Research Papers

J. Vib. Acoust. 2018;140(6):061001-061001-8. doi:10.1115/1.4039961.

In this paper, natural frequencies and modeshapes of a transversely vibrating Euler–Bernoulli beam carrying a discrete two-degree-of-freedom (2DOF) spring–mass system are obtained from a wave vibration point of view in which vibrations are described as waves that propagate along uniform structural elements and are reflected and transmitted at structural discontinuities. From the wave vibration standpoint, external forces applied to a structure have the effect of injecting vibration waves to the structure. In the combined beam and 2DOF spring–mass system, the vibrating discrete spring–mass system injects waves into the distributed beam through the spring forces at the two spring attached points. Assembling these wave relations in the beam provides an analytical solution to vibrations of the combined system. Accuracy of the proposed wave analysis approach is validated through comparisons to available results. This wave-based approach is further extended to analyze vibrations in a planar portal frame that carries a discrete 2DOF spring–mass system, where in addition to the transverse motion, the axial motion must be included due to the coupling effect at the angled joint of the frame. The wave vibration approach is seen to provide a systematic and concise technique for solving vibration problems in combined distributed and discrete systems.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2018;140(6):061002-061002-15. doi:10.1115/1.4039799.

This paper presents an experimental and theoretical study of vibration of a four-span continuous plate with two rails on top and four extra supports excited by one or two moving model cars, which is meant to represent vehicle–track–bridge dynamic interaction. Measured natural frequencies of the plate structure are used to update the finite element (FE) model of the structure. Four laser displacement transducers are placed on the ground to measure the displacements of the plate. A laser-Doppler vibrometer is used to measure the real-time speed of the moving cars, which reveals that the speeds decrease with time at a small and almost constant deceleration which can affect the structural dynamic response. A fascinating experiment is the use of two cars connected in series, which is very rare and has never been done on a multispan structure. Vibration of the plate structure excited by two moving cars separated at a distance is also measured and exhibits interesting dynamic behavior too. A theoretical model of the whole structure is constructed and an iterative method is developed to determine the dynamic response. The numerical and the experimental results are found to agree very well, in particular when deceleration is considered in the theoretical model.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2018;140(6):061003-061003-8. doi:10.1115/1.4039931.

Blade tip timing (BTT) is a noncontact method for measuring turbomachinery blade vibration. Proximity sensors are mounted circumferentially around the turbomachine casing and used to measure the tip displacements of blades during operation. Tip deflection data processing is nontrivial due to complications such as aliasing and high levels of noise. Specialized BTT algorithms have been developed to extract the utmost amount of information from the signals. The effectiveness of these algorithms is, however, influenced by the circumferential spacing between the proximity sensors. If the spacing is suboptimal, an algorithm can fail to measure dangerous blade vibration. This paper presents a novel optimization approach that determines the optimal spacing between proximity sensors.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2018;140(6):061004-061004-11. doi:10.1115/1.4039932.

It has been shown that exponentially tapering the width of a vibration-based piezoelectric energy harvester will result in increasing electric power per mass in a specified frequency. In this paper, a nonlinear solution of an exponentially decreasing width piezoelectric energy harvester is presented. Piezoelectric, inertial, and geometric nonlinearities are included in the presented model, while the exponentially tapered piezoelectric beam's mass normalized mode shapes are utilized in Galerkin discretization. The developed nonlinear coupled equations of motion are solved using method of multiple scales (MMS), and the steady states results are verified by experiment in high amplitude excitation. Finally, the exponentially tapering parameter effect is studied, and it is concluded that the voltage per mass of the energy harvester is improved by tapering at high exciting acceleration amplitudes.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2018;140(6):061005-061005-8. doi:10.1115/1.4039960.

Targeted energy transfer from one acoustical mode to a Helmholtz resonator (HR) with nonlinear behaviors is studied. For the HR, nonlinear restoring forces and nonlinear damping are taken into account. A time multiple scale method around a 1:1 resonance is used to detect slow invariant manifold (SIM) of the system, its equilibrium and singular points. Analytical predictions are compared with those which are obtained by direct numerical integration of system equations. Experimental verifications are performed and presented for free and forced vibrating system.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2018;140(6):061006-061006-14. doi:10.1115/1.4039933.

In this paper, a new approach is presented for linearization of piecewise linear systems with variable dry friction, proportional with absolute value of relative displacement. The transmissibility factors of considered systems, defined in terms of root-mean-square (RMS) values, are obtained by numerical time integration of motion equations for a set of harmonic inputs with constant amplitude and different frequencies. A first-order linear differential system is attached to the considered piecewise linear system such as the first component of solution vector of attached system to have the same transmissibility factor as the chosen output of nonlinear system. This method is applied for the semi-active control of vibration with balance logic strategy. Applications to base isolation of rotating machines and vehicle suspensions illustrate the effectiveness of the proposed linearization method.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2018;140(6):061007-061007-11. doi:10.1115/1.4040045.

In this study, a novel passive vibration control device, the three-element vibration absorber–inerter (TEVAI) is proposed. Inerter-based vibration absorbers, which utilize a mass that rotates due to relative translational motion, have recently been developed to take advantage of the potential high inertial mass (inertance) of a relatively small mass in rotation. In this work, a novel configuration of an inerter-based absorber is proposed, and its effectiveness at suppressing the vibration of a single-degree-of-freedom system is investigated. The proposed device is a development of two current passive devices: the tuned-mass-damper–inerter (TMDI), which is an inerter-base tuned mass damper (TMD), and the three-element dynamic vibration absorber (TEVA). Closed-form optimization solutions for this device connected to a single-degree-of-freedom primary structure and loaded with random base excitation are developed and presented. Furthermore, the effectiveness of this novel device, in comparison to the traditional TMD, TEVA, and TMDI, is also investigated. The results of this study demonstrate that the TEVAI possesses superior performance in the reduction of the maximum and root-mean-square (RMS) response of the underlying structure in comparison to the TMD, TEVA, and TMDI.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2018;140(6):061008-061008-12. doi:10.1115/1.4040042.

Centrifugal pendulum vibration absorber (CPVA) has been used as a torsional vibration suppression device. Recently, downsizing turbotechnology is widespread and it causes a torsional vibration in the drivetrains of automobiles, and CPVA is used for torsional vibration suppression. In such cases of vibration suppression of the drive-train shaft, it should be modeled as a multi degrees-of-freedom system and considered the suppression of its multiple modes. However, most of researches on CPVA so far have focused on a one degree-of-freedom system, and the vibration analysis and its suppression of the torsional vibration caused in the multi degrees-of-freedom system has been hardly investigated. In this paper, the dynamical characteristic of torsional vibration of the multi degrees-of-freedom system with CPVAs is investigated both theoretically and experimentally. Vibration suppression mechanism of CPVA on the torsional vibration of the multi degrees-of-freedom system is studied by the eigenvalue analysis. The vibration suppression effect of CPVA on the harmonic resonances, and the occurrence of superharmonic resonances in multiple modes are observed by the numerical simulation. Then, nonlinear theoretical analyses of harmonic resonances and superharmonic resonances are performed and the vibration suppression effects of CPVA are explained. These obtained theoretical results are confirmed by experiments.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2018;140(6):061009-061009-9. doi:10.1115/1.4040041.

This paper introduces a novel method called extended phase space topology (EPST) for machinery diagnostics and pattern recognition. In particular, the research focuses on fault detection and diagnostics of rolling element bearings. The proposed method is based on mapping the vibrational response onto the density space and approximating the density using orthogonal functions. The method has been applied to vibration data of a rotating machine where the data were measured by proximity probes. The method was applied to two operating conditions: constant operating speed and variable operating speed. As will be shown, the proposed feature extraction method has an outstanding capability in characterizing the system response and diagnosing the system. The method is evidently robust to noise, does not depend on expert knowledge about the system, requires no feature ranking or selection, and can easily be applied in an automated process. Finally, a comparison with utilization of statistical features is performed for each operating condition, which demonstrates that the proposed method performs better than the traditional statistical methods.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2018;140(6):061010-061010-11. doi:10.1115/1.4039570.

Different from elastic waves in linear periodic structures, those in phononic crystals (PCs) with nonlinear properties can exhibit more interesting phenomena. Linear dispersion relations cannot accurately predict band-gap variations under finite-amplitude wave motions; creating nonlinear PCs remains challenging and few examples have been studied. Recent studies in the literature mainly focus on discrete chain-like systems; most studies only consider weakly nonlinear regimes and cannot accurately obtain some relations between wave propagation characteristics and general nonlinearities. This paper presents propagation characteristics of longitudinal elastic waves in a thin rod and coupled longitudinal and transverse waves in an Euler–Bernoulli beam using their exact Green–Lagrange strain relations. We derive band structure relations for a periodic rod and beam and predict their nonlinear wave propagation characteristics using the B-spline wavelet on the interval (BSWI) finite element method. Influences of nonlinearities on wave propagation characteristics are discussed. Numerical examples show that the proposed method is more effective for nonlinear static and band structure problems than the traditional finite element method and illustrate that nonlinearities can cause band-gap width and location changes, which is similar to results reported in the literature for discrete systems. The proposed methodology is not restricted to weakly nonlinear systems and can be used to accurately predict wave propagation characteristics of nonlinear structures. This study can provide good support for engineering applications, such as sound and vibration control using tunable band gaps of nonlinear PCs.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2018;140(6):061011-061011-9. doi:10.1115/1.4040047.

The equivalent source method (ESM) and monopole time reversal method (MTRM) are two popular techniques for noise source localization. These two methods have some similar characteristics, such as using the pressure field measured by a microphone array as the input and using similar propagation matrices obtained from the Green's function. However, the spatial resolutions of results obtained by these two methods are different. The aim of this paper is to reveal the reason resulting in this difference from a theoretical analysis and compare the performance of these two methods using results from numerical simulations and experiments. Using the singular value decomposition (SVD) technique, the difference between the two methods is found to be only the diagonal matrices of singular values, and the two methods are equivalent after simply replacing the diagonal matrix in the MTRM with its inverse. Comparison of the results demonstrates that the ESM can calculate the real source strength and obtain a high spatial resolution due to the significant amplification of evanescent waves in the inverse process. However, it does not work when the signal-to-noise ratio (SNR) is low or the measurement distance is large. The performance of ESM under these situations can be significantly improved by introducing a regularization procedure. While the MTRM fails to calculate the real source strength and locate the source at low frequencies due to the loss of information of evanescent waves, it works well at high frequencies even with a low SNR and a large measurement distance.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2018;140(6):061012-061012-14. doi:10.1115/1.4040229.

Although the vibration suppression effects of precisely adjusted dynamic vibration absorbers (DVAs) are well known, multimass DVAs have recently been studied with the aim of further improving their performance and avoiding performance deterioration due to changes in their system parameters. One of the present authors has previously reported a solution that provides the optimal tuning and damping conditions of the double-mass DVA and has demonstrated that it achieves better performance than the conventional single-mass DVA. The evaluation index of the performance used in that study was the minimization of the compliance transfer function. This evaluation function has the objective of minimizing the absolute displacement response of the primary system. However, it is important to suppress the absolute velocity response of the primary system to reduce the noise generated by the machine or structure. Therefore, in the present study, the optimal solutions for DVAs were obtained by minimizing the mobility transfer function rather than the compliance transfer function. As in previous investigations, three optimization criteria were tested: the H optimization, H2 optimization, and stability maximization criteria. In this study, an exact algebraic solution to the H optimization of the series-type double-mass DVA was successfully derived. In addition, it was demonstrated that the optimal solution obtained by minimizing the mobility transfer function differs significantly at some points from that minimizing the compliance transfer function published in the previous report.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2018;140(6):061013-061013-9. doi:10.1115/1.4040236.

