Research Papers

J. Vib. Acoust. 2018;140(4):041001-041001-11. doi:10.1115/1.4038734.

Delamination frequently occurs in a laminated composite structure and can cause prominent local anomalies in curvature vibration shapes associated with vibration shapes of the composite structure. Spatially dense vibration shapes of a structure can be rapidly obtained by use of a continuously scanning laser Doppler vibrometer (CSLDV) system, which sweeps its laser spot over a vibrating surface of the structure. This paper introduces a continuous scanning scheme for general quadrangular scan areas assigned on plates and extends two damage identification methods for beams to identify delamination in laminated composite plates using a CSLDV system. One method is based on the technique that a curvature vibration shape from a polynomial that fits a vibration shape of a damaged structure can well approximate an associated curvature vibration shape of an undamaged structure and local anomalies caused by structural damage can be identified by comparing the curvature vibration shape of the damaged structure with that from the polynomial fit, and the other is based on the technique that a continuous wavelet transform can directly identify local anomalies in a curvature vibration shape caused by structural damage. The two methods yield corresponding damage indices and local anomalies in curvature vibration shapes can be identified in neighborhoods with high damage index values. Both numerical and experimental investigations on effectiveness of the two methods are conducted on a laminated composite plate with a delamination area. In the experimental investigation, delamination identification results from the two methods were compared with that from a C-scan image of the composite plate.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2018;140(4):041002-041002-7. doi:10.1115/1.4038955.

The building structural vibration control by an active mass damper (AMD) with delayed acceleration feedback is studied. The control is designed with a multi-objective optimal approach. The stable region in a parameter space of the control gain and time delay is obtained by using the method of stability switch and the numerical code of NDDEBIFTOOL. The control objectives include the setting time, total power consumption, peak time, and the maximum power. The multi-objective optimization problem (MOP) for the control design is solved with the simple cell mapping (SCM) method. The Pareto set and Pareto front are found to consist of two clusters. The first cluster has negative feedback gains, i.e., the positive acceleration feedback. We have shown that a proper time delay can enhance the vibration suppression with controls from the first cluster. The second cluster has positive feedback gains and is located in the region which is sensitive to time delay. A small time delay will deteriorate the control performance in this cluster. Numerical simulations and experiments are carried out to demonstrate the analytical findings.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2018;140(4):041003-041003-11. doi:10.1115/1.4038941.

The operable frequency range of the delayed resonators (DR) is known to be narrow due to stability issues. This study presents a novel approach for DR design with a combined feedback strategy that consists of a delayed velocity and nondelayed position feedback to extend the operable frequency range of the DR method. The nondelayed position feedback is used to alter the natural frequency of the DR artificially while delayed velocity feedback is employed to tune the frequency of DR matching with the undesired vibrations. The proposed method also introduces an optimization parameter that provides freedom for the designer to obtain fast vibration suppression while improving the stability range of the DR. An optimization approach is also provided within the scope of this study. Theoretical findings are verified over an experiment utilizing the active suspension system of the Quanser Company.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2018;140(4):041004-041004-10. doi:10.1115/1.4038943.

An array of cantilevers offers an alternative approach to standard single beam measurement in the context of atomic force microscopy (AFM). In comparison to a single beam, a multi-degrees-of-freedom system offers a greater level of flexibility with regard to parameter selection and tuning. By utilizing changes in the system eigenmodes as a feedback signal, it is possible to enhance the sensitivity of AFM to changes in sample topography above what is achievable with standard single beam techniques. In this paper, we analyze a two-beam array operated in FM-AFM mode. The array consists of a single active cantilever that is excited with a 90 deg phase-shifted signal and interacts with the sample surface. The active beam is mechanically coupled to a passive beam, which acts to vary the response between synchronized and unsynchronized behavior. We use a recently developed mathematical model of the coupled cantilever array subjected to nonlinear tip forces to simulate the response of the described system with different levels of coupling. We show that the sensitivity of the frequency feedback signal can be increased significantly in comparison to the frequency feedback from a single beam. This is a novel application for an AFM array that is not present in the literature.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2018;140(4):041005-041005-10. doi:10.1115/1.4039238.

