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In Memoriam

J. Vib. Acoust. 2017;139(4):040101-040101-1. doi:10.1115/1.4036505.
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Dr. Ali Hasan Nayfeh, University Distinguished Professor Emeritus of Virginia Tech, Blacksburg, VA, passed away rather suddenly on Mar. 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.

Commentary by Dr. Valentin Fuster

Guest Editorial

J. Vib. Acoust. 2017;139(4):040301-040301-2. doi:10.1115/1.4036699.
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Since the pioneering work of Harvey Nathanson and his collaborators in the mid-1960s, microelectromechanical systems (MEMS) that leverage dynamic behavior for practical purpose have been of distinct research interest [1,2]. From roughly 1980 to 2000, research in this area grew appreciably, paced by advancements in the integrated circuit community and fueled by the promise of resonant microsystems in applications ranging from chemical, biological, and inertial sensing to atomic force microscopy and radio frequency signal processing. While this measurable growth was largely spurred on by researchers with circuits and systems expertise, the early 2000s saw an influx of biologists and physicists into the research area, rightly drawn to the topic by the potential of exploring the very foundations of their own fields with these small-scale devices.

Commentary by Dr. Valentin Fuster

SPECIAL SECTION PAPERS

J. Vib. Acoust. 2017;139(4):040901-040901-11. 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 direct current (DC) load. Then, the forced dynamic behavior is investigated by applying a harmonic alternating current (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 the 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 (ROM) based on the Galerkin procedure to simulate the mechanical behavior of the microplate. We compare the theoretical results with the 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.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;139(4):040902-040902-5. 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 direct current (DC) bias revealing hardening, mixed, and softening behavior of the microbeam. A multimode 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 a good agreement with the experimental data.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;139(4):040903-040903-9. doi:10.1115/1.4036632.

The dynamic motion of a parametrically excited microbeam-string affected by nonlinear damping is considered asymptotically and numerically. It is assumed that the geometrically nonlinear beam-string, subject to only modulated alternating current 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 resonance are investigated. Such conditions are derived analytically from a reduced-order nonlinear model for the first three modes of the microbeam-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 nonstationary quasi-periodic solutions and chaotic strange attractors.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;139(4):040904-040904-7. doi:10.1115/1.4036452.

Effect of stochastic fluctuations in angular velocity on the stability of two degrees-of-freedom ring-type microelectromechanical systems (MEMS) gyroscopes is investigated. The governing stochastic differential equations (SDEs) 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 (LLEs) are employed for validation purposes due to lack of similar analytical or experimental data. The response of the gyroscope under different noise fluctuation magnitudes has 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.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;139(4):040905-040905-8. doi:10.1115/1.4036400.

Arch microbeams have been utilized and proposed for many uses over the past few years due to their large tunability and bistability. However, recent experimental data have shown different mechanical behaviors of arches when subjected to axial loads, i.e., their stiffness may increase or decrease with applied axial loads. This paper aims to investigate in depth, the influence of the competing effects of initial rise and axial loads on the mechanical behavior of micromachined arches; mainly their static deflection and resonant frequencies. Based on analytical solutions, the static response and eigenvalue problems are analyzed for various values of initial rises and axial loads. Universal curves showing the variation of the first three resonance frequencies of the arch are generated for various values of initial rise under both tensile and compressive axial loads. This study shows that increasing the tensile or compressive axial loads for different values of initial rise may lead to either increase in the stiffness of the beam or initial decrease in the stiffness, which later increases as the axial load is increased depending on the dominant effect of the initial rise of the arch and the axial load. The obtained universal curves represent useful design tools to predict the tunability of arches under axial loads for various values of initial rises. The use of the universal curves is demonstrated with an experimental case study. Analytical formulation is developed to predict the point of minimum where the trend of the resonance frequency versus axial loads changes qualitatively due to the competing effects of axial loads and initial curvature.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;139(4):040906-040906-7. doi:10.1115/1.4036397.

In this paper, we study the occurrence of synchronization between the two degenerate resonance modes of a microdisk resonator gyroscope. Recently, schemes involving the simultaneous actuation of the two vibration modes of the gyroscope have been implemented as a promising new method to increase their performance. However, this strategy might result in synchronization between the two modes, which would maintain frequency mode-matching but also may produce problems, such as degrading stability and sensitivity. Here, we demonstrate for the first time synchronization between the degenerate modes of a microgyroscope and show that synchronization arising from mutual coupling dramatically reduces frequency instability at the cost of increased amplitude instability. We present an alternative synchronization scheme that suppresses this drawback while still taking advantage of a passive frequency mode-match operation.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;139(4):040907-040907-11. doi:10.1115/1.4036624.

Robustness is a highly desirable quality in microelectromechanical 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.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;139(4):040908-040908-10. 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 this 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 (PZT) 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 built using Galerkin decomposition, the electrostatic force was obtained by means of three-dimensional (3D) finite elements (FEs) 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 biosensors as well as in atomic force microscopy (AFM).

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;139(4):040909-040909-8. 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 modeling results and within 20% of the experimental results for thin shells, showing the fidelity of the predictive model. The postprocessing 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 to increase the mechanical quality factor of the device.

Commentary by Dr. Valentin Fuster

Research Papers

J. Vib. Acoust. 2017;139(4):041001-041001-12. doi:10.1115/1.4036453.

Fluid–structure interaction (FSI) is investigated in this study for vortex-induced vibration (VIV) of a flexible, backward skewed hydrofoil. An in-house finite element structural solver finite element analysis nonlinear (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 Reynolds-averaged Navier–Stokes–large eddy simulation (RANS–LES) is used. Simulations are first performed to investigate key modeling aspects that include the influence of CFD mesh resolution and topology (structured versus unstructured mesh), time-step size, and turbulence model (delayed-detached-eddy-simulation and kω shear stress transport-scale adaptive simulation). Final FSI simulations are then performed and compared against experimental data acquired from the Penn State-ARL 12 in 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).

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;139(4):041002-041002-9. doi:10.1115/1.4036209.

A sound–structure interaction model is established to study the vibroacoustic characteristics of a semisubmerged cylindrical shell using the wave propagation approach (WPA). The fluid free surface effect is taken into account by satisfying the sound pressure release condition. Then, the far-field sound pressure is predicted with shell's vibration response using the stationary phase method. Modal coupling effect arises due to the presence of the fluid free surface. New approaches are proposed to handle this problem, i.e., diagonal coupling acoustic radiation model (DCARM) and column coupling acoustic radiation model (CCARM). New approaches are proved to be able to deal with the modal coupling problem efficiently with a good accuracy at a significantly reduced computational cost. Numerical results also indicate that the sound radiation characteristics of a semisubmerged cylindrical shell are quite different from those from the shell fully submerged in fluid. But the far-field sound pressure of a semisubmerged shell fluctuates around that from the shell ideally submerged in fluid. These new approaches can also be used to study the vibroacoustic problems of cylindrical shells partially coupled with fluid.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;139(4):041003-041003-10. doi:10.1115/1.4036105.

A technique for generating reduced-order models (ROMs) of bladed disks with small geometric mistuning is proposed. Discrepancies in structural properties (mistuning) from blade to blade can cause a significant increase in the maximum vibratory stress. The effects of mistuning have been studied over the past few decades. Many researchers have studied the dynamic behavior of mistuned bladed disks by using ROMs. Many of these techniques rely on the fact that the modes of a mistuned system can be approximated by a linear combination of modes of the corresponding tuned system. In addition, the tuned system modes have been modeled in component mode mistuning by using modal participation factors of cantilevered blade modes. Such techniques assume that mistuning can be well modeled as variations in blade-alone frequencies. However, since geometric deformations contain stiffness and mass variations, mistuning can no longer be captured by cantilevered blade modes alone. To address this, several studies have focused on large and small geometric mistuning. These studies exploited the difference between tuned (with perturbed geometry) and nominal tuned mode shapes. In this work, we extend on that approach and devote particular attention to the development of ROMs of bladed disks with small geometric mistuning. The methodology requires only sector-level calculations and therefore can be applied to highly refined, realistic models of industrial size.

Topics: Disks , Blades , Modeling
Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;139(4):041004-041004-13. doi:10.1115/1.4036103.

In order to accurately study the effect of curvature on panel aeroelastic behaviors, a fluid–structure coupling algorithm is adopted to analyze the curved panel flutter in transonic and supersonic airflows. First, the governing equation for the motion of the curved panel and the structure solver are presented. Then, the fluid governing equations, the fluid solver, and the fluid–structure coupling algorithm are introduced briefly. Finally, rich aeroelastic responses of the curved panel are captured using this algorithm. And the mechanisms of them are explored by various analysis tools. It is found that the curvature produces initial aerodynamic loads above the panel. Thus, the static aeroelastic deformation exists for the curved panel in stable state. At Mach 2, with its stability lost on this static aeroelastic deformation, the curved panel shows asymmetric flutter. At Mach 0.8 and 0.9, the curved panel exhibits only positive static aeroelastic deformation due to this initial aerodynamic load. At Mach 1.0, as the dynamic pressure increases, the curved panel loses its static and dynamic stability in succession, and behaves as static aeroelastic deformations, divergences, and flutter consequentially. At Mach 1.2, with its stability lost, the curved panel flutters more violently toward the negative direction. The results obtained could guide the panel design and panel flutter suppression for flight vehicles with high performances.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;139(4):041005-041005-15. doi:10.1115/1.4036108.

This paper addresses a new method for estimating axial load in tie-rods using indirect measurements. This information is of great importance for assessing the health of the tie-rod itself and the health of the entire structure that the beam is inserted into. The method is based on dynamic measurements and requires the experimental estimation of the tie-rod eigenfrequencies and mode shapes at a limited number of points. Furthermore, the approach requires the development of a simple finite element model (FEM), which is then cross-correlated with the experimental data using a model update procedure. Extensive numerical simulations and experimental tests have demonstrated the ability of the new approach to yield accurate estimates of the tie-rod axial load and overcome various limitations of the methods currently available in the literature.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;139(4):041006-041006-14. doi:10.1115/1.4036213.

An approach is proposed to obtain the global analytical modes (GAMs) and establish discrete dynamic model with low degree-of-freedom for a three-axis attitude stabilized spacecraft installed with a pair of solar arrays. The flexible spacecraft is simplified as a hub–plate system which is a typical rigid-flexible coupling system. The governing equations of motion and the corresponding boundary conditions are derived by using the Hamiltonian principle. Describing the rigid motion and elastic vibration of all the system components with a uniform set of generalized coordinates, the system GAMs are solved from those dynamic equations and boundary conditions, which are used to discretize the equations of motion. For comparison, another discrete model is also derived using assumed mode method (AMM). Using ansys software, a finite element model is established to verify the GAM and AMM models. Subsequently, the system global modes are investigated using the GAM approach. Further, the performance of GAM model in dynamic analysis and cooperative control for attitude motion and solar panel vibration is assessed by comparing with AMM model. The discrete dynamic model based on GAMs has the capability to carry out spacecraft dynamic analysis in the same accuracy as a high-dimensional AMM model. The controller based on GAM model can suppress the oscillation of solar panels and make the control torque stable in much shorter time.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;139(4):041007-041007-13. doi:10.1115/1.4036277.

Component-centric reduced order models (ROMs) are introduced here as small-size ROMs providing an accurate prediction of the linear response of part of a structure (the β component) without focusing on the rest of it (the α component). Craig–Bampton (CB) substructuring methods are first considered. In one method, the β component response is modeled with its fixed interface modes while the other adopts singular value eigenvectors of the β component deflections of the linear modes of the entire structure. The deflections in the α component induced by harmonic motions of these β component modes are processed by a proper orthogonal decomposition (POD) to model the α component response. A third approach starts from the linear modes of the entire structure which are dominant in the β component response. Then, the contributions of other modes in this part of the structure are approximated in terms of those of the dominant modes with close natural frequencies and similar mode shapes in the β component, i.e., these nondominant modal contributions are “lumped” onto dominant ones. This lumping permits to increase the accuracy in the β component at a fixed number of modes. The three approaches are assessed on a structural finite element model of a nine-bay panel with the modal lumping-based method yielding the most “compact” ROMs. Finally, good robustness of the ROM to changes in the β component properties (e.g., for design optimization) is demonstrated and a similar sensitivity analysis is carried out with respect to the loading under which the ROM is constructed.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;139(4):041008-041008-13. 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 boundary element (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.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;139(4):041009-041009-13. doi:10.1115/1.4036211.

Passive control of vibrations in an elastic structure subjected to horizontal, harmonic excitation by utilizing a nearly square liquid tank is investigated. When the natural frequency ratio 1:1:1 is satisfied among the natural frequencies of the structure and the two predominant sloshing modes (1,0) and (0,1), the performance of a nearly square tank as a tuned liquid damper (TLD) is expected to be superior to rectangular TLDs due to internal resonance. In the theoretical analysis, Galerkin's method is used to determine the modal equations of motion for liquid sloshing considering the nonlinearity of sloshing. Then, van der Pol's method is used to obtain the expressions for the frequency response curves for the structure and sloshing modes. Frequency response curves and bifurcation set diagrams are shown to investigate the influences of the aspect ratio of the tank cross section and the tank installation angle on the system response. From the theoretical results, the optimal values of the system parameters can be determined in order to achieve maximum efficiency of vibration suppression for the structure. Hopf bifurcations occur and amplitude modulated motions (AMMs) may appear depending on the values of the system parameters. Experiments were also conducted, and the theoretical results agreed well with the experimental data.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;139(4):041010-041010-9. doi:10.1115/1.4036276.

The necessity of reducing CO2 emissions has lead to an increased number of passenger cars that utilize turbocharging to maintain performance when the internal combustion (IC) engines are downsized. Charge air coolers (CACs) are used on turbocharged engines to enhance the overall gas exchange efficiency. Cooling of charged air increases the air density and thus the volumetric efficiency and also increases the knock margin (for petrol engines). The acoustic properties of charge coolers have so far not been extensively treated in the literature. Since it is a large component with narrow flow passages, it includes major resistive as well as reactive properties. Therefore, it has the potential to largely affect the sound transmission in air intake systems and should be accurately considered in the gas exchange optimization process. In this paper, a frequency domain acoustic model of a CAC for a passenger car is presented. The cooler consists of two conical volumes connected by a matrix of narrow ducts where the cooling of the air takes place. A recently developed model for sound propagation in narrow ducts that takes into account the attenuation due to thermoviscous boundary layers and interaction with turbulence is combined with a multiport representation of the tanks to obtain an acoustic two-port representation where flow is considered. The predictions are compared with experimental data taken at room temperature and show good agreement. Sound transmission loss increasing from 5 to over 10 dB in the range 50–1600 Hz is demonstrated implying good noise control potential.

Commentary by Dr. Valentin Fuster

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