Accepted Manuscripts

Michael Leamy and Matthew Fronk
J. Vib. Acoust   doi: 10.1115/1.4036501
Recent studies have presented first-order multiple time scale approaches for exploring amplitude-dependent plane-wave dispersion in weakly nonlinear chains and lattices characterized by cubic stiffness. These analyses have yet to assess solution stability, which requires an analysis incorporating damping. Furthermore, due to their first-order dependence, they make an implicit assumption that cubic stiffness influences dispersion shifts to a greater degree than quadratic stiffness, and they thus ignore quadratic shifts. This paper addresses these limitations by carrying-out higher-order, multiple scales perturbation analyses of linearly-damped nonlinear monoatomic and diatomic chains. The study derives higher-order dispersion corrections informed by both quadratic and cubic stiffness, and quantifies plane wave stability using evolution equations resulting from the multiple scales analysis and numerical experiments. Additionally, by reconstructing plane waves using both homogeneous and particular solutions at multiple orders, the study introduces a new interpretation of multiple scales results in which predicted waveforms are seen to exist over all space and time, constituting an invariant, multi-harmonic wave of infinite extent analogous to cnoidal waves in continuous systems. Using example chains characterized by dimensionless parameters, numerical studies confirm that the spectral content of the predicted waveforms exhibits less growth/decay over time as higher-order approximations are used in defining the simulations’ initial conditions. Thus the study results suggest that higher-order multiple scales perturbation analysis captures long-term, non-localized invariant plane waves, which have the potential for propagating coherent information over long distances.
TOPICS: Stability, Waves, Stiffness, Chain, Damping, Engineering simulation, Approximation, Spacetime, Simulation
Sannia Mareta, Dunant Halim and Atanas A Popov
J. Vib. Acoust   doi: 10.1115/1.4036499
This work proposes a method for controlling vibration using compliant-based actuators. The compliant actuator combines a conventional actuator with elastic elements in a series configuration. The benefits of compliant actuators for vibration control applications, demonstrated in this work, are twofold: (i) vibration reduction over a wide frequency bandwidth by passive control means; (ii) improvement of vibration control performance when active control is applied using the compliant actuator. The vibration control performance is compared with the control performance achieved using the well-known vibration absorber and conventional rigid actuator systems. The performance comparison showed that the compliant actuator provided a better flexibility in achieving vibration control over a certain frequency bandwidth. The passive and active control characteristics of the compliant actuator are investigated, which shows that the control performance is highly dependent on the compliant stiffness parameter. The active control characteristics are analyzed by using the Proportional and Derivative (PD) control strategy which demonstrated the capability of effectively changing the respective effective stiffness and damping of the system. These attractive dual passive-active control characteristics are therefore advantageous for achieving an effective vibration control system, particularly for controlling the vibration over a specific wide frequency bandwidth.
TOPICS: Actuators, Vibration, Vibration control, Stiffness, Passive control, Vibration absorbers, Vibration control equipment, Damping
Francesco Ripamonti, Lorenzo Orsini and Ferruccio Resta
J. Vib. Acoust   doi: 10.1115/1.4036502
Many mechanical systems often show nonlinear behaviour related to particular operating conditions or to the nonlinear characteristic of the elements (springs, dampers, etc.) making up the system. In these cases, common engineering practice is to linearize the equation of motion around a particular operating point, and to design a linear controller. Although this approach is simple, its main disadvantage is that stability properties and validity of the controller are only local. For these reasons, over the last decades, non-linear control techniques have been investigated more and more in order to improve control performance. In particular, in this paper the model-based sliding-mode-control (SMC) technique is considered because of its easy implementation and the considerable robustness of the controller even under significant model uncertainties. This technique is analysed numerically with respect to the pendulum system, to better understand the influence of the control action on the system dynamics, and then experimentally in order to control a highly nonlinear system, consisting of a three-link flexible manipulator. For this system, a nonlinear modal model is developed and a nonlinear observer is designed. Results of experimental tests on the manipulator are also reported.
TOPICS: Sliding mode control, Vibration, Flexible manipulators, Control equipment, System dynamics, Equations of motion, Stability, Manipulators, Pendulums, Robustness, Springs, Uncertainty, Dampers, Design, Nonlinear systems
Alwathiqbellah Ibrahim, Shahrzad Towfighian and Mohammad Younis
J. Vib. Acoust   doi: 10.1115/1.4036503
Vibration energy harvesting can be an effective method for scavenging wasted mechanical energy for use by wireless sensors that have limited battery life. Two major goals in designing energy harvesters are enhancing the power scavenged at low frequency and improving efficiency by increasing the frequency bandwidth. To achieve these goals, we derived a magneto-elastic beam operated at the transition between mono- and bi-stable regions. By improving the mathematical model of the interaction of magnetic force and beam dynamics, we obtained a precise prediction of natural frequencies as the distance of magnets varies. Using the shooting technique for the improved model, we present a fundamental understanding of interesting combined softening and hardening responses that happen at the transition between the two regimes. The transition regime is proposed as the optimal region for energy conversion in terms of frequency bandwidth and output voltage. Using this technique, low frequency vibration energy harvesting at around 17 Hz was possible. The theoretical results were in good agreement with the experimental results. The target application is to power wildlife bio-logging devices from bird flights that have consistent high power density around 16 Hz [1].
TOPICS: Dynamics (Mechanics), Vibration, Energy harvesting, Flight, Battery life, Power density, Sensors, Magnets, Magnetic fields, Hardening, Energy conversion, Design
Mohammed Daqaq and Abdraouf Abusoua
J. Vib. Acoust   doi: 10.1115/1.4036504
This article describes a new parametric method for the development of nonlinear models with parameters identified from an experimental setting. The approach is based on applying a strong non-resonant high-frequency harmonic excitation to the unknown nonlinear system and monitoring its influence on the slow modulation of the system’s response. In particular, it is observed that the high-frequency excitation induces a shift in the slow-modulation frequency and a static bias in the mean of the dynamic response. Such changes can be directly related to the amplitude and frequency of the strong excitation offering a unique methodology to identify the unknown nonlinear parameters. The proposed technique is implemented to identify the nonlinear restoring-force coefficients of three experimental systems. Results demonstrate that this technique is capable of identifying the nonlinear parameters with relatively good accuracy.
TOPICS: Nonlinear systems, Excitation, Resonance, Dynamic response
Weeraphan Jiammeepreecha and Somchai Chucheepsakul
J. Vib. Acoust   doi: 10.1115/1.4036500
Nonlinear axisymmetric free vibration analysis of liquid-filled spherical shells with volume constraint condition using membrane theory is presented in this paper. The energy functional of the shell and contained liquid can be expressed based on the principle of virtual work using surface fundamental form, and are written in the appropriate forms. Natural frequencies and corresponding mode shapes for specified axisymmetric vibration amplitude of liquid-filled spherical shells can be calculated by finite element method. A nonlinear numerical solution can be obtained by the modi?ed direct iteration technique. The results indicate that the Lagrange multiplier is a parameter for adapting the internal pressure in order to sustain the shell in equilibrium state for each mode of vibration with the constraint volume condition. The axisymmetric mode shapes of the liquid-filled spherical shells under volume constraint condition were found to be in close agreement with those in existing literature for an empty spherical shell. Finally, the effects of support condition, thickness, initial internal pressure, bulk modulus of internal liquid, and elastic modulus on the nonlinear axisymmetric free vibration and change of pressure of the liquid-filled spherical shells with constraint volume were demonstrated. The parametrically studies showed that the change of pressure has a major impact on the fundamental vibration mode when compared with the higher vibration modes.
TOPICS: Free vibrations, Spherical shells, Vibration, Pressure, Mode shapes, Shells, Bulk modulus, Equilibrium (Physics), Finite element methods, Virtual work principle, Elastic moduli, Membranes
Chuan-Xing Bi, Bi-Chun Dong, Xiao-Zheng Zhang and Yong-Bin Zhang
J. Vib. Acoust   doi: 10.1115/1.4036498
To identify sound sources situated in a fluid flow, an equivalent source method-based nearfield acoustic holography (NAH) in a moving medium is proposed, and two types of acoustic inputs, pressure and particle velocity, are considered. In particular, an analytical relationship between the particle velocity perpendicular to the flow direction and the equivalent source strength is deduced, which makes it possible to realize the reconstruction with particle velocity input. Compared to the planar NAH in a moving medium, the proposed method is applicable to sound sources with more complicated geometries. Numerical simulations with sound sources distributed over two types of geometries including planar geometry and non-planar one are conducted to test the performances of the proposed method. The results indicate that the proposed method provides satisfactory reconstructed results whatever with pressure input or with particle velocity input, and it is valid and robust over a wide range of flow velocities and frequencies and under different levels of background noise.
TOPICS: Holography, Acoustics, Particulate matter, Pressure, Flow (Dynamics), Fluid dynamics, Computer simulation, Noise (Sound), Geometry
In Memoriam  
Bala Balachandran, Mohammad Younis and I. Y. (Steve) Shen
J. Vib. Acoust   doi: 10.1115/1.4036505
Dr. Ali Hasan Nayfeh, University Distinguished Professor Emeritus of Virginia Tech, Blacksburg, VA, passed away rather suddenly on March 27, 2017, at the age of 84, in his home at Amman, Jordan. The communities of applied mechanics, nonlinear dynamics, vibration and control, and applied mathematics have lost a premier scientist and engineer, who has been an extraordinarily influential scholar over the past five decades.
TOPICS: Engineers, Engineering teachers, Engineering mathematics, Engineering mechanics, Vibration, Nonlinear dynamics
Lourdes Rubio, José Fernández-Sáez and Antonino Morassi
J. Vib. Acoust   doi: 10.1115/1.4036467
In this paper new exact closed form solutions for free longitudinal vibration of a one-parameter countable family of cantilever rods with one end tip mass are obtained. The analysis is based on the reduction of the equation governing the longitudinal vibration to the Sturm-Liouville canonical form and on the use of double Darboux transformations. The rods for which exact eigensolutions are provided are explicitly determined in terms of an initial rod with known closed-form eigensolutions. The method can be also extended to include longitudinally vibrating rods with tip mass at both ends.
TOPICS: Rods, Vibration, Cantilevers
A B M Tahidul Haque, Ratiba F. Ghachi, Wael I. Alnahhal, Amjad Aref and Jongmin Shim
J. Vib. Acoust   doi: 10.1115/1.4036469
The finite element (FE) method offers an efficient framework to investigate the evolution of phononic crystals which possess materials or geometric nonlinearity subject to external loading. Despite its superior efficiency, the FE method suffers from spectral distortions in the dispersion analysis of waves perpendicular to the layers in infinitely periodic multilayered composites. In this study, the analytical dispersion relation for sagittal elastic waves is re-formulated in a substantially concise form, and it is employed to reproduce spatial aliasing-induced spectral distortions in FE dispersion relations. Furthermore, through an anti-aliasing condition and the effective elastic modulus theory, a FE modeling general guideline is provided to overcome the observed spectral distortions in FE dispersion relations of infinitely periodic multilayered composites and its validity is also demonstrated.
TOPICS: Finite element methods, Composite materials, Dispersion relations, Finite element analysis, Modeling, Elastic moduli, Phononic crystals, Waves, Elastic waves
Yusuf Ziya Umul
J. Vib. Acoust   doi: 10.1115/1.4036470
The scattered acoustic waves by a transmissive half-plane, which is illuminated by a line source, are investigated. The high-frequency diffracted wave expressions are obtained by taking into account a resistive half-screen that is defined in electromagnetics. The uniform diffracted fields are expressed in terms of the Fresnel cylinder functions. The behavior of the waves is compared with the case when the uniform theory of diffraction is considered. The geometrical optics and diffracted fields are examined numerically.
