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### Research Papers

J. Vib. Acoust. 2017;139(6):061001-061001-8. doi:10.1115/1.4036866.

In this paper, we study the phenomenon of separation of traveling and standing waves in a one-dimensional rigid-walled circular duct. The underlying mechanism for separation, mode complexity, is linear and introduced here by a damped side branch representing an impedance discontinuity. The left end of the duct is driven at a single frequency by a harmonic acoustic source, and the right end is a rigid termination. The position and impedance of the side branch are independent parameters in the analysis. Sufficient conditions for acoustic wave separation in the duct are derived analytically and employed in a three-dimensional finite element analysis to verify the theoretical result. A physical experiment, consisting of a circular duct with a damped side branch, was constructed based on analytical predictions, the physical parameters were measured or identified, and its performance was documented. These experimental parameters were employed in a second three-dimensional finite element analysis to obtain a direct comparison with experimental results. The comparison reveals the extent to which higher-order (unmodeled) effects degrade the separation phenomenon. It is demonstrated that an intermediate damped side branch used as a nonresonant device can be predictively designed to achieve nearly ideal separation of traveling and standing waves in a rigid-walled circular duct in order to direct and control acoustic energy transmission through the duct system.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;139(6):061002-061002-6. doi:10.1115/1.4036869.

This paper deals with the vibroacoustic behavior of an electric window-lift gear motor for automotive vehicle which consists of a direct current (DC) motor and a worm gear. After describing the overall vibroacoustic behavior of this system and identifying the various excitation sources involved, this study focuses on the excitation sources associated to the contacts between brushes and commutator. To that end, a specific test bench is designed. It makes use of a modified gear motor for which various specific rotors are driven with an external brushless motor. It allows the discrimination of some excitation sources associated to the contact between brushes and commutator by removing them one after the other. The respective weight of friction, mechanical shocks, electrical current flow, and commutation arcs occurring jointly at the brush/commutator interface are dissociated and evaluated. The friction and the mechanical shocks between brushes and commutator blades increase the vibroacoustic response of the window-lift gear motor. The flowing of electrical current in brushes/commutator contacts tends to moderate the frictional component of excitation sources, while commutation arcs induce their rising, leading to a global additive contribution to the dynamic response.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;139(6):061003-061003-12. doi:10.1115/1.4036868.

In this work, the damping characteristics of circular cylindrical sandwich shell with a three-layered viscoelastic composite core are investigated. The new composite core is composed of the identical inclusions of graphite-strips which are axially embedded within a cylindrical viscoelastic core at its middle surface. The physical configuration of the composite core is attributed in the form of a cylindrical laminate of two identical monolithic viscoelastic layers over the inner and outer cylindrical surfaces of middle viscoelastic composite layer so that it is a three-layered viscoelastic composite core. A finite element (FE) model of the overall shell is developed based on the layerwise deformation theory and Sander's shell theory. Using this FE model, the damping characteristics of the shell are studied within an operating frequency range after configuring the size and circumferential distribution of graphite-strips in optimal manner. The numerical results reveal significantly improved damping in the sandwich shell for the use of present three-layered composite core instead of traditional single-layered viscoelastic core. It is also found that the three-layered core provides the advantage in achieving damping at different natural modes as per their assigned relative importance while it is impossible in the use of single-layered viscoelastic core.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;139(6):061004-061004-9. doi:10.1115/1.4036888.

Studies on dissipative metamaterials have uncovered means to suppress vibration and wave energy via resonant and bandgap phenomena through such engineered media, while global post-buckling of the infinitely periodic architectures is shown to tailor the attenuation properties and potentially magnify the effective damping effects. Yet, despite the promise suggested, the practical aspects of deploying metamaterials necessitates a focus on finite, periodic architectures, and the potential to therefore only trigger local buckling features when subjected to constraints. In addition, it is likely that metamaterials may be employed as devices within existing engineering systems, so as to motivate investigation on the usefulness of metamaterials when embedded within excited distributed or multidimensional structures. To illuminate these issues, this research undertakes complementary computational and experimental efforts. An elastomeric metamaterial, ideal for embedding into a practical engineering structure for vibration control, is introduced and studied for its relative change in broadband damping ability as constraint characteristics are modified. It is found that triggering a greater number of local buckling phenomena provides a valuable balance between stiffness reduction, corresponding to effective damping magnification, and demand for dynamic mass that may otherwise be diminished in globally post-buckled metamaterials. The concept of weakly constrained metamaterials is also shown to be uniformly more effective at broadband vibration suppression of the structure than solid elastomeric dampers of the same dimensions.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;139(6):061005-061005-13. doi:10.1115/1.4036928.