A flexoelectric cantilever beam actuated by the converse flexoelectric effect is evaluated and its analytical and experimental data are compared in this study. A line-electrode on the top beam surface and a bottom surface electrode are used to generate an electric field gradient in the beam, so that internal stresses can be induced and applied to distributed actuations. The dynamic control effectiveness of the beam is investigated with a mathematical model and is validated by laboratory experiments. Analyses show that the actuation stress induced by the converse flexoelectric effect is in the longitudinal direction and results in a bending control moment to the flexoelectric beam since the stress in the thickness is inhomogeneous. It is found that thinner line-electrode radius and thinner flexoelectric beam lead to larger control effects on the beam. The position of the line-electrode on the top surface of the beam also influences the control effect. When the line-electrode is close to the fixed end, it induces a larger tip displacement than that is close to the free end. Analytical results agree well with laboratory experimental data. This study of flexoelectric actuation and control provides a fundamental understanding of flexoelectric actuation mechanisms.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2018;140(4):041006-041006-11. doi:10.1115/1.4039244.

We study first-crossing problem of two-degrees-of-freedom (2DOF) strongly nonlinear mechanical oscillators analytically. The excitation is the combination of a deterministic harmonic function and Gaussian white noises (GWNs). The generalized harmonic function is used to approximate the solutions of the original equations. Four cases are studied in terms of the types of resonance (internal or external or both). For each case, the method of stochastic averaging is used and the stochastically averaged Itô equations are obtained. A backward Kolmogorov (BK) equation is set up to yield the failure probability and a Pontryagin equation is set up to yield average first-crossing time (AFCT). A 2DOF Duffing-van der Pol oscillator is chosen as an illustrative example to demonstrate the effectiveness of the analytical method. Numerically analytical solutions are obtained and validated by digital simulation. It is shown that the proposed method has high efficiency while still maintaining satisfactory accuracy.

Topics: Resonance , Excitation
Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2018;140(4):041007-041007-15. doi:10.1115/1.4039242.

Magnetorheological elastomer (MRE)-based semi-active vibration mitigation device demands a mathematical representation of its smart characteristics. To model the material behavior over broadband frequency, the simplicity of the mathematical formulation is very important. Material modeling of MRE involves the theory of viscoelasticity, which describes the properties intermediate between the solid and the liquid. In the present study, viscoelastic property of MRE is modeled by an integer and fractional order derivative approaches. Integer order-based model comprises of six parameters, and the fraction order model is represented by five parameters. The parameters of the model are identified by minimizing the error between the response from the model and the dynamic compression test data. Performance of the model is evaluated with respect to the optimized parameters estimated at different sets of regularly spaced arbitrary input frequencies. A linear and quadratic interpolation function is chosen to generalize the variation of parameters with respect to the magnetic field and frequency. The predicted response from the model revealed that the fractional order model describes the properties of MRE in a simplest form with reduced number of parameters. This model has a greater control over the real and imaginary part of the complex stiffness, which facilitates in choosing a better interpolating function to improve the accuracy. Furthermore, it is confirmed that the realistic assessment on the performance of a model is based on its ability to reproduce the results obtained from optimized parameters.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2018;140(4):041008-041008-12. doi:10.1115/1.4039240.