Great amount of work has been dedicated to eliminate residual vibrations in rest-to-rest motion. Considerable amount of these methods is based on convolving a general input signal with a sequence of timed impulses. These impulses usually have large jumps in their profiles and are chosen depending on the system modal parameters. Furthermore, classical input shaping methods are usually used for constant cable length and are sensitive to any change in the system parameters. To overcome these limitations, polynomial command shapers with adjustable maneuvering time are proposed. The equation of motion of a simple pendulum with the effect of hoisting is derived, linearized, and solved in order to eliminate residual vibrations in rest-to-rest maneuvers. Several cases including smooth, semi-smooth and unsmooth continuous shapers are simulated numerically and validated experimentally on an experimental overhead crane. Numerical and experimental results show that the proposed polynomial command shaper eliminates residual vibrations effectively. The effect of linear hoisting is also included and discussed. To enhance the shaper performance, extra parameters are added to the polynomial function to reduce shaper sensitivity. Results show that the effect of adding these parameters greatly enhances the shaper performance.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2018;140(6):061014-061014-14. doi:10.1115/1.4040475.

Tuned mass dampers (TMDs) are typically introduced and calibrated as natural passive control devices for the vibration mitigation of the steady-state response of primary structures subjected to persistent excitations. Otherwise, this work investigates the optimum tuning of TMDs toward minimizing the transient structural response. Specifically, a single-degree-of-freedom (SDOF) system is considered as a primary structure, with added TMD, subjected to pulse-like excitations. First, the system is analytically analyzed, within the time domain, for unit impulse base displacement, through Laplace transform. Then, the tuning process is numerically explored by an optimization procedure focused on an average response index, to extract the optimum condition toward best TMD calibration. The efficiency of the proposed control device is then assessed and demonstrated through further post-tuning numerical tests, by considering as dynamic loadings: first, a time unit impulse base displacement, coherent with the source description above; second, different pulse-like excitations, to detect the effectiveness of the so-conceived TMD for generic ideal shock actions; third, a set of nonstationary earthquake excitations, to enquire the achievable level of seismic isolation. It is shown that this leads to a consistent passive TMD in such a transient excitation context, apt to mitigate the average response. Additionally, the present tuning forms a necessary optimum background for a possible upgrade to a hybrid TMD, with the potential addition of an active controller to the so-optimized TMD, to achieve even further control performance, once turned on, specifically for abating the peak response, too.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2018;140(6):061015-061015-9. doi:10.1115/1.4040521.

Conventional frequency domain beamforming (FDBF) relies on the measured cross-spectral matrix (CSM). However, in wind tunnel tests, the CSM diagonal is contaminated by the interference of incoherent noise after long-time averaging which leads the source map to poor resolution. Diagonal removal (DR) can suppress the noise in beamforming results via the deletion of CSM diagonal, but this method leads to the underestimation of source levels and some negative powers in source maps. Some advanced methods, such as background subtraction, make use of background noise reference to counteract the effects of contamination; however, the results usually become unreliable, because the background noise is difficult to keep constant in different measurements. Diagonal denoising (DD) beamforming is a recent approach to suppress the contamination effects, but it attenuates the noise suppression performance. To overcome the limitations of the above methods, a new method called denoising weighting beamforming (DWB) is proposed in this study on the basis of CSM DD and an iterative regularization method is applied to solve the acoustical inverse problem. Besides, in order to correct the phase mismatch caused by the influence of flow on sound propagation, the shear flow correction is added before using DWB. Experiments on sound source reconstruction are conducted in the environment with the flow. Acoustics data obtained via this method show the successful removal of incoherent noise and the corrected phase mismatch. Furthermore, the sound source localization results are promising and the proposed method is simple to implement.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2018;140(6):061016-061016-15. doi:10.1115/1.4040514.

Sandwich structures that are embedded with cellular materials show excellent performance in terms of mechanics, electromagnetics, and acoustics. In this paper, sandwich panels with hybrid cellular cores of hexagonal, re-entrant hexagonal, and rectangular configurations along the panel surface are designed. The spectral element method (SEM) is applied to accurately predict the dynamic performance of the sandwich panels with a reduced number of elements and the system scale within a wide frequency range. The mechanical performance and the acoustic performance at normal incidence of the proposed structures are investigated and compared with conventional honeycomb panels with fixed cell geometries. It was found that the bending stiffness, fundamental frequencies, and sound transmission loss (STL) of the presented sandwich panels can be effectively changed by adjusting their hybrid cellular core configurations. Shape optimization designs of a hybrid cellular core for maximum STL are presented for specified tonal and frequency band cases at normal incidence. Hybrid sandwich panels increase the sound insulation property by 24.7%, 20.6%, and 109.6% for those cases, respectively, compared with conventional panels in this study. These results indicate the potential of sandwich structures with hybrid cellular cores in acoustic attenuation applications. Hybrid cellular cores can lead to inhomogeneous mechanical performance and constitute a broader platform for the optimum mechanical and acoustic design of sandwich structures.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2018;140(6):061017-061017-9. doi:10.1115/1.4040513.

The present paper investigates friction-induced self-excited vibration of a bistable compliant mechanism. A pseudo-rigid-body representation of the mechanism is used containing a hardening nonlinear spring and a viscous damper. The mass is suspended from above with the spring-damper combination leading to the addition of geometric nonlinearity in the equation of motion and position- and velocity-dependent normal contact force. Friction input provided by a moving belt in contact with the mass. An exponentially decaying function of sliding velocity describes the friction coefficient and, thereby, incorporates Stribeck effect of friction. Eigenvalue analysis is employed to investigate the local stability of the steady-state fixed points. It is observed that the oscillator experiences pitchfork and Hopf bifurcations. The effects of the spring nonlinearity and precompression, viscous damping, belt velocity, and the applied normal force on the number, position, and stability of the equilibrium points are investigated. Global system behavior is studied by establishing trajectory maps of the system. Critical belt speed is derived analytically and shown to be only the result of Stribeck effect of friction. It is found that one equilibrium point dominates the steady-state response for very low damping and negligible spring nonlinearity. The presence of damping and/or spring nonlinearity tends to diminish this dominance.

Commentary by Dr. Valentin Fuster

Technical Brief

J. Vib. Acoust. 2018;140(6):064501-064501-6. doi:10.1115/1.4039724.

In traditional active flutter control, piezoelectric materials are used to increase the stiffness of the aeroelastic structure by providing an active stiffness, and usually the active stiffness matrix is symmetric. That is to say that the active stiffness not only cannot offset the influence of the aerodynamic stiffness which is an asymmetric matrix, but also will affect the natural frequency of the structural system. In other words, by traditional active flutter control method, the flutter bound can just be moved backward but cannot be eliminated. In this investigation, a new active flutter control method which can suppress the flutter effectively and without affecting the natural frequency of the structural system is proposed by exerting active control forces on some discrete points of the structure. In the structural modeling, the Kirchhoff plate theory and supersonic piston theory are applied. From the numerical results, it can be noted that the present control method is effective on the flutter suppression, and the control effects will be better if more active control forces are exerted. After being controlled by the present control method, the natural frequency of the structure remains unchanged.

Commentary by Dr. Valentin Fuster

Expert View

J. Vib. Acoust. 2018;140(6):064701-064701-6. doi:10.1115/1.4040046.

Parameter sweeps are commonly used to explore the behavior of dynamical systems. This paper derives exact solutions for the instances in time to stroboscopically sample the response of a dynamical system subject to varying input excitations. This work will enable more accurate bifurcation diagrams and Poincaré sections in parameter regimes where numerical approaches may lead to incorrect behavior characterization. The simplest case of a linear frequency sweep is first considered before generalizing the results to include more complex functions with nonlinear sweep rates and arbitrary phase shifts.

Commentary by Dr. Valentin Fuster

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