Accepted Manuscripts

Sang-Myeong Kim, Joao A. Pereira, Antonio E. Turra and Jun-Ho Cho
J. Vib. Acoust   doi: 10.1115/1.4036722
This paper describes a theoretical and experimental investigation into an electrical Helmholtz resonator (EHR): that is, an active noise control loudspeaker used in conjunction with a microphone and a feedback controller for suppressing resonant noise in an acoustic cavity. The microphone is collocated with the loudspeaker and a band pass filter of second order is used as the control filter. The EHR is configured as such in order to suppress an acoustic mode that is within the volume velocity drive frequency range of the loudspeaker used. The concepts of impedance and passivity are used to develop the mathematical model as well as to study its dynamics. From these, it has been theoretically shown that the EHR is an extremely low-impedance acoustic damping device that electrically realizes the pressure neutralization mechanism of a conventional Helmholtz resonator. Experimental work is also presented, in which an EHR is constructed to suppress the Helmholtz mode of an acoustic cavity at about 40 Hz by more than 40 dB, to justify the mathematical model and also to verify the dynamic control mechanism.
TOPICS: Resonance, Dynamic analysis, Modeling, Noise (Sound), Acoustics, Loudspeakers, Microphones, Filters, Cavities, Feedback, Dynamics (Mechanics), Pressure, Noise control, Control equipment, Damping
Guest Editorial  
Jeffrey F. Rhoads, Hanna Cho, John Judge, Slava Krylov, Steven W. Shaw and Mohammad Younis
J. Vib. Acoust   doi: 10.1115/1.4036699
TOPICS: Dynamics of MEMS, Nanoelectromechanical systems
Meng-Xin He, Fu-Rui Xiong and Jian-Qiao Sun
J. Vib. Acoust   doi: 10.1115/1.4036680
This paper presents a study of multi-objective optimization of elastic beams with minimum weight and radiated sound power. The goal of this research is to discover the potentials to design multi-objective optimal elastic structures for better acoustic performance. We discuss various structural-acoustic properties of the Pareto solutions of the multi-objective optimization problem. We have found that geometrical and dynamic constraints can substantially reduce the volume fraction of feasible solutions in the design space, which can make it difficult to search for the optimal solutions. Several case studies with different boundary conditions are studied to demonstrate the multi-objective optimal designs of the structure.
TOPICS: Noise control, Pareto optimization, Acoustics, Design, Boundary-value problems, Weight (Mass)
Yusheng Wang, Mohammad H. Asadian and Andrei M. Shkel
J. Vib. Acoust   doi: 10.1115/1.4036679
In this paper, we developed an analytical model, supported by experimental results, on the effect of imperfections in glassblown micro wineglass fused quartz resonators. The analytical model predicting the frequency mismatch due to imperfections was derived based on a combination of the Rayleigh’s energy method and the generalized collocation method. The analytically predicted frequency of the n=2 wineglass mode shape was within 10% of the finite element results and within 20% of the experimental results for thin shells, showing the fidelity of the predictive model. The post-processing methods for improvement of the resonator surface quality were also studied. We concluded that the thermal reflow of fused quartz achieves the best result, followed in effectiveness by the RCA-1 surface treatment. All the analytical models developed in this paper are to guide the manufacturing methods to reduce the frequency and damping mismatch, and increase the quality factor of the device.
TOPICS: Modeling, Quartz, Surface finishing, Thin shells, Surface quality, Mode shapes, Q-factor, Manufacturing, Damping, Finite element analysis
Dayuan Ju and Qiao Sun
J. Vib. Acoust   doi: 10.1115/1.4036633
In wind turbine blade modeling, the coupling between rotor rotational motion and blade vibration has not been thoroughly investigated. The inclusion of the coupling terms in the wind turbine dynamics equations helps us understand the phenomenon of rotor oscillation due to blade vibration and possibly fault diagnosis. In this study, a dynamics model of a rotor blade system for a horizontal axis wind turbine which describes the coupling terms between the blade elastic movement and rotor gross rotation is developed. This model captures two-way interactions between aerodynamic wind flow and structural response. On the aerodynamic side, both steady and unsteady wind flow conditions are considered. On the structural side, blades are considered to deflect in both flap and edge directions while the rotor is treated as a rigid body. The developed model is cross-validated against a model developed in the simulation software FAST (Fatigue, Aerodynamics, Structure, and Turbulence). The coupling effects are excluded during the comparison since FAST does not include these terms. Once verified, we added coupling terms to our model to investigate the effects of blade vibration on rotor movement which has direct influences on the generator behavior. The significance of the coupling terms in applications such as blade fault detection is discussed. It is illustrated that the inclusion of coupling effects can increase the sensitivity of detecting blade faults. The proposed model can be used to investigate the effects of different terms as well as analyze fluid structure interaction.
TOPICS: Blades, Modeling, Rotors, Wind turbines, Vibration, Wind, Dynamics (Mechanics), Rotation, Flow (Dynamics), Aerodynamics, Fatigue, Turbulence, Simulation, Computer software, Fault diagnosis, Flaw detection, Generators, Oscillations, Fluid structure interaction, Horizontal axis wind turbines
Karin Mora and Oded Gottlieb
J. Vib. Acoust   doi: 10.1115/1.4036632
The dynamic motion of a parametrically excited micro-beam-string affected by nonlinear damping is considered asymptotically and numerically. It is assumed that the geometrically nonlinear beam-string, subject to only modulated AC voltage, is closer to one of the electrodes, thus resulting in an asymmetric dual gap configuration. A consequence of these novel assumptions is a combined parametric and hard excitation in the derived continuum-based model that incorporates both linear viscous and nonlinear viscoelastic damping terms. To understand how these assumptions influence the beam's performance, the conditions that lead to both principal parametric resonance and a three-to-one internal resonances are investigated. Such conditions are derived analytically from a reduced-order nonlinear model for the first three modes of the micro-beam-string using the asymptotic multiple-scales method which requires reconstitution of the slow-scale evolution equations to deduce an approximate spatio-temporal solution. The response is investigated analytically and numerically and reveals a bifurcation structure that includes coexisting in-phase and out-of-phase solutions, Hopf bifurcations, and conditions for the loss of orbital stability culminating with non-stationary quasiperiodic solutions and chaotic strange attractors.
TOPICS: String, Damping, Electrodes, Dynamics (Mechanics), Excitation, Resonance, Bifurcation, Attractors, Stability
Astitva Tripathi and Anil K. Bajaj
J. Vib. Acoust   doi: 10.1115/1.4036624
Robustness is a highly desirable quality in Micro Electro Mechanical Systems (MEMS). Sensors and resonators operating on nonlinear dynamic principles such as internal resonances are no exception to this and in addition, when nonlinear dynamic phenomena are used to enhance device sensitivity their requirements for robustness may even be greater. This work discusses two aspects as they relate to the robustness and performance of nonlinear resonators. In the first aspect, different resonator designs are compared to find which among them have a better capacity to deliver reliable and reproducible performance in face of variations from the nominal design due to manufacturing process uncertainties/tolerances. The second aspect attempts to identify the inherent topological features that, if present in a resonator, enhance its robustness. Thus, the first part of this work is concerned with uncertainty analysis of several candidate nonlinear resonators operating under the principle of 1:2 internal resonance and obtained via a Hierarchical Optimization Method introduced by the authors. The second part discusses specific changes to the computational design process that can be made so as to enhance the robustness and reliability of the candidate resonators.
TOPICS: Reliability, Design, Robustness, Microelectromechanical systems, Resonance, Sensors, Manufacturing, Uncertainty, Uncertainty analysis, Optimization
Naftaly Krakover and Slava Krylov
J. Vib. Acoust   doi: 10.1115/1.4036625
Bistable microstructures are distinguished by their ability to stay in two different stable configurations at the same loading. They manifest rich behavior and are advantageous in applications such as switches, nonvolatile memories and sensors. Bistability of initially curved or buckled double clamped beams, curved plates and shells is associated with mechanical geometric nonlinearity appearing due to coupling between bending and compressive axial/in-plane stress. The bistable behavior is achieved by using a combination of carefully tailored initial shape and constrained boundaries. However, these statically indeterminate structures suffer from high sensitivity to temperature and residual stress. In the present work we show using the model that by combining electrostatic actuation by fringing fields with direct transversal forcing by a parallel plate electrode or piezoelectric transducer bistable behavior can be obtained in a simple cantilever structure distinguished by robustness and low thermal sensitivity. Reduced order model of the cantilever was build using Galerkin decomposition, the electrostatic force was obtained by means of three-dimensional finite elements modeling. We also demonstrate that operation of the device in the vicinity of the bistability threshold may enhance the frequency sensitivity of the cantilever to loading. This sensitivity enhancement approach may have applications in a broad range of resonant microelectromechanical inertial, force, mass and bio sensors as well as in atomic force microscopy.
TOPICS: Electric fields, Cantilevers, Sensors, Stress, Electrodes, Finite element analysis, Modeling, Piezoelectric transducers, Plates (structures), Atomic force microscopy, Resonance, Temperature, Robustness, Shapes, Shells, Switches
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)

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