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Research Papers

J. Vib. Acoust. 2019;141(5):051001-051001-9. doi:10.1115/1.4043353.

Nonlinear energy interaction is a fascinating feature of nonlinear oscillators and has been drawing the attention of researchers since the last few decades. Omnipresent friction in mechanical systems can play a crucial role in modifying these interactions. Using post-buckled flexible inverted pendulum as a candidate system we characterize here, theoretically and experimentally, significant changes in the nonlinear energy transfer in the presence of friction at the input side. Particularly, even with relatively low friction, the energy gets transferred in the higher harmonics of excitation close to a resonant mode as against the transfer to higher modes reported previously. We term this new phenomenon as “excitation harmonic resonance locking.” Theoretical modeling and simulations, considering large deformations, based on assumed modes method, and using a simple friction model reasonably capture the experimental observation. In summary, the paper explicates the role of friction in shifting energy transfer frequencies and can be useful in understanding and designing of oscillators and nonlinear vibrating systems.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2019;141(5):051002-051002-13. doi:10.1115/1.4043411.

The authors present an improved formulation for the axisymmetric solid harmonic finite element (FE) modeling of a flexible, spinning rotor. A thorough comparison of beam-type FE and axisymmetric solid FE rotor models is presented, indicating the errors that result from beam FE usage for various nondimensional rotor topologies. The axisymmetric rotor is meshed in only two dimensions: axial and radial, with both displacement fields being represented with Fourier series expansions. Centrifugal stress-stiffening and spin-softening effects are included in all elements and most importantly in modeling flexible disks. Beam FE and axisymmetric FE natural frequencies, mode shapes, and critical speeds are compared to identify shaft geometries where the beam model yields a significant error. Finally, limitations of beam FE models and guidance for utilizing axisymmetric solid FE models in rotor dynamic simulations are provided.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2019;141(5):051003-051003-11. doi:10.1115/1.4042932.

A simple passive technique of vibration isolation for flexible structures by nonlinear boundaries is investigated, which to our best knowledge is the first study of its kind reported in the literature. The equations of the structure are derived with Hamilton’s principle. An iterative analytic method is investigated to improve the accuracy of the response prediction. The effect of nonlinear boundaries of the structure is studied compared with the linear structure. It is found that stronger nonlinearities in the boundary make the system more stable. Analytical and simulation results show that nonlinear boundaries can significantly reduce the vibration and stress of flexible structures. It is important to point out that with the help of nonlinear boundaries, structural vibration and stress control can be achieved without altering the original structure.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2019;141(5):051004-051004-12. doi:10.1115/1.4043508.

Wayside acoustic defective bearing detector (ADBD) system is a potential technique in ensuring the safety of traveling vehicles. However, Doppler distortion and multiple moving sources aliasing in the acquired acoustic signals decrease the accuracy of defective bearing fault diagnosis. Currently, the method of constructing time-frequency (TF) masks for source separation was limited by an empirical threshold setting. To overcome this limitation, this study proposed a dynamic Doppler multisource separation model and constructed a time domain-separating matrix (TDSM) to realize multiple moving sources separation in the time domain. The TDSM was designed with two steps of (1) constructing separating curves and time domain remapping matrix (TDRM) and (2) remapping each element of separating curves to its corresponding time according to the TDRM. Both TDSM and TDRM were driven by geometrical and motion parameters, which would be estimated by Doppler feature matching pursuit (DFMP) algorithm. After gaining the source components from the observed signals, correlation operation was carried out to estimate source signals. Moreover, fault diagnosis could be carried out by envelope spectrum analysis. Compared with the method of constructing TF masks, the proposed strategy could avoid setting thresholds empirically. Finally, the effectiveness of the proposed technique was validated by simulation and experimental cases. Results indicated the potential of this method for improving the performance of the ADBD system.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2019;141(5):051005-051005-6. doi:10.1115/1.4043509.

The Lamb wave propagation through a thin plate with periodic spatiotemporal variation of material property was investigated through numerical simulations. It was found that regular oscillations of Young's modulus in both space and time can lead to the creation of distinct band gaps for different modes of Lamb wave. Moreover, the dispersion relation for each mode was dependent on the direction of wave propagation (i.e., nonreciprocal). These results allow the Lamb wave modes to be reduced to a single mode traveling in a single direction for specific frequencies. This frequency range was observed to widen with an increasing modulation amplitude of Young's modulus but was not significantly altered by the modulation frequency. The insights derived from this study indicate that spatiotemporal control of material property can be used to effectively isolate Lamb wave modes and reduce reflections, leading to an improvement in the accuracy of the structural health monitoring of materials.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2019;141(5):051006-051006-11. doi:10.1115/1.4043510.

This paper considers the problem of controlling the vibration of a lightweight thin-walled rotor with a distributed actuation magnetic bearing (DAMB). A theoretical flexible rotor model is developed that shows how multiharmonic vibration arises due to small noncircularity of the rotor cross section. This model predicts a series of resonance conditions that occur when the rotational frequency matches a subharmonic of a system natural frequency. Rotor noncircularity can be measured offline, and the measurement data used to cancel its effect on the position sensor signals used for feedback control. A drawback of this approach is that noncircularity is difficult to measure exactly and may vary over time due to changing thermal or elastic state of the rotor. Moreover, any additional multiharmonic excitation effects will not be compensated. To overcome these issues, a harmonic vibration control algorithm is applied that adaptively modifies the harmonic components of the actuator control currents to match a target vibration control performance, but without affecting the stabilizing feedback control loops. Experimental results for a short thin-walled rotor with a single DAMB are presented, which show the effectiveness of the techniques in preventing resonance during operation. By combining sensor-based noncircularity compensation with harmonic vibration control, a reduction in vibration levels can be achieved without precise knowledge of the rotor shape and with minimal bearing forces.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2019;141(5):051007-051007-9. doi:10.1115/1.4043511.
FREE TO VIEW

This paper aims to investigate the airfoil flutter damage-mitigating problem in hypersonic flow. A new adaptive robust nonlinear predictive control law is designed in this paper to mitigate the damage during airfoil flutter of a generic hypersonic flight vehicle. A three-degrees-of-freedom airfoil dynamic motion model is established, in which the third piston theory is employed to derive the unsteady aerodynamics. Then, the complicated responses of the hypersonic airfoil flutter model are analyzed. In order to mitigate the damage of the airfoil, a predictive controller is designed by introducing an adaptive predictive period, and asymptotical stability analysis of the robust nonlinear predictive controller is performed. Subsequently, based on the nonlinear aerodynamics of the airfoil and damage accumulation model, the damage of the airfoil is observed online. Simulation results illustrate the effectiveness of the proposed method.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2019;141(5):051008-051008-12. doi:10.1115/1.4043543.

At present, the mean value of the meshing stiffness and the gear backlash is a fixed value in the nonlinear dynamic model. In this study, wear is considered in the model of the gear backlash and time-varying stiffness. With the increase of the operating time, the meshing stiffness decreases and the gear backlash increases. A six degrees-of-freedom nonlinear dynamic model of a new rigid-flexible gear pair is established with time-varying stiffness and time-varying gear backlash. The dynamic behaviors of the gear transmission system are studied through bifurcation diagrams with the operating time as control parameters. Then, the dynamic characteristics of the gear transmission system are analyzed using excitation frequency as control parameters at four operating time points. The bifurcation diagrams, Poincaré maps, fast Fourier transform (FFT) spectra, phase diagrams, and time series are used to investigate the state of motion. The results can provide a reference for the gear transmission system with wear.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2019;141(5):051009-051009-10. doi:10.1115/1.4043610.

Vibrotactile feedback may be able to compensate for the loss of sensory input in lower-limb prosthesis users to improve the mobility function. Designing an effective vibrotactile feedback system requires that users are able to perceive and respond to vibrotactile stimuli correctly and in a timely manner. Our study explored four key tactor configuration variables (i.e., tactors’ prosthetic layer, vibration intensity, prosthetic pressure, and spacing between adjacent tactors) through two experiments. The vibration propagation experiment investigated the effects of tactor configurations on vibration amplitude at the prosthesis–limb interface. Results revealed a positive relationship between vibration amplitude and intensity and a weak relationship between vibration amplitude and prosthetic pressure. Highest vibration amplitudes were observed when the tactor was located on the inner socket layer. The second experiment involving a sample of ten able-bodied and three amputee subjects investigated the effects of tactor configurations on user perception measured by response time, accuracy identifying tactors’ stimulation patterns, and spatial error in locating the tactors. Results showed that placing the tactors on the inner socket layer, greater spacing between adjacent tactors, and higher vibration intensity resulted in better user perception. The above findings can be directly applied to the design of vibrotactile feedback systems to increase the user response accuracy and decrease the response time required for dynamic tasks such as gait. They can also help to inform future clinical trials informing the optimization of tactor configuration variables.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2019;141(5):051010-051010-11. doi:10.1115/1.4043609.

This research concerns the uncertainty analysis and quantification of the vibration system utilizing the frequency response function (FRF) representation with statistical metamodeling. Different from previous statistical metamodels that are built for individual frequency points, in this research we take advantage of the inherent correlation of FRF values at different frequency points and resort to the multiple response Gaussian process (MRGP) approach. To enable the analysis, vector fitting method is adopted to represent an FRF using a reduced set of parameters with high accuracy. Owing to the efficiency and accuracy of the statistical metamodel with a small set of parameters, Bayesian inference can then be incorporated to realize model updating and uncertainty identification as new measurement/evidence is acquired. The MRGP metamodel developed under this new framework can be used effectively for two-way uncertainty propagation analysis, i.e., FRF prediction and uncertainty identification. Case studies are conducted for illustration and verification.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2019;141(5):051011-051011-11. doi:10.1115/1.4043783.

Reciprocity is a property of linear, time-invariant systems whereby the energy transmission from a source to a receiver is unchanged after exchanging the source and receiver. Nonreciprocity violates this property and can be introduced to systems if time-reversal symmetry and/or parity symmetry is lost. While many studies have induced nonreciprocity by active means, i.e., odd-symmetric external biases or time variation of system properties, considerably less attention has been given to acoustical structures that passively break reciprocity. This study presents a lattice structure with strong stiffness nonlinearities, internal scale hierarchy, and asymmetry that breaks acoustic reciprocity. Macroscopically, the structure exhibits periodicity yet asymmetry exists in its unit cell design. A theoretical study, supported by experimental validation, of a two-scale unit cell has revealed that reciprocity is broken locally, i.e., within a single unit cell of the lattice. In this work, global breaking of reciprocity in the entire lattice structure is theoretically analyzed by studying wave propagation in the periodic arrangement of unit cells. Under both narrowband and broadband excitation, the structure exhibits highly asymmetrical wave propagation, and hence a global breaking of acoustic reciprocity. Interpreting the numerical results for varying impulse amplitude, as well as varying harmonic forcing amplitude and frequency/wavenumber, provides strong evidence that transient resonant capture is the driving force behind the global breaking of reciprocity in the periodic structure. In a companion work, some of the theoretical results presented herein are experimentally validated with a lattice composed of two-scale unit cells under impulsive excitation.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2019;141(5):051012-051012-11. doi:10.1115/1.4043716.

The nonlinear behavior of a piezoelectrically actuated clamped–clamped beam has been examined numerically while highlighting the nonsymmetric response of the system. The nonlinearly coupled electromechanical model of the piezoelectric beam system is developed employing the Bernoulli–Euler theory along with the piezoelectric stress–voltage equations. A general nonsymmetric configuration is considered with a piezoelectric patch partially covering the beam. The geometric nonlinearities of stretching type are taken into account for both the piezoelectric patch and the beam. Through use of the generalized Hamilton's principle, the nonlinearly coupled electromechanical equations of transverse and longitudinal motions of the piezoelectrically actuated beam are derived. A high-dimensional Galerkin scheme is utilized to recast the equations of partial differential type into ordinary differential type. For comparison and benchmark purposes, a three-dimensional finite element model is developed using abaqus/cae to verify the model developed in this study. It is shown that the response of the system is strongly nonsymmetric and that it is essential to retain many degrees-of-freedom to ensure converged results.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2019;141(5):051013-051013-13. doi:10.1115/1.4043815.