This paper presents a study of the dynamics and control of clutchless automated manual transmissions (CLAMT) for the purpose of investigating the system behavior during up and down shifts. To achieve this, a multibody dynamic model of the proposed powertrain is implemented to simulate the transient behavior of the system, including a direct current (DC) equivalent model of the electric machine (EM) and a synchronizer mechanism model. Closed-loop control of motor speed and torque is used in conjunction with synchronizer mechanism actuation to functionally achieve gear shifting without the need for a primary friction clutch. This includes nested torque–speed closed-loops to implement alternative motor control functionalities at different stages of gear change. To evaluate the performance of shift control, shift metrics including longitudinal jerk, vibration dose value (VDV), and shifting duration are evaluated from simulation results. These results demonstrate the most significant impact on the transient response of the powertrain results from the reduction and reinstatement of motor torque during shift control. Speed control of the motor during the shift transient directly impacts on the duration of shifting, but not the transient response of the powertrain.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;139(6):061006-061006-12. doi:10.1115/1.4036926.

A novel, unique squeak test apparatus was developed to measure squeak propensity of a given pair of materials with a purpose to build a database for automotive engineers. The apparatus employs a sprag-slip mechanism to generate friction-induced, unstable sliding motion between the two materials that leads to a repeatable squeak noise to enable quantitative rating of the squeak propensity of a given pair of materials. An analytical model of the system was developed to study dynamic characteristics of the mechanism to gain insights to design the test apparatus. Stability analysis of the system identified unstable regions of the motion in parameter planes defined by the kinetic coefficient of friction and the attack angle. Furthermore, the effect of these system parameters on the amplitude of the limit cycle was investigated to obtain guidance to design the device. An automatic rating algorithm of squeak noises previously developed by authors was employed to calculate the squeak propensity of the material pairs. A practical engineering procedure is envisioned that can handle squeak problems in the design stage more effectively by taking advantage of such a squeak propensity database.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;139(6):061007-061007-10. doi:10.1115/1.4036930.

Material and physical properties of a frequency-dependent visco-elastic sandwich beam are modeled as a set of spatial random fields and represented by means of the Karhunen–Loève expansion. Variability analysis of frequency and loss factor are performed. An efficient approach based on modal stability procedure (MSP) is used, the so-called Monte Carlo simulation (MCS)–MSP method. The latter provides very reliable results and allows to analyze the impact of the input variability of a high number of random spatial quantities on the output response. The effect of independent and correlated couples of spatial random fields is investigated. It is shown that the output variability is generally more important for damping than for natural frequencies. Moreover, it is demonstrated that the input variability in geometrical properties are the most impacting for damping and frequency. The influence of input coefficient of variation on output variability is also studied. It is shown that a negative correlation between the face and core thicknesses result in high levels of output variability, when one parameter increases as the other decreases.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;139(6):061008-061008-7. doi:10.1115/1.4036927.

This paper evaluates the differences between two existing ways to derive the governing equations of axisymmetric rotors in an inertial frame of reference. According to the first approach, only a skew-symmetric gyroscopic matrix appears into the equations of motion. In the second approach, besides the gyroscopic term, a convective tensor is obtained from the kinetic energy expression. This contribution is proportional to the square of the rotational speed, and it modifies the elastic energy of the rotor. The weak form of the equations of motion has been solved using high-fidelity one-dimensional finite elements, which have been developed with the Carrera Unified Formulation (CUF). The fundamental nuclei of the gyroscopic and the convective matrices are presented in CUF form, for the first time. To highlight the differences between the two approaches, numerical simulations have been carried out on relatively simple rotor configurations, whose dynamic behaviors were already studied. The current results have been compared with the solutions presented in the literature to verify the correctness of the proposed formulation. For some structures, the results computed with the two approaches differ to a significant extent.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;139(6):061009-061009-10. doi:10.1115/1.4036929.