TOPICS: Waves, Diffraction, Acoustics, Electromagnetism, Geometric optics, Electromagnetic force, Bessel functions
Technical Brief  
Hanbo Jiang, Alex Siu Hong Lau and Xun Huang
J. Vib. Acoust   doi: 10.1115/1.4036471
Acoustic liner optimization calls for very efficient simulation methods. A highly efficient and straightforward algorithm is proposed here for the Wiener-Hopf solver, which also takes advantage of the parallel processing capability of the emerging graphics processing unit (GPU) technology. The proposed algorithm adopts a simple concept that re-arranges the formulations of the Wiener-Hopf solver to appropriate matrix forms. This concept is surprisingly succinct and leads to a stunningly efficient computational performance. By examining the computational performance of two representative set-ups (lined duct and duct radiations), the current study shows the superior performance of the proposed algorithm, particularly with GPU. The much improved computational efficiency further suggests the potential of the proposed algorithm and the use of GPU for practical low noise aircraft engine design and optimization.
TOPICS: Acoustics, Algorithms, Ducts, Graphics processing units, Optimization, Parallel processing, Aircraft engines, Design, Simulation, Noise (Sound)
Sachiko Ishida, Kohki Suzuki and Haruo Shimosaka
J. Vib. Acoust   doi: 10.1115/1.4036465
We present a prototype vibration isolator whose design is inspired by origami-based foldable cylinders with torsional buckling patterns. The vibration isolator works as a nonlinear spring that has quasi-zero spring stiffness in a given frequency region, where it does not transmit vibration in theory. We evaluate the performance of the prototype vibration isolator through excitation experiments via the use of harmonic oscillations and seismic-wave simulations of the Tohoku-Pacific Ocean and Kobe earthquakes. The results indicate that the isolator with the current specification is able to suppress the transmission of vibrations with frequencies of over 6 Hz. The functionality and constraints of the isolator are also clarified. It has been known that origami-based foldable cylinders with torsional buckling patterns provide bistable folding motions under given conditions. In a previous study, we proposed a vibration isolator utilizing the bistability characteristics and numerically confirmed the device's validity as a vibration isolator. Here, we attempt prototyping the isolator with the use of versatile metallic components and experimentally evaluate the isolation performance.
TOPICS: Design, Vibration isolators, Experimental analysis, Stiffness, Springs, Engineering prototypes, Vibration, Buckling, Cylinders, Earthquakes, Engineering simulation, Oscillations, Seismic waves, Simulation, Oceans, Pacific Ocean, Excitation
Farhad Farzbod
J. Vib. Acoust   doi: 10.1115/1.4036466
Periodic structures have interesting acoustic and vibration properties making them suitable for a wide variety of applications. In a periodic structure, the number of frequencies for each wavevector depends on the degree of freedom of the unit cell. In this paper, we investigate the number of wavevectors for each frequency. This analysis defines the upper bound for the maximum number of wavevectors for each frequency in a general periodic structure which might include damping. Investigation presented in this paper can also provide an insight for designing materials in which the interaction between unit cells is not limited to the closest neighbor. As an example application of this work, we investigate phonon dispersion curves in hexagonal form of Boron Nitride to show that first neighbor interaction is not sufficient to model dispersion curves with force-constant-model.
TOPICS: Periodic structures, Boron, Acoustics, Phonons, Degrees of freedom, Damping, Design, Vibration
N. Dolatabadi, S. Theodossiades and S. J. Rothberg
J. Vib. Acoust   doi: 10.1115/1.4036468
The impulsive behaviour of the piston in the cylinder liner plays a key role in the Noise, Vibration and Harshness (NVH) of internal combustion engines. There have been several studies on the identification and quantification of piston impact action under various operation conditions. In the current study, the dynamics of the piston secondary motion are initially explored in order to describe the aggressive oscillations, energy loss and noise generation. The control of piston secondary motion (and thus, impacts) is investigated using a new passive approach based on energy transfer of the highly transient oscillations to a nonlinear absorber. The effectiveness of this new method for improving the piston impact behaviour is discussed using a preliminary parametric study that leads to the conceptual design of a nonlinear energy absorber.
TOPICS: Pistons, Passive control, Oscillations, Noise (Sound), Internal combustion engines, Vibration, Cylinders, Dynamics (Mechanics), Energy transformation, Energy dissipation, Transients (Dynamics), Conceptual design
Abe H. Lee, Robert L. Campbell, Brent A. Craven and Stephen A. Hambric
J. Vib. Acoust   doi: 10.1115/1.4036453
Fluid-structure interaction (FSI) is investigated in this study for vortex-induced vibration of a flexible, backward skewed hydrofoil. An in-house finite-element structural solver FEANL is tightly coupled with the open-source computational fluid dynamics (CFD) library OpenFOAM to simulate the interaction of a flexible hydrofoil with vortical flow structures shed from a large upstream rigid cylinder. To simulate the turbulent flow at a moderate computational cost, hybrid RANS-LES is used. Simulations are first performed to investigate key modeling aspects that include the influence of CFD mesh resolution and topology (structured vs unstructured mesh), time step size, and turbulence model (Delayed-Detached-Eddy-Simulation and k-omega SST-SAS). Final FSI simulations are then performed and compared against experimental data acquired from the Penn State-ARL 12-inch water tunnel at two flow conditions, 2.5 m/s and 3.0 m/s, corresponding to Reynolds numbers of 153,000 and 184,000 (based on the cylinder diameter), respectively. Comparisons of the hydrofoil tip-deflections, reaction forces and velocity fields (contours and profiles) show reasonable agreement between the tightly-coupled FSI simulations and experiments. The primary motivation of this study is to assess the capability of a tightly coupled FSI approach to model such a problem and to provide modeling guidance for future FSI simulations of rotating propellers in crashback (reverse propeller operation).
TOPICS: Simulation, Hydrofoil, Vortex-induced vibration, Fluid structure interaction, Engineering simulation, Computational fluid dynamics, Turbulence, Modeling, Cylinders, Propellers, Reynolds-averaged Navier–Stokes equations, Topology, Vortex flow, Deflection, Eddies (Fluid dynamics), Reynolds number, Resolution (Optics), Water tunnels, Flow (Dynamics), Finite element analysis
Samuel F. Asokanthan, Soroush Arghavan and Mohamed Bognash
J. Vib. Acoust   doi: 10.1115/1.4036452
Effect of stochastic fluctuations in angular velocity on the stability of two-degree-of-freedom ring-type MEMS gyroscopes is investigated. The governing Stochastic Differential Equations are discretized using the higher-order Milstein scheme in order to numerically predict the system response assuming the fluctuations to be white noise. Simulations via Euler scheme as well as a measure of Largest Lyapunov Exponents are employed for validation purposes due to lack of similar analytical or experimental data. The response of the gyroscope under different noise fluctuation magnitudes have been computed to ascertain the stability behavior of the system. External noise that affect the gyroscope dynamic behavior typically results from environment factors and the nature of the system operation can be exerted on the system at any frequency range depending on the source. Hence, a parametric study is performed to assess the noise intensity stability threshold for a number of damping ratio values. The stability investigation predicts the form of threshold fluctuation intensity dependence on damping ratio. Under typical gyroscope operating conditions, nominal input angular velocity magnitude and mass mismatch appear to have minimal influence on system stability.
TOPICS: Stability, Microelectromechanical systems, Noise (Sound), Fluctuations (Physics), Damping, Differential equations, Engineering simulation, White noise, Simulation
Atanu Sahu, Arup Guha Niyogi, Michael Rose and Partha Bhattacharya
J. Vib. Acoust   doi: 10.1115/1.4036390
A two-stage numerical model is developed to understand the energy transmission characteristics through a finite double-leaf structure placed in an infinite baffle subjected to an external excitation and subsequently the sound radiation behavior of the same into the semi-infinite receiving side. In the first stage, a mobility based coupled finite element - boundary element (FE-BE) technique is implemented to model the energy transmission from the primary panel to the secondary panel through an air-gap. In the second stage, a separate BE based model is developed to estimate the sound power radiated by the radiating (secondary) panel into the receiving side which is assumed to be semi - infinite. The advantage of the proposed approach is that it is sufficient to mesh the structural panels alone, thereby reducing the problem dimensions and the difficulty in modeling. Moreover, the developed model can be easily implemented for structures made up of various constituent materials (isotropic or laminated composites) with complex boundary conditions and varying panel geometries. Numerical experiments are carried out for different material models by varying air-gap thicknesses and also by introducing alternate energy transmission path in terms of mechanical links and the obtained results are discussed.
TOPICS: Composite materials, Radiation (Physics), Computer simulation, Dimensions, Sound, Boundary element methods, Finite element analysis, Modeling, Boundary-value problems, Structural panels, Mechanical admittance, Excitation
Shahid Saghir, Saad Ilyas, Nizar Jaber and Mohammed Ibrahim Younis
J. Vib. Acoust   doi: 10.1115/1.4036398
We investigate the static and dynamic behavior of a multilayer clamped-free-clamped-free (CFCF) microplate, which is made of polyimide, gold, chromium, and nickel. The microplate is slightly curved away from a stationary electrode and is electrostatically actuated. The free and forced vibrations of the microplate are examined. First, we experimentally investigate the variation of the first natural frequency under the electrostatic DC load. Then, the forced dynamic behavior is investigated by applying a harmonic AC voltage superimposed to a DC voltage. Results are shown demonstrating the transition of the dynamic response of the microplate from hardening to softening as the DC voltage is changed as well the dynamic pull-in phenomenon. For theoretical model, we adopt a dynamic analog of the von-Karman governing equations accounting for initial curvature imperfection. These equations are then used to develop a reduced order model based on the Galerkin procedure to simulate the mechanical behavior of the microplate. We compare the theoretical results with experimental data and show excellent agreement among the results. We also examine the effect of the initial rise on the natural frequencies of first three symmetric-symmetric modes of the plate.
TOPICS: Mechanical behavior, Microplates, Accounting, Vibration, Dynamic response, Nickel, Stress, Hardening, Electrodes
Nizar R. Jaber, Karim M. Masri and Mohammed Ibrahim Younis
J. Vib. Acoust   doi: 10.1115/1.4036399
This work aims to investigate theoretically and experimentally various nonlinear dynamic behaviors of a doubly clamped microbeam near its primary resonance. Mainly, we investigate the transition behavior from hardening, mixed, and then softening behavior. We show in a single frequency-response curve, under a constant voltage load, the transition from hardening to softening behavior demonstrating the dominance of the quadratic electrostatic nonlinearity over the cubic geometric nonlinearity of the beam as the motion amplitudes becomes large, which may lead eventually to dynamic pull-in. The microbeam is fabricated using polyimide as a structural layer coated with nickel from top and chromium and gold layers from the bottom. Frequency sweep tests are conducted for different values of DC bias revealing hardening, mixed, and softening behavior of the microbeam. A multi-mode Galerkin model combined with a shooting technique are implemented to generate the frequency response curves and to analyze the stability of the periodic motions using the Floquet theory. The simulated curves show good agreement with the experimental data.
TOPICS: Resonance, Microbeams, Nonlinear dynamics, Hardening, Frequency response, Stability, Nickel, Stress

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