This article presents exact algebraic solutions to optimization problems of a double-mass dynamic vibration absorber (DVA) attached to a viscous damped primary system. The series-type double-mass DVA was optimized using three optimization criteria (the H optimization, H2 optimization, and stability maximization criteria), and exact algebraic solutions were successfully obtained for all of them. It is extremely difficult to optimize DVAs when there is damping in the primary system. Even in the optimization of the simpler single-mass DVA, exact solutions have been obtained only for the H2 optimization and stability maximization criteria. For H optimization, only numerical solutions and an approximate perturbation solution have been obtained. Regarding double-mass DVAs, an exact algebraic solution could not be obtained in this study in the case where a parallel-type DVA is attached to the damped primary system. For the series-type double-mass DVA, which was the focus of the present study, an exact algebraic solution was obtained for the force excitation system, in which the disturbance force acts directly on the primary mass; however, an algebraic solution was not obtained for the motion excitation system, in which the foundation of the system is subjected to a periodic displacement. Because all actual vibration systems involve damping, the results obtained in this study are expected to be useful in the design of actual DVAs. Furthermore, it is a great surprise that an exact algebraic solution exists even for such complex optimization problems of a linear vibration system.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2019;141(5):051014-051014-16. doi:10.1115/1.4043817.

Rotor-to-stator or rotor-to-guide rubbing in rotating machines is a serious problem. The contact (rub and impact) between the rotor and the guide creates an excessive vibration which may lead to permanent damage of the mechanical system. In the present work, the rubbing phenomenon between the rotor and the guide is investigated by simulation and experiment. Two different types of clearance bearings are implemented, which are based on circular and lemon-type guides. Rigorous mathematical models for the lemon-type guide as well as for the traditional circular clearance bearing are derived. Then, a Jeffcott rotor model is simulated for the investigation of the rubbing behavior for the two types of bearings. The numerical model is developed in matlab simulink. For different clearances and friction levels between rotor and guide, and several initial conditions, the rubbing phenomena are studied and evaluated. Finally, a comparison between experimental and simulation work is carried out to validate the overall scenarios in this research work. Results indicate that the lemon-type bearing can reduce the likelihood of sustained rubbing, compared with the circular clearance bearing, for the considered test cases.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2019;141(5):051015-051015-8. doi:10.1115/1.4043944.

High-speed water tunnels are typically used to investigate the single-phase and two-phase flows around hydrofoils for hydraulic machinery applications but their dynamic behavior is not usually evaluated. The modal analysis of an NACA0009 hydrofoil inside the test section was calculated with a coupled acoustic fluid–structure model, which shows a good agreement with the experimental results. This numerical model has been used to study the influence on the hydrofoil modes of vibration of the acoustic properties of the surrounding fluid and of the tunnel test section dimensions. It has been found that the natural frequencies of the acoustic domain are inversely proportional to the test section dimensions. Moreover, these acoustic frequencies decrease linearly with the reduction of the speed of sound in the fluid medium. However, the hydrofoil frequencies are not affected by the change of the speed of sound except when they match an acoustic frequency. If both mode shapes are similar, a strong coupling occurs and the hydrofoil vibration follows the linear reduction of natural frequency induced by the acoustic mode. If both mode shapes are dissimilar, a new mode appears whose frequency decreases linearly with speed of sound while keeping the acoustic mode of vibration. This new fluid–structure mode of vibration appears in between two hydrofoil structure modes and its evolution with sound speed reduction has been called “mode transition.” Overall, these findings reinforce the idea that fluid–structure interaction effects must be taken into account when studying the induced vibrations on hydrofoils inside water tunnels.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2019;141(5):051016-051016-13. doi:10.1115/1.4043816.

We numerically analyze, with the finite element method, free vibrations of incompressible rectangular plates under different boundary conditions with a third-order shear and normal deformable theory (TSNDT) derived by Batra. The displacements are taken as unknowns at the nodes of a 9-node quadrilateral element and the hydrostatic pressure at four interior nodes. The plate theory satisfies the incompressibility condition, and the basis functions satisfy the Babuska-Brezzi condition. Because of the singular mass matrix, Moler's QZ algorithm (also known as the generalized Schur decomposition) is used to solve the resulting eigenvalue problem. Computed results for simply supported, clamped, and clamped-free rectangular isotropic plates agree well with the corresponding analytical frequencies of simply supported plates and with those found using the commercial software, abaqus, for other edge conditions. In-plane modes of vibrations are clearly discerned from mode shapes of square plates of aspect ratio 1/8 for all three boundary conditions. The magnitude of the transverse normal strain at a point is found to equal the sum of the two axial strains implying that higher-order plate theories that assume null transverse normal strain will very likely not provide good solutions for plates made of rubberlike materials that are generally taken to be incompressible. We have also compared the presently computed through-the-thickness distributions of stresses and the hydrostatic pressure with those found using abaqus.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2019;141(5):051017-051017-11. doi:10.1115/1.4043945.