The growing of railway infrastructures in urban environments demands accurate methods to predict and mitigate potential annoyance of the inhabitants of the surrounding buildings. The present paper aims to contribute to the goal by proposing a numerical model to predict vibrations and reradiated noise due to railway traffic. The model is based on a substructuring approach, where the whole propagation media are considered, from the vibration source (the vehicle–track interaction) to the receiver (the building and its interior acoustic environment). The system track–ground–building is simulated by a 2.5D finite element method–perfectly matched layers (FEM–PML) model, formulated in the frequency-wavenumber domain. The reradiated noise assessment is based on a 2.5D FEM–method of fundamental solutions (MFS) model, where the FEM is used to obtain the structural dynamic response. The structural displacements computed are used as the vibration input for the MFS model in order to assess the acoustic response inside the building's compartments. An application example is presented to assess vibrations and reradiated noise levels inside the building due to railway traffic. This is then followed by a discussion about the potential benefits of the introduction of floating-slab-track systems.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;139(6):061010-061010-14. doi:10.1115/1.4036951.

Wind turbine blades undergo high operational loads, experience variable environmental conditions, and are susceptible to failure due to defects, fatigue, and weather-induced damage. These large-scale composite structures are fundamentally enclosed acoustic cavities and currently have limited, if any, structural health monitoring (SHM) in place. A novel acoustics-based structural sensing and health monitoring technique is developed, requiring efficient algorithms for operational damage detection of cavity structures. This paper describes the selection of a set of statistical features for acoustics-based damage detection of enclosed cavities, such as wind turbine blades, as well as a systematic approach used in the identification of competent machine learning algorithms. Logistic regression (LR) and support vector machine (SVM) methods are identified and used with optimal feature selection for decision-making via binary classification algorithms. A laboratory-scale wind turbine with hollow composite blades was built for damage detection studies. This test rig allows for testing of stationary or rotating blades, of which time and frequency domain information can be collected to establish baseline characteristics. The test rig can then be used to observe any deviations from the baseline characteristics. An external microphone attached to the tower will be utilized to monitor blade health while blades are internally ensonified by wireless speakers. An initial test campaign with healthy and damaged blade specimens is carried out to arrive at several conclusions on the detectability and feature extraction capabilities required for damage detection.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;139(6):061011-061011-9. doi:10.1115/1.4036952.

An efficient methodology to predict the nonlinear response of bladed disks with a dry friction ring damper is proposed. Designing frictional interfaces for bladed-disk systems is an important approach to dissipate vibration energy. One emerging technology uses ring dampers, which are ringlike substructures constrained to move inside a groove at the root of the blades. Such rings are in contact with the bladed disk due to centrifugal forces, and they create nonlinear dissipation by relative motion between the ring and the disk. The analysis of the dynamic response of nonlinear structures is commonly done by numerical integration of the equations of motion, which is computationally inefficient, especially for steady-state responses. To address this issue, reduced-order models (ROMs) are developed to capture the nonlinear behavior due to contact friction. The approach is based on expressing the nonlinear forces as equivalent nonlinear damping and stiffness parameters. The method requires only sector-level calculations and allows precalculation of the response-dependent equivalent terms. These factors contribute to the increase of the computational speed of the iterative solution methods. A model of a bladed disk and damper is used to demonstrate the method. Macro- and micro-slip are used in the friction model to account for realistic behavior of dry friction damping. For validation, responses due to steady-state traveling wave excitations are examined. Results computed by ROMs are compared with results from transient dynamic analysis (TDA) in ansys with the full-order model. It is found that the steady-state responses predicted from the ROMs and the results from ansys are in good agreement, and that the ROMs reduce computation time significantly.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;139(6):061012-061012-13. doi:10.1115/1.4036870.

A theoretical method is employed to study the free vibration characteristics of a finite ring-stiffened elliptic cylindrical shell. Vibration equations of the elliptic cylindrical shell are derived based on Flügge shell theory, and the effects of the ring stiffeners are evaluated via “smeared” stiffener theory whereby the properties of the stiffeners are averaged over the shell surface. The displacements of the shell are expanded in double Fourier series in the axial and circumferential directions, and the circumferential curvature is expanded in single Fourier series in the circumferential direction. The partial differential characteristic equations with variable coefficients are converted into a set of linear equations with constant coefficients which couple with each other about the circumferential modal parameters. Then, the natural frequencies of the finite ring-stiffened cylindrical shell are obtained. To verify the accuracy of the present method, the finite ring-stiffened elliptic cylindrical shell is degenerated into two models: one of which is a ring-stiffened circular cylindrical shell and the other of which is an elliptic cylindrical shell without ring stiffeners. The present results of the two degenerated shells show good agreements with available results from the literature. The effects of main parameters, including the ellipticity, the shell length ratio, the stiffener's interval, the stiffener's depth, and the stiffener's eccentricity, on the free vibration of the ring-stiffened elliptic cylindrical shell are examined in detail. The ellipticity makes the difference between the symmetric and antisymmetric modal frequencies of the shell. The stiffeners have a greater influence on the free vibration at relatively higher order circumferential modal parameters. The circumferential modal parameters corresponding to the fundamental frequency are affected by the ellipticity, shell length, stiffeners' interval, and depth. The eccentricity of the ring stiffeners has a weak effect on the vibration of the structure.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;139(6):061013-061013-10. doi:10.1115/1.4036931.

Accurate determination of acousto-elastic natural frequencies in centrifugal compressors is important in order to avoid resonance events that may lead to machine failure. Compressors operating with CO2 at high pressures, especially near its transition to supercritical state, deal with a wide variation in density and speed of sound. Natural frequency behavior under these conditions is studied here. A finite element method (FEM) based coupled acousto-elastic solver has been developed to study the modal coupling and interactions between the impeller and the side-cavity modes for an idealized compressor geometry. Pressure in the side-cavities is increased up to a very high value of 20 MPa and existence of fluid- and structure-dominant acousto-elastic modes is observed. The variation of the natural frequencies of these modes with pressure exhibits contrasting trends as CO2 transitions from gaseous to supercritical state.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;139(6):061014-061014-9. doi:10.1115/1.4037301.

The complex modes of an end-damped cantilevered beam are studied as an experimental example of a nonmodally damped continuous system. An eddy-current damper is applied, for its noncontact and linear properties, to the end of the beam, and is then characterized to obtain the effective damping coefficient. The state-variable modal decomposition (SVMD) is applied to extract the modes from the impact responses in the cantilevered beam experiments. Characteristics of the mode shapes and modal damping are examined for various values of the end-damper damping coefficient. The modal frequencies and mode shapes obtained from the experiments have a good consistency with the results of the finite element model. The variation of the modal damping ratio and modal nonsynchronicity with varying end-damper damping coefficient also follow the prediction of the model. Over the range of damping coefficients studied in the experiments, we observe a maximum damping ratio in the lowest underdamped mode, which correlates with the maximum modal nonsynchronicity. Complex orthogonal decomposition (COD) is applied in comparison to the modal identification results obtained from SVMD.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;139(6):061015-061015-13. doi:10.1115/1.4037138.

Rolling mill system may lose its stability due to the change of lubrication conditions. Based on the rolling mill vertical–torsional–horizontal coupled dynamic model with nonlinear friction considered, the system stability domain is analyzed by Hopf bifurcation algebraic criterion. Subsequently, the Hopf bifurcation types at different bifurcation points are judged. In order to restrain the instability oscillation induced by the system Hopf bifurcation, a linear and nonlinear feedback controller is constructed, in which the uncoiling speed of the uncoiler is selected as the control variable, and variations of tensions at entry and exit as well as system vibration responses are chosen as feedback variables. On this basis, the linear control of the controller is studied using the Hopf bifurcation algebraic criterion. And the nonlinear control of the controller is studied according to the center manifold theorem and the normal form theory. The results show that the system stability domain can be expanded by reducing the linear gain coefficient. Through choosing an appropriate nonlinear gain coefficient, the occurring of the system subcritical bifurcation can be suppressed. And system vibration amplitudes reduce as the increase of the nonlinear gain coefficient. Therefore, introducing the linear and nonlinear feedback controller into the system can improve system dynamic characteristics significantly. The production efficiency and the product quality can be guaranteed as well.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;139(6):061016-061016-9. doi:10.1115/1.4037299.

