Accepted Manuscripts

Toshihiko Asami
J. Vib. Acoust   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.
TOPICS: Vibration absorbers, Algebra, Optimization, Excitation systems, Stability, Damping, Design, Linear vibration, Vibration equipment, Displacement
Lisha Yuan and Romesh C. Batra
J. Vib. Acoust   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 nodes of an 8-node serendipity 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 transverse normal strain at a point is found to be nearly one-half of the axial strain implying that higher-order plate theories that assume the transverse normal strain equal to zero 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.
TOPICS: Pressure, Finite element analysis, Vibration, Elastic plates, Plates (structures), Hydrostatic pressure, Plate theory, Boundary-value problems, Computer software, Eigenvalues, Free vibrations, Mode shapes, Shear (Mechanics), Finite element methods, Algorithms, Stress
Enaiyat Ghani Ovy
J. Vib. Acoust   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 guide creates an excessive vibration which may lead to permanent damage of the mechanical system. In the present work, the rubbing phenomenon between rotor and 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.
TOPICS: Machinery, Bearings, Rotors, Clearances (Engineering), Simulation, Friction, Computer simulation, Vibration, Matlab, Stators, Damage
Matthew D. Fronk, Sameh Tawfick, Chiara Daraio, Shuangbao Li, Alexander F. Vakakis and Michael J. Leamy
J. Vib. Acoust   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. Non-reciprocity violates this property and can be introduced to systems if time-reversal symmetry and/or parity symmetry is lost. While many studies have induced non-reciprocity 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.
TOPICS: Acoustics, Wave propagation, Excitation, Resonance, Parity (Physics), Time reversal, Transients (Dynamics), Impulse (Physics), Design, Periodic structures, Stiffness, Time-invariant systems
Mergen H. Ghayesh and Hamed Farokhi
J. Vib. Acoust   doi: 10.1115/1.4043716
The nonlinear behaviour 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 piezoelectric patch and the beam. Through use of the generalised 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 utilised 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 in 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.
TOPICS: Computer-aided engineering, Stress, Hamilton's principle, Degrees of freedom, Finite element model, Nonlinear dynamics
Sophie Nalbach, Gianluca Rizzello and Stefan Seelecke
J. Vib. Acoust   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 kHz, 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, pre-loaded 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.
TOPICS: Lasers, Elastomers, Actuators, Vibration, Experimental analysis, Membranes, Electrodes, Stress, Geometry, Design, Acoustics, Oscillations, Resonance, Deformation, Transducers, Frequency response, Signals, Springs, Laser Doppler vibrometers, Excitation
Xiongtao Cao, Mingsheng Wang and Lei Shi
J. Vib. Acoust   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 [1], which alleges an error in Eq. (18) of [2]. The other is Eq. (2) in [1], which alleges a second error in Eq. (19) of [2]. Then, Roumeliotis presented alternative expressions based on the changes he suggested in Eqs. (1) and (2) in [1]. We here give our explanations to the issues raised in the discussion by Roumeliotis [1].
TOPICS: Acoustics, Sound, Errors
John A. Roumeliotis
J. Vib. Acoust   doi: 10.1115/1.4043607
In their paper [1] Cao, Wang and Shi have presented the sound radiation from point acoustic sources with shield of large prolate spheroidal baffles. The author of this discussion has found some errors in their analysis, which will be presented in detail in the following section, together with the corresponding corrections.
TOPICS: Acoustics, Sound, Errors
Wangbai Pan, Guoan Tang and Jiong Tang
J. Vib. Acoust   doi: 10.1115/1.4043609
This research concerns the uncertainty analysis and quantification of 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.
TOPICS: Vibration equipment, Uncertainty analysis, Uncertainty, Fittings, Frequency response
Sam Shi, Matthew J. Leineweber and Jan Andrysek
J. Vib. Acoust   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 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, 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 10 able-bodied and 3 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 user response accuracy and decrease 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.
TOPICS: Prostheses, Feedback, Vibration, Artificial limbs, Pressure, Design, Optimization, Mechanical admittance, Errors
Zhibo Geng, Ke Xiao, Jiaxu Wang and Junyang Li
J. Vib. Acoust   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 6-degree-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 4 operating time points. The bifurcation diagrams, Poincaré maps, FFT spectra, phase diagrams and time series are used to investigate the state of motion. The results can provide reference for gear transmission system with wear.
TOPICS: Wear, Gears, Stiffness, Dynamic models, Bifurcation, Poincaré maps, Spectra (Spectroscopy), Phase diagrams, Excitation, Time series
Yao Zhang, Hai-Sheng Zhao and Seng Tjhen Lie
J. Vib. Acoust   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 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. Lab-scale experimental validation shows that the new technique is capable of identifying the first three mode shapes accurately.
TOPICS: Mode shapes, Excitation systems, Sensors, Accelerometers, Algorithms
Xiaohui Zhang, Yu-Hui Wang, Xingkai Feng and Siyuan Hou
J. Vib. Acoust   doi: 10.1115/1.4043511
This paper aims to investigate the airfoil flutter damage-mitigating problem in hypersonic flow. A new adaptive robust nonlinear predictive control (RNPC) law is designed in this paper to mitigate the damage during the airfoil flutter of a generic hypersonic flight vehicle. A three-degree-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 RNPC is performed. Subsequently, based on the nonlinear aerodynamics of the airfoil and damage accumulation model, the damage of airfoil is observed online. Simulation results illustrate the effectiveness of the proposed method.
TOPICS: Flutter (Aerodynamics), Vehicles, Predictive control, Flight, Airfoils, Damage, Aerodynamics, Control equipment, Simulation results, Hypersonic flow, Pistons, Stability
David Griese, Joshua D. Summers and Lonny Thompson
J. Vib. Acoust   doi: 10.1115/1.4029043
This work defines a finite element model to study the sound transmission properties of aluminium honeycomb sandwich panels. Honeycomb cellular metamaterial structures offer many distinct advantages over homogenous materials because their effective material properties depend on both their constituent material properties and their geometric cell configuration. From this, a wide range of targeted effective material properties can be achieved thus supporting forward design by tailoring the honeycomb cellular materials for specific applications. One area that has not been fully explored is the set of acoustic properties of honeycomb materials and how these can offer increased acoustic design flexibility. Understanding these relations, the designer can effectively tune designs to perform better in specific acoustic applications. One such example is the insulation of target sound frequencies to prevent sound transmission through a panel. This work explores how certain geometric and effective structural properties of in-plane honeycomb cores in sandwich panels affect the sound pressure transmission loss properties of the panel. The two acoustic responses of interest in this work are the general level of sound transmission loss of the panel and the location of the resonance frequencies that exhibit high levels of sound transmission, or low sound pressure transmission loss. Constant mass honeycomb core models are studied with internal cell angles ranging from -45° to +45°. It is shown in this work that models with lower core internal cell angles, under constant mass constraints, have more resonances in the 1-1000 Hz range, but exhibit a higher sound pressure transmission loss between resonant frequencies.
TOPICS: Sound, Honeycomb structures, Geometry, Acoustics, Materials properties, Sound pressure, Resonance, Design, Finite element model, Insulation, Metamaterials, Aluminum, Mechanical properties, Acoustical properties

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