The smooth orthogonal decomposition (SOD) is an output-only modal analysis method, which has simple structure and gives good results for undamped or lightly damped vibration systems. In the present study, the SOD method is extended to incorporate various measurements that contain the displacement, the velocity, the acceleration, and even the jerk (derivation of the acceleration). Several generalized eigenvalue problems (EVPs) are put forward considering different measurement combinations, and it is proved that all these EVPs can reduce to the eigenvalue problems of the undamped vibration system. These different methods are called extended smooth orthogonal decomposition (ESOD) methods in this paper. For the damped vibration system, the frequencies obtained by different ESOD methods are different from each other. Thus, a cost function is defined and a search algorithm is proposed to find the optimal frequency and damping ratio that can explain these differences. Although the search algorithm is derived for the single-degree-of-freedom (SDOF) vibration systems, it is effective for the multi-degrees-of-freedom (MDOF) vibration system after assuming that the smooth orthogonal coordinates (SOCs) computed by the ESOD methods are approximate to the modal coordinate responses. In order to verify the ESOD methods and the search algorithm, simulations are carried out and the results indicate that all ESOD methods reach correct results for undamped vibration systems and the search algorithm can give accurate frequency and damping ratio for damped systems. In addition, the effects of measurement noises are considered and the results show that the proposed method has anti-noise property to some extent.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2018;140(4):041009-041009-10. doi:10.1115/1.4039245.

Hysteresis exists widely in intelligent materials, such as piezoelectric and giant magnetostrictive ones, and it significantly affects the precision of vibration control when a controlled object moves at a range of micrometers or even smaller. Many measures must be implemented to eliminate the influence of hysteresis. In this work, the hysteresis characteristic of a proposed piezoelectric actuator (PEA) is tested and modeled based on the adaptive neuro fuzzy inference system (ANFIS). A linearization control method with feedforward hysteresis compensation and proportional–integral–derivative (PID) feedback is established and simulated. A linear quadratic Gaussian with loop transfer recovery (LQG/LTR) regulator is then designed as a vibration controller. Verification experiments are conducted to evaluate the effectiveness of the control method in vibration isolation. Experiment results demonstrate that the proposed vibration control system with a feedforward feedback linearization controller and an LQG/LTR regulator can significantly improve the performance of a vibration isolation system in the frequency range of 5–200 Hz with low energy consumption.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2018;140(4):041010-041010-14. doi:10.1115/1.4039246.

Based on the requirements of the dynamic design of geared turbofan (GTF) engines, the vibration characteristic of the fan shaft is investigated. The effect of sudden imbalance caused by blade off, the time-varying meshing stiffness, and meshing errors on the vibration characteristics is fully considered in the dynamic model. The improved Euler–Bernoulli beam element considering the effects of shear deformation is employed and a coupled relationship between the gear–shaft–bearing–casing is established. Under windmilling condition with a single blade completely lost, the vibration characteristics of the fan shaft of the turbofan engine with and without a gearbox system are compared. The effect of the gear system on the vibration of the fan shaft under different rotating speeds is examined. The results show that the orbit of the fan shaft center in the turbofan engine with the gearbox system exhibits a multifrequency whirling motion and has a stable limit cycle. Under windmilling condition, the meshing frequency and the modal frequency have multiple intersection points. The critical speed is dense and the peak value of the transient vibration of the GTF engine gearbox shows a wave rise with an increase in speed. The results of this study could provide a reference for the parameter design and optimization of GTF engines.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2018;140(4):041011-041011-9. doi:10.1115/1.4039239.

A dynamic model for a shell-type amplified piezoelectric actuator (APA) is proposed. The dimensions of the shell of a typical shell-type actuator allow one to model it as a set of connected beams. The contribution of the geometric nonlinearity in the axial direction of the beams due to bending is accounted for in the formulation. Subsequent nonlinear analysis using both analytical and numerical approaches reveals the presence of second harmonic in the response spectrum. This occurrence is also seen experimentally. A frequency regime is also identified within which the effect of quadratic nonlinearity is minimal and the actuator exhibits high fidelity. Dependence of the response spectrum on the actuator geometry has been studied. For a given forcing frequency, a certain geometric configuration is shown to exist, which maximizes the nonlinear effects. The effect of prestressing of the piezoelectric stack on the frequency spectrum is also studied. The obtained results are expected to lead to improved design of such actuators.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2018;140(4):041012-041012-10. doi:10.1115/1.4039296.