In this paper, a new model is proposed to study the coupled axial–torsional vibration of the drill string. It is assumed that rotary table angular speed is constant and equals to the nominal angular speed of the drill string. In addition, axial displacement of any point on the drill string is considered to be as the sum of rigid-body motion and elastic vibrations. The depth of cut is defined using instantaneous dynamic states instead of using the delayed model as presented in previous researches. A velocity-weakening function is introduced for modeling the behavior of the frictional component of the torque-on-bit (TOB) with respect to the bit angular speed. After discretizing vibration equations, stability analysis of the system is investigated by linearizing the nonlinear system around its steady-state response point. Considering nominal weight-on-bit (WOB) ($W0$) and nominal rotational speed ($Ω$) as the input parameters of the drilling, variation of maximum allowable value of ($W0$) is presented with respect to variation of $Ω$ . It is shown that the maximum allowable value of $W0$ has an increasing–decreasing behavior with respect to $Ω$. The effect of drill string upper and lower part lengths is studied on the stability of the system, and practical results are presented both in the condition that $W0$ is constant and in the condition that the hook upward force is constant. It is shown that by increasing the drill string length, the system is more exposed to instability, and this must be considered in regulating the input parameters of drilling.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;139(6):061017-061017-11. doi:10.1115/1.4037139.

This paper deals with the theoretical and experimental study of an electromechanical system (EMS) actuated by a chemo-inspired oscillator, namely, the Brusselator oscillator. The modeling of such a system is presented. Theoretical results show that the displacement or flexion of the EMS undergoes spiking oscillations. This kind of oscillation is due to the transfer of the Brusselator electronic circuit signal to the mechanical arm. The theoretical results are confirmed by an experimental study with a good qualitative agreement.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;139(6):061018-061018-6. doi:10.1115/1.4037137.

The moving web is widely used to make printing and packaging products, flexible electronics, cloths, etc. The impact of the variable density on printing web dynamic behavior is considered. The density changes in the form of sine half-wave in the lateral direction. Based on the D'Alembert's principle, the transverse vibration differential equation of moving printing web with variable density is established and is discretized by using the differential quadrature method (DQM). The complex characteristic equation is derived. The impacts of the density coefficient and the dimensionless speed on the web stability and vibration characteristics are discussed. The results show that it is feasible to use the DQM to analyze the problem of transverse vibration of printing web with varying density; the tension ratio and the density coefficient have important impacts on the stability of moving printing web. This study provides theoretical guidance and basis for optimizing the structure of printing press and improving the stable working speed of printing press and web.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;139(6):061019-061019-15. doi:10.1115/1.4037143.

Most of the technological developments achieved in the turbomachinery field during the last years have been obtained through the introduction of fluid dynamic bearings, in particular tilting pad journal bearings (TPJBs). However, even those bearings can be affected by thermal instability phenomena as the Morton effect at high peripheral speeds. In this work, the authors propose a new iterative finite element method (FEM) approach for the analysis of those thermal–structural phenomena: the proposed model, based on the coupling between the rotor dynamic and the thermal behavior of the system, is able to accurately reproduce the onset of thermal instabilities. The authors developed two versions of the model, one in the frequency domain and the other in the time domain; both models are able to assure a good tradeoff between numerical efficiency and accuracy. The computational efficiency is critical when dealing with the typical long times of thermal instability. The research activity has been carried out in cooperation with General Electric Nuovo Pignone SPA, which provided both the technical and experimental data needed for the model development and validation.

Topics: Bearings , Rotors
Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;139(6):061020-061020-6. doi:10.1115/1.4037395.

This research introduces a new approach to analytically derive the differential equations of motion of a thin spherical shell. The approach presented is used to obtain an expression for the relationship between the transverse and surface displacements of the shell. This relationship, which is more explicit than the one that can be obtained through use of the Airy stress function, is used to uncouple the surface and normal displacements in the spatial differential equation for transverse motion. The associated Legendre polynomials are utilized to obtain analytical solutions for the resulting spatial differential equation. The spatial solutions are found to exactly satisfy the boundary conditions for the simply supported and the clamped hemispherical shell. The results to the equations of motion indicate that the eigenfrequencies of the thin spherical shell are independent of the azimuthal coordinate. As a result, there are several mode shapes for each eigenfrequency. The results also indicate that the effects of midsurface tensions are more significant than bending at low mode numbers but become negligible as the mode number increases.

Commentary by Dr. Valentin Fuster