborious and in no way assures an optimal design. In response to the need for an effective and fast methodology, the guided tuning of turbine blades method (GTTB) is developed and presented in this paper. A practical tuning technique, the GTTB method is based on structural perturbations to the mass and stiffness at critical locations, as determined by the methodology described herein. This shifts the excited natural frequency out of the operating speed range, while leaving the other structural frequencies largely undisturbed. The methodology is demonstrated here in the redesign of an actual turbine blade. The numerical results are experimentally validated using a laser vibrometer. The results indicate that the proposed method is not computationally intensive and renders effective results that jibe with experiments.

Commentary by Dr. Valentin Fuster