The analysis of the influence of cracks on the dynamics of bladed disks is critical for design, failure prognosis, and structural health monitoring. Predicting the dynamics of cracked bladed disks is computationally challenging for two reasons: (1) the model size is quite large and (2) the piecewise-linear nonlinearity caused by contact eliminates the use of linear analysis tools. Recently, a technique referred to as the X-Xr approach was developed to efficiently reduce the model size of the cracked bladed disks. The method employs relative coordinates to describe the motion of crack surfaces such that an effective model reduction can be achieved using single sector calculations. More recently, a method referred to as the generalized bilinear amplitude approximation (BAA) was developed to approximate the amplitude and frequency of piecewise-linear nonlinear systems. This paper modifies the generalized BAA method and combines it with the X-Xr approach to efficiently predict the dynamics of the cracked bladed disks. The combined method is able to construct the reduced-order model (ROM) of full disks using single-sector models only and estimate the amplitude and frequency with a significantly reduced computational effort. The proposed approach is demonstrated on a three degrees-of-freedom (DOF) spring–mass system and a cracked bladed disk.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2018;140(4):041013-041013-8. doi:10.1115/1.4039401.

Precisions of localization are a function of the size of an array. A kind of parasitoid fly, Ormia ochracea, performs an extraordinary directional hearing ability despite its tiny-scaled auditory organ. In this paper, vibration modes and transfer functions of the Ormia ochracea's ear model were calculated, and the phase difference amplification in responses are analyzed to investigate the directional hearing mechanism. A novel three-element bionic model is proposed for spatial sound source localization for small distance-wavelength ratios. The amplification of the phase difference of this model is verified. In order to realize the bionic localization model, based on electric-mechanic analogy method, a system that consists of a triangular acoustic array and a bionic coupling circuit is designed and tested. Frequency responses of the circuit output, as a means of transfer function of the system, are taken into estimation of the source directions. The result has shown that this circuit design has better performance in estimating the direction of sound sources compared to the uncoupled array with same size.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2018;140(4):041014-041014-12. doi:10.1115/1.4039402.

This work presents a new aeroelastic model that governs the extensional, chordwise, flapwise, and torsional vibrations of an isolated horizontal axis wind turbine blade. The model accounts for the sectional offsets between the shear, aerodynamic, and mass centers. The centrifugal stiffening effects are also accounted for by including nonlinear strains based on an ordering scheme that retains terms up to second-order. Aerodynamic loading is derived based on a modified Theodorsen's theory adapted to account for the blade rotational motion. A set of four coupled nonlinear partial differential equations are derived using the Hamiltonian approach that are then linearized about the steady-state extensional position. The finite element method (FEM) is then employed to spatially discretize the resulting equations with the aim of obtaining an approximate solution to the blade's dynamic response, utilizing state space techniques and complex modal analysis. Investigation of the blade's flutter stability limit is carried out. Effects of parameters such as wind speed and blade sectional offsets on the flutter limit and dynamic response are also investigated.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2018;140(4):041015-041015-8. doi:10.1115/1.4039407.

This paper describes an experimental investigation into the vibration control of multiple electrical machines installed on a large-scale floating raft system. Vibration transmission to a flexible hull-like structure that supports the floating raft is controlled by adjusting the phases of the electrical power supply to the machines—a technique known as synchrophasing. Each machine is driven by a phase asynchronous motor and has two counter rotating shafts with adjustable eccentric masses, which allows the dynamic force generated by each machine to be set independently. Up to four rotating machines are considered. A genetic algorithm is used in the search for the optimum relative phases between each machine, because it is impractical to carry out an exhaustive search of the huge number of possible phase combinations. It is demonstrated that vibration control using synchrophasing is feasible in a marine environment, and can achieve significant vibration reduction, by simply adding some sensors and a control system. Reduction in the total transmitted vibration, as measured by the sum of the squared accelerations from 22 error sensors on the hull-like structure, was found to be up to 13 dB, and vibration reduction at higher harmonic frequencies was found to be up to 51 dB.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2018;140(4):041016-041016-14. doi:10.1115/1.4039403.

Sound radiation from stationary and rotating point acoustic sources with shield of rigid prolate spheroidal baffles is explored in the prolate spheroidal coordinate system. The formulae of far-field sound pressure and acoustic power are derived and acoustic power spectral density (PSD) in terms of circumferential and azimuthal wavenumber is manifested from the low frequency range to high frequency range. Acoustic wave propagation features in the spherical coordinate system as a particular case of the prolate spheroidal coordinate system are presented. Rotating sound sources cause the frequency veering phenomenon and change the patterns of PSD. Some spheroidal harmonic waves with lower and higher wavenumber for the large prolate spheroids cannot contribute to far-field sound radiation in the high frequency range when sound sources are close to the axes of the spheroids. Sound pressure directivity and acoustic power of stationary point sound sources are also analyzed with the variation of source location.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2018;140(4):041017-041017-10. doi:10.1115/1.4039421.

It can be predicted by Rayleigh's interlacing eigenvalue theorem that structural modifications of a spinning disk can shift the first critical speed of the system up to a known limit. In order to corroborate this theorem, it is shown numerically, and verified experimentally that laterally constraining of a free spinning flexible thin disk with tilting and translational degree-of-freedom (DOF), the first critical speed of the disk cannot increase more than the second critical speed of the original system (the disk with no constraint). The governing linear equations of transverse motion of a spinning disk with rigid body translational and tilting DOFs are used in the analysis of eigenvalues of the disk. The numerical solution of these equations is used to investigate the effect of the constraints on the critical speeds of the spinning disk. Experimental tests were conducted to verify the results.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2018;140(4):041018-041018-10. doi:10.1115/1.4039404.

It is confirmed experimentally that in case of a rotor with crack, multiple harmonics are generated when the rotor revolves at a particular frequency. Only few modeling techniques successfully predict this particular behavior of the cracked rotor. It is observed in this research that modeling cracked rotors using conventional finite element methods cannot predict this particular behavior successfully. A nonlinear dynamic model of the flexible rotor with ball bearings is developed using discrete mass spring damper elements combined with an existing model of the crack to truly predict this confirmed experimental behavior. Certain crack detection techniques based on the steady-state response work well on this basic concept of the multiharmonics generation due to nonlinearities caused by cracks in the rotor. The presence of ball bearings, rotor-coupling misalignment, rotor-stator rub, and rotor bow can also cause significant nonlinearities in the overall system. These additional nonlinearities render these crack detection techniques to lose their effectiveness. Our work justifies through simulations that the Jeffcott rotors are the over simplified version of real-life rotor-bearing systems. Hence, these crack detection techniques cannot be efficiently applied for condition monitoring of real-life rotor-bearing systems. The proposed model also helps to understand that the presence of flexible bearing supports affects the dynamics of the system considerably and negatively affects the effectiveness of these crack detection techniques.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2018;140(4):041019-041019-9. doi:10.1115/1.4039405.

A hybrid approach is proposed to evaluate the probability of unacceptable performance with respect to uncertain parameters. The evaluation of structural reliability and the solution of maximum vibration response are performed simultaneously. A constrained optimization problem is deduced for which several techniques have been developed to obtain the reliability index. The nonlinear equality constraints of the optimization problem are constructed based on the harmonic balance equations, the optimality condition of the maximum vibration response with respect to the vibration frequency and the limit state failure function. With the nonlinear equality constraints imposed on the harmonic balance equations and the derivative of the maximum vibration response with respect to the vibration frequency, the inner loop for solving the maximum vibration response is avoided. The sensitivity gradients are derived by virtue of the adjoint method. The original optimization formulation is then solved by means of the sequential quadratic programming method (SQP) method. Finally, the developed approach has been verified by comparison with reference values from Monte Carlo simulation (MCS). Numerical results reveal that the proposed method is capable of predicting the failure probability of nonlinear structures with random uncertainty.

Commentary by Dr. Valentin Fuster

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