Showing papers in "Journal of Vibration and Acoustics in 2014"

Band Gap Control in an Active Elastic Metamaterial With Negative Capacitance Piezoelectric Shunting

Abstract: Elastic metamaterials have been extensively investigated due to their significant effects on controlling propagation of elastic waves. One of the most interesting properties is the generation of band gaps, in which subwavelength elastic waves cannot propagate through. In the study, a new class of active elastic metamaterials with negative capacitance piezoelectric shunting is presented. We first investigated dispersion curves and band gap control of an active mass-in-mass lattice system. The unit cell of the mass-in-mass lattice system consists of the inner masses connected by active linear springs to represent negative capacitance piezoelectric shunting. It was demonstrated that the band gaps can be actively controlled and tuned by varying effective stiffness constant of the linear spring through appropriately selecting the value of negative capacitance. The promising application was then demonstrated in the active elastic metamaterial plate integrated with the negative capacitance shunted piezoelectric patches for band gap control of both the longitudinal and bending waves. It can be found that the location and the extent of the induced band gap of the elastic metamaterial can be effectively tuned by using shunted piezoelectric patch with different values of negative capacitance, especially for extremely low-frequency cases.

Vibration Characteristics of Metamaterial Beams With Periodic Local Resonances

Abstract: Vibration characteristics of metamaterial beams manufactured of assemblies of periodic cells with built-in local resonances are presented. Each cell consists of a base structure provided with cavities filled by a viscoelastic membrane that supports a small mass to form a source of local resonance. This class of metamaterial structures exhibits unique band gap behavior extending to very low-frequency ranges. A finite element model (FEM) is developed to predict the modal, frequency response, and band gap characteristics of different configurations of the metamaterial beams. The model is exercised to demonstrate the band gap and mechanical filtering capabilities of this class of metamaterial beams. The predictions of the FEM are validated experimentally when the beams are subjected to excitations ranging between 10 and 5000 Hz. It is observed that there is excellent agreement between the theoretical predictions and the experimental results for plain beams, beams with cavities, and beams with cavities provided with local resonant sources. The obtained results emphasize the potential of the metamaterial beams for providing significant vibration attenuation and exhibiting band gaps extending to low frequencies. Such characteristics indicate that metamaterial beams are more effective in attenuating and filtering low-frequency structural vibrations than plain periodic beams of similar size and weight.

Experimental Investigation and Design Optimization of Targeted Energy Transfer Under Periodic Forcing

Abstract: In this paper, the dynamic response of a harmonically forced Linear Oscillator (LO) strongly coupled to a Nonlinear Energy Sink (NES) is investigated both theoretically and experimentally. The system studied comprises a LO with an embedded, purely cubic NES. The behavior of the system is analyzed in the vicinity of 1 : 1 resonance. The complexification-averaging technique is used to obtain modulation equations and the associated fixed points. These modulation equations are analyzed using asymptotic expansion to study the regimes related to relaxation oscillation of the slow flow called Strongly Modulated Response (SMR). The zones where SMR occurs are computed using a mapping procedure. The Slow Invariant Manifolds (SIM) is used to derive a proper optimization procedure. It is shown that there is an optimal zone in the forcing amplitude-nonlinear stiffness parameter plane, where SMR occurs without having a high amplitude detached resonance tongue. Two experimental setups are presented. One is not optimized and has a relatively high mass ratio (≈ 13%) and the other one is optimized and exhibits strong mass asymmetry (mass ratio ≈ 1%). Different frequency response curves and associated zones of SMR are obtained for various forcing amplitudes. The reported experimental results confirm the design procedure, and the possible application of NES for vibration mitigation under periodic forcing.

The Power and Efficiency Limits of Piezoelectric Energy Harvesting

Abstract: The fundamental limits of cantilevered piezoelectric energy harvesters have not been well established. As with any other power generation technology, it is critical to establish the limits of power output and efficiency. Mathematical models for piezoelectric energy harvester power output have seen continued refinement, but these models have mainly been used and compared to individual harvester designs. Moreover, existing models all assume power scales with acceleration input, and take no account for the upper limit of the acceleration due to the ultimate strength of the piezoelectric material. Additionally, models for efficiency have been developed, but the limits have not been thoroughly explored. In this paper, we present the upper limits of input acceleration and output power for a piezoelectric harvester device. We then use these expressions, along with a previously developed ideal design method, to explore the upper limits of power production across a range of system masses and excitation frequencies. We also investigate general efficiency limits of these devices. We show the upper limit using an existing model and develop an alternate model that is applicable to excitation sources that are not capable of energy recovery.

On the Performance of a Two-Stage Vibration Isolation System Which has Geometrically Nonlinear Stiffness

Abstract: Linear single-stage vibration isolation systems have a limitation on their performance, which can be overcome passively by using linear two-stage isolations systems. It has been demonstrated by several researchers that linear single-stage isolation systems can be improved upon by using nonlinear stiffness elements, especially for low-frequency vibrations. In this paper, an investigation is conducted into whether the same improvements can be made to a linear two-stage isolation system using the same methodology for both force and base excitation. The benefits of incorporating geometric stiffness nonlinearity in both upper and lower stages are studied. It is found that there are beneficial effects of using nonlinearity in the stiffness in both stages for both types of excitation. Further, it is found that this nonlinearity causes the transmissibility at the lower resonance frequency to bend to the right, but the transmissibility at the higher resonance frequency is not affected in the same way. Generally, it is found that a nonlinear two-stage system has superior isolation performance compared to that of a linear two-stage isolator.

Detecting Loosening of Bolted Connections in a Pipeline Using Changes in Natural Frequencies

Abstract: Loosening of bolted connections in a structure can significantly reduce the load-bearing capacities of the structure. Detecting loosening of bolted connections at an early stage can avoid failure of the structure. Due to the complex geometry of a bolted connection and the material discontinuity between the clamped components, it is difficult to detect loosening of a bolted connection using conventional non-destructive test methods. A vibration-based method that uses changes in natural frequencies of a structure to detect the locations and extent of damage can be used to detect loosening of bolted connections, since the method focuses on detecting a stiffness reduction, which can result from loosening of the bolted connections. Experimental and numerical damage detection using the vibration-based method was conducted to detect the loosening of the bolted connections in a fullsize steel pipeline with bolted flanges. With the recent development of a predictive modeling technique for bolted connections in thin-walled structures, an accurate physics-based finite element model of the pipeline that is required by the vibration-based damage detection method is developed. A trust-region search strategy is employed to improve the damage detection method so that convergence of the damage detection algorithm can be ensured for under-determined systems, and the robustness of the algorithm can be enhanced when relatively large modeling error and measurement noise are present. The location and extent of the loosened bolted connections were successfully detected in experimental damage detection using changes in the natural frequencies of the first several modes; the exact location and extent of the loosened bolted connections can be detected in the numerical simulation where there are no modeling error and measurement noise.Copyright © 2011 by ASME

Comparison of Poroviscoelastic Models for Sound and Vibration in the Lungs

Abstract: Noninvasive measurement of mechanical wave motion (sound and vibration) in the lungs may be of diagnostic value, as it can provide information about the mechanical properties of the lungs, which in turn are affected by disease and injury. In this study, two previously derived theoretical models of the vibroacoustic behavior of the lung parenchyma are compared: (1) a Biot theory of poroviscoelasticity and (2) an effective medium theory for compression wave behavior (also known as a "bubble swarm" model). A fractional derivative formulation of shear viscoelasticity is integrated into both models. A measurable "fast" compression wave speed predicted by the Biot theory formulation has a significant frequency dependence that is not predicted by the effective medium theory. Biot theory also predicts a slow compression wave. The experimentally measured fast compression wave speed and attenuation in a pig lung ex vivo model agreed well with the Biot theory. To obtain the parameters for the Biot theory prediction, the following experiments were undertaken: quasistatic mechanical indentation measurements were performed to estimate the lung static shear modulus; surface wave measurements were performed to estimate lung tissue shear viscoelasticity; and flow permeability was measured on dried lung specimens. This study suggests that the Biot theory may provide a more robust and accurate model than the effective medium theory for wave propagation in the lungs over a wider frequency range.

Cauchy and Signaling Problems for the Time-Fractional Diffusion-Wave Equation

Abstract: In this paper, some known and novel properties of the Cauchy and signaling problems for the one-dimensional time-fractional diffusion-wave equation with the Caputo fractional derivative of order b;1 � b � 2 are investigated. In particular, their response to a localized disturbance of the initial data is studied. It is known that, whereas the diffusion equation describes a process where the disturbance spreads infinitely fast, the propagation velocity of the disturbance is a constant for the wave equation. We show that the time-fractional diffusion-wave equation interpolates between these two different responses in the sense that the propagation velocities of the maximum points, centers of gravity, and medians of the fundamental solutions to both the Cauchy and the signaling problems are all finite. On the other hand, the disturbance spreads infinitely fast and the time-fractional diffusion-wave equation is nonrelativistic like the classical diffusion equation. In this paper, the maximum locations, the centers of gravity, and the medians of the fundamental solution to the Cauchy and signaling problems and their propagation velocities are described analytically and calculated numerically. The obtained results for the Cauchy and the signaling problems are interpreted and compared to each other. [DOI: 10.1115/1.4026892]

Prospects for Nonlinear Energy Harvesting Systems Designed Near the Elastic Stability Limit When Driven by Colored Noise

Abstract: Ambient vibration sources in many prime energy harvesting applications are characterized as having stochastic response with spectra concentrated at low frequencies and steadily reduced power density as frequency increases (colored noise). To overcome challenges in designing linear resonant systems for such inputs, nonlinear restoring potential shaping has become a popular means of extending a harvester’s bandwidth downward towards the highest concentration of excitation energy available. Due to recent works which have individually probed by analysis, simulation, or experiment the opportunity for harvester restoring potential shaping near the elastic stability limit (buckling transition) to improve power generation in stochastic environments—in most cases focusing on postbuckled designs and in some cases arriving at conflicting conclusions— we seek to provide a consolidated and insightful investigation for energy harvester performance employing designs in this critical regime. Practical aspects drive the study and encourage evaluation of the role of asymmetries in restoring potential forms. New analytical, numerical, and experimental investigations are conducted and compared to rigorously assess the opportunities and reach well-informed conclusions. Weakly bistable systems are shown to potentially provide minor performance benefits but necessitate a priori knowledge of the excitation environment and careful avoidance of asymmetries. It is found that a system designed as close to the elastic stability limit as possible, without passing the buckling transition, may be the wiser solution to energy harvesting in colored noise environments. [DOI: 10.1115/1.4026212]

A Disturbance Cancellation Perspective on Vibration Control Using a Bistable Snap-Through Attachment

Abstract: One approach to vibration control is to apply a force to a primary structure that opposes the excitation, effectively canceling the external disturbance. A familiar passive example of this approach is the linear-tuned mass absorber. In this spirit, the utility of a bistable attachment for attenuating vibrations, especially in terms of the high-orbit, snap-through dynamic, is investigated using the harmonic balance method and experiments. Analyses demonstrate the fundamental harmonic snap-through dynamic, having commensurate frequency with the single-frequency harmonic excitation, may generate adverse constructive forces that substantially reinforce the applied excitation, primarily at lower frequencies. However, both analyses and experiments indicate that such high-orbit dynamics may be largely destabilized by increased bistable attachment damping. Destructive forces, which substantially oppose the excitation, are unique in that they lead to a form of vibration attenuation analogous to strictly adding damping to the host structure, leaving its spectral characteristics largely unaltered. The experiments verify the analytical findings and also uncover nonlinear dynamics not predicted by the analysis, which render similar attenuation effects.

Free Vibration of a Multilayered One-Dimensional Quasi-Crystal Plate

Abstract: An exact closed-form solution of free vibration of a simply supported and multilayered one-dimensional (1D) quasi-crystal (QC) plate is derived using the pseudo-Stroh formulation and propagator matrix method. Natural frequencies and mode shapes are presented for a homogenous QC plate, a homogenous crystal plate, and two sandwich plates made of crystals and QCs. The natural frequencies and the corresponding mode shapes of the plates show the influence of stacking sequence on multilayered plates and the different roles phonon and phason modes play in dynamic analysis of QCs. This work could be employed to further expand the applications of QCs especially if used as composite materials.

Multiphysics Investigations on the Dynamics of Differential Hypoid Gears

Abstract: Vehicular differential hypoid gears play an important role on the noise, vibration, and harshness (NVH) signature of the drivetrain system. Additionally, the generated friction between their mating teeth flanks under varying load-speed conditions is a source of power loss in a drivetrain while absorbing some of the vibration energy. This paper deals with the coupling between system dynamics and analytical tribology in multiphysics, multiscale analysis. Elastohydrodynamic lubrication (EHL) of elliptical point contact of partially conforming hypoid gear teeth pairs with non-Newtonian thermal shear of a thin lubricant film is considered, including boundary friction as the result of asperity interactions on the contiguous surfaces. Tooth contact analysis (TCA) has been used to obtain the input data required for such an analysis. The dynamic behavior and frictional losses of a differential hypoid gear pair under realistic operating conditions are therefore determined. The detailed analysis shows a strong link between NVH refinement and transmission efficiency, a finding not hitherto reported in literature.

Performance Degradation Assessment for Bearing Based on Ensemble Empirical Mode Decomposition and Gaussian Mixture Model

Abstract: This paper proposes a novel performance degradation assessment method for bearing based on ensemble empirical mode decomposition (EEMD), and Gaussian mixture model (GMM). EEMD is applied to preprocess the nonstationary vibration signals and get the feature space. GMM is utilized to approximate the density distribution of the lower-dimensional feature space processed by principal component analysis (PCA). The confidence value (CV) is calculated based on the overlap between the distribution of the baseline feature space and that of the testing feature space to indicate the performance of the bearing. The experiment results demonstrate the effectiveness of the proposed method.

Experimental and Numerical Studies on Spherical Roller Bearings Using Multivariable Regression Analysis

Abstract: Many industries make wide use of rotor bearing systems such as high speed turbines and generators. However, the vibration of antifriction rotor–bearings is a key factor in reducing the life of the bearings; thus significantly influencing the performance and working life of the whole power plant. In earlier research on the vibration characteristics of high speed rotor–bearing systems, such as in induced draft (ID) fans, an application used in sugar cane factories, the supporting antifriction bearings were simplified as a particle on a shaft with radial stiffness and damping coefficient. However, such simplification neglects the effects of the bearing structure on the vibration performance of the rotor–bearing system. This paper demonstrates the benefits of a more holistic approach and establishes a numerical model of the stiffness of the spherical roller bearing through Buckingham's π theorem (BPT). On the basis of this model, we argue for the benefits of a new dimensional analysis (DA) technique for rotor–bearing systems. Our new DA also considers the influences of the bearing structure parameters on the vibration of rotor–bearing systems. We demonstrate the effectiveness of our approach by conducting a comparative BPT study using an ID fan, a rotor–bearing system in use in sugar cane factories. We first analyzed an ID fan using the simplified model to obtain the defect frequencies and vibration amplitude responses of the ID fan system. Subsequently the same ID fan rotor was also analyzed using our new multivariable regression analysis (MVRA) approach to verify the validity of our new and holistic BPT. The results indicate that the new method we propose in this paper for the calculation of vibration characteristics of a high speed rotor–bearing (ID fan) is credible and will save time and costs by the accurate detection of imminent bearing failure.

Analysis and Interpretation of Longitudinal Waves in Periodic Multiphase Rods Using the Method of Reverberation-Ray Matrix Combined With the Floquet-Bloch Theorem

Abstract: The method of reverberation-ray matrix (MRRM) combined with the Floquet-Bloch theorem, which serves as an alternative method, is presented for accurately analyzing longitudinal waves in general periodic multiphase rods. Closed-form dispersion relation of periodic quaternary rods is derived. Based on this relation, the functions of constituent-rod parameters in the formation of longitudinal-wave band structures are analytically revealed. Numerical examples validate the proposed method and indicate the characteristics/applications of all kinds of dispersion curves that include the frequency-wave number spectra, the frequency-wavelength spectra, the frequency-phase velocity spectra, the wave number-phase velocity spectra and the wavelength-phase velocity spectra. The effect of unit-cell layout on the frequency band properties and the functions of constituent-rod parameters in the band structure formation are also illustrated numerically. The analysis and interpretation of longitudinal waves in periodic multiphase rods given in this paper will push forward the design of periodic structures for longitudinal wave filtering/guiding and vibration isolation/control applications.

Tilting-Pad Journal Bearings With Active Lubrication Applied as Calibrated Shakers: Theory and Experiment

Abstract: In recent years, a continuous research effort has transformed the conventional tilting-pad journal bearing into a mechatronic machine element. The addition of electromechanical elements provides the possibility of generating controllable forces over the rotor as a function of a suitable control signal. Such forces can be applied in order to perform parameter identification procedures in-situ, which enables evaluation of the mechanical condition of the machine in a non-invasive way. The usage of a controllable bearing as a calibrated shaker requires obtaining the bearing specific frequency dependent calibration function, i.e. the transfer function between control signal and force over the rotor. This work presents a theoretical model of the calibration function for a tilting-pad journal bearing with active lubrication. The bearing generates controllable forces by injecting pressurized oil directly into the bearing clearance. The injected flow is controlled by means of a servovalve. The theoretical model includes the dynamics of the hydraulic system using a lumped parameter approach, which is coupled with the bearing oil film using a modified form of the Reynolds equation. The oil film model is formulated considering an elastothermohydrodynamic lubrication regime. New contributions to the mathematical modeling are presented, such as the inclusion ∗Address all correspondence to this author. Journal of Vibration and Acoustics. Received November 19, 2013; Accepted manuscript posted September 01, 2014. doi:10.1115/1.4028452 Copyright (c) 2014 by ASME Downloaded From: http://vibrationacoustics.asmedigitalcollection.asme.org/ on 09/01/2014 Terms of Use: http://asme.org/terms Ac ce pt ed M an us cr ip t N ot C op ye di te d of the dynamics of the hydraulic pipelines, and the obtention of the bearing calibration function by means of harmonic analysis of a linearized form of the controllable bearing constitutive equations. The mathematical model is used to study the relevance and effects of different parameters on the calibration function, aiming at providing general guidelines for the active bearing design. Finally, experimental results regarding the calibration function and the usage of the studied bearing as a calibrated shaker provide insight into the possibilities of application of

Wave Characteristics of Two-Dimensional Hierarchical Hexagonal Lattice Structures

Abstract: Hierarchical structures are structures that themselves contain structural elements. Hier-archical lattice structures are counterparts of the traditional lattice structures, whosewalls are replaced by some kind of structure. In this paper, wave propagation in two-dimensional hierarchical hexagonal lattice structures is calculated by the finite elementmethod with the Bloch theory. Attention is devoted to the comparison of the band gap,wave mode, dispersion surface, and phase and group velocities between the second-orderhierarchical hexagonal lattice structures and their first-order traditional counterpart.The results show that the former structures have more band gaps and similar isotropicwave behavior in the low frequency compared to the latter structure. The structure hier-archy is favorable for the periodic lattice structure to filtering or guiding wave at somecircumstances to meet the demands of engineering. [DOI: 10.1115/1.4025550]Keywords: Bloch theory, band gap, finite element method, hierarchical lattice structure

Characterization of variable hydrodynamic coefficients and maximum responses in two-dimensional vortex-induced vibrations with dual resonances

Abstract: A phenomenological model and analytical-numerical approach to systematically characterize variable hydrodynamic coefficients and maximum achievable responses in two-dimensional vortex-induced vibrations with dual two-to-one resonances are presented. The model is based on double Duffing and van der Pol oscillators which simulate a flexibly-mounted circular cylinder subjected to uniform flow and oscillating in simultaneous cross-flow/in-line directions. Depending on system quadratic and cubic nonlinearities, amplitudes, oscillation frequencies and phase relationships, analytical closed-form expressions are derived to parametrically evaluate key hydrodynamic coefficients governing the fluid excitation, inertia and added mass force components, as well as maximum dual-resonant responses. The amplification of the mean drag is ascertained. Qualitative validations of numerical predictions with experimental comparisons are discussed. Parametric investigations are performed to highlight the important effects of system nonlinearities, mass, damping and natural frequency ratios.

Piezoelectric Shunt Vibration Damping of Structural-Acoustic Systems: Finite Element Formulation and Reduced-Order Model

Abstract: For noise and vibration attenuation, various approaches can be employed depending on the frequency range to attenuate. Generally, active or passive piezoelectric techniques are effective in the low-frequency range, while dissipative materials, such as viscoelastic or porous treatments, are efficient for higher-frequency domain. In this work, a reducedorder model is developed for the approximation of a fully coupled electromechanicalacoustic system using modal projection techniques. The problem consists of an elastic structure with surface-mounted piezoelectric patches coupled with a compressible inviscid fluid. The piezoelectric elements, connected with resonant shunt circuits, are used for the vibration damping of the coupled system. Numerical examples are presented in order to illustrate the accuracy and the versatility of the proposed reduced-order model, especially in terms of prediction of attenuation. Copyright