This paper addresses the optimal design of a novel nontraditional inerter-based dynamic vibration absorber (NTIDVA) installed on an undamped primary system of single degree-of-freedom under harmonic and transient excitations. Our NTIDVA is based on the traditional dynamic vibration absorber (TDVA) with the damper replaced by a grounded inerter-based mechanical network. Closed-form expressions of optimal parameters of NTIDVA are derived according to an extended version of fixed point theory developed in the literature and the stability maximization criterion. The transient response of the primary system is optimized when the coupled system becomes defective, namely having three pairs of coalesced conjugate poles, the proof of which is also spelt out in this paper. Moreover, the analogous relationship between NTIDVA and electromagnetic dynamic vibration absorber is highlighted, facilitating the practical implementation of the proposed absorber. Finally, numerical studies suggest that compared with TDVA, NTIDVA can decrease the peak vibration amplitude of the primary system and enlarge the frequency bandwidth of vibration suppression when optimized by the extended fixed point technique, while the stability maximization criterion shows an improved transient response in terms of larger modal damping ratio and accelerated attenuation rate.

Commentary by Dr. Valentin Fuster

Technical Brief

J. Vib. Acoust. 2019;141(5):054501-054501-5. doi:10.1115/1.4043542.

This paper shows an approach to evaluate mode shapes for beams through using a passing auxiliary mass. The coupled system of an auxiliary mass passing over a beam is time-dependent, and the corresponding instantaneous frequencies (IFs) are equivalent to the mode shapes. Hence, reconstruction of the mode shapes is easy to be achieved through estimating the IFs. A simple algorithm based on ridge detection is proposed to reconstruct the mode shapes. This method is effective if the beam is light or the lumped mass is heavy. It is convenient since it requires an accelerometer mounted on the passing auxiliary mass rather than a serious of sensors mounted on the structure itself. It is also more practical because it is usually difficult to install external exciter. A lab-scale experimental validation shows that the new technique is capable of identifying the first three mode shapes accurately.

Topics: Mode shapes
Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2019;141(5):054502-054502-7. doi:10.1115/1.4043715.

Dielectric elastomer (DE) membrane transducers are well known for exhibiting large deformations when subject to high voltage. Furthermore, DEs are characterized by an actuation bandwidth of several kilohertz, which allows their use in high-frequency applications, e.g., acoustic ones. The frequency response of DE membranes depends on many parameters such as geometry, pre-stress, and electrode pattern. By properly designing such parameters, it is possible to control vibration modes and resonance frequencies of the membrane, opening up a number of application scenarios. Motivated by this fact, this work presents the first experimental study of continuous vibrations generated in DE membranes via high-voltage excitation. The system under investigation consists of a squared DE membrane with a circular electrode, preloaded out of plane with a linear spring. Vibrations are generated by applying a broadband high-voltage signal to the DE membrane. A 3D laser vibrometer is used to reconstruct the three-dimensional oscillations of scanning points on the membrane surface. Experimental investigations are performed to study the effects of DE geometry and pre-stress on the membrane motion, in terms of resulting frequency spectrum and vibration modes.

Commentary by Dr. Valentin Fuster

Discussion

Closure

J. Vib. Acoust. 2019;141(5):056001-056001-2. doi:10.1115/1.4043608.

Roumeliotis raised two major issues in his discussion [1] regarding a prior publication of the authors [2]. One is Eq. (1) in Ref. [1], which alleges an error in Eq. (18) of Ref. [2]. The other is Eq. (2) in Ref. [1], which alleges a second error in Eq. (19) of Ref. [2]. Then, Roumeliotis presented alternative expressions based on the changes he suggested in Eqs. (1) and (2) in Ref. [1]. We hereby give our explanations to the issues raised in the discussion by Roumeliotis [1].

Topics: Acoustics , Sound , Errors
Commentary by Dr. Valentin Fuster

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