Showing papers in "Journal of Vibration and Acoustics in 2013"

Energy Harvesting, Ride Comfort, and Road Handling of Regenerative Vehicle Suspensions

Abstract: This paper presents a comprehensive assessment of the power that is available for harvesting in the vehicle suspension system and the tradeoff among energy harvesting, ride comfort, and road handing with analysis, simulations, and experiments. The excitation from road irregularity is modeled as a stationary random process with road roughness suggested in the ISO standard. The concept of system H2 norm is used to obtain the mean value of power generation and the root mean square values of vehicle body acceleration (ride quality) and dynamic tire-ground contact force (road handling). For a quarter car model, an analytical solution of the mean power is obtained. The influence of road roughness, vehicle speed, suspension stiffness, shock absorber damping, tire stiffness, and the wheel and chasses masses to the vehicle performances and harvestable power are studied. Experiments are carried out to verify the theoretical analysis. The results suggest that road roughness, tire stiffness, and vehicle driving speed have great influence on the harvesting power potential, where the suspension stiffness, absorber damping, and vehicle masses are insensitive. At 60 mph on good and average roads, 100–400 W average power is available in the suspensions of a middle-sized vehicle.

Theoretical and Experimental Study of Locally Resonant and Bragg Band Gaps in Flexural Beams Carrying Periodic Arrays of Beam-Like Resonators

Abstract: In this paper, we present a design of locally resonant (LR) beams using periodic arrays of beam-like resonators (or beam-like vibration absorbers) attached to a thin homogeneous beam. The main purpose of this work is twofold: (i) providing a theoretical characterization of the proposed LR beams, including the band gap behavior of infinite systems and the vibration transmittance of finite structures, and (ii) providing experimental evidence of the associated band gap properties, especially the coexistence of LR and Bragg band gaps, and their evolution with tuned local resonance. For the first purpose, an analytical method based on the spectral element formulations is presented, and then an in-depth numerical study is performed to examine the band gap effects. In particular, explicit formulas are provided to enable an exact calculation of band gaps and an approximate prediction of band gap edges. For the second purpose, we fabricate several LR beam specimens by mounting 16 equally spaced resonators onto a free-free host beam. These specimens use the same host beam, but the resonance frequencies of the resonators on each beam are different. We further measure the vibration transmittances of these specimens, which give evidence of three interesting band gap phenomena: (i) transition between LR and Bragg band gaps; (ii) near-coupling effect of the local resonance and Bragg scattering; and (iii) resonance frequency of local resonators outside of the LR band gap. [DOI: 10.1115/1.4024214]

Measurements of Piezoelectric Coefficient d33 of Lead Zirconate Titanate Thin Films Using a Mini Force Hammer

Abstract: Lead zirconate titanate (PbZrxTi1-xO3, or PZT) is a piezoelectric material widely used as sensors and actuators. For microactuators, PZT often appears in the form of thin films to maintain proper aspect ratios. One major challenge encountered is accurate measurement of piezoelectric coefficients of PZT thin films. In this paper, we present a simple, low-cost, and effective method to measure piezoelectric coefficient d33 of PZT thin films through use of basic principles in mechanics of vibration. A small impact hammer with a tiny tip acts perpendicularly to the PZT thin-film surface to generate an impulsive force. In the meantime, a load cell at the hammer tip measures the impulsive force and a charge amplifier measures the responding charge of the PZT thin film. Then the piezoelectric coefficient d33 is obtained from the measured force and charge based on piezoelectricity and a finite element modeling. We also conduct a thorough parametric study to understand the sensitivity of this method on various parameters, such as substrate material, boundary conditions, specimen size, specimen thickness, thickness ratio, and PZT thin-film material. Two rounds of experiments are conducted to demonstrate the feasibility and accuracy of this new method. The first experiment is to measure d33 of a PZT disk resonator whose d33 is known. Experimental results show that d33 measured via this method is as accurate as that from the manufacturer's specifications within its tolerance. The second experiment is to measure d33 of PZT thin films deposited on silicon substrates. With the measured d33, we predict the displacement of PZT thin-film membrane microactuators. In the meantime, the actuator displacement is measured via a laser Doppler vibrometer. The predicted and measured displacements agree very well validating the accuracy of this new method.

Dual-Functional Energy-Harvesting and Vibration Control: Electromagnetic Resonant Shunt Series Tuned Mass Dampers.

Abstract: This paper proposes a novel retrofittable approach for dual-functional energy-harvesting and robust vibration control by integrating the tuned mass damper (TMD) and electromagnetic shunted resonant damping. The viscous dissipative element between the TMD and primary system is replaced by an electromagnetic transducer shunted with a resonant RLC circuit. An efficient gradient based numeric method is presented for the parameter optimization in the control framework for vibration suppression and energy harvesting. A case study is performed based on the Taipei 101 TMD. It is found that by tuning the TMD resonance and circuit resonance close to that of the primary structure, the electromagnetic resonant-shunt TMD achieves the enhanced effectiveness and robustness of double-mass series TMDs, without suffering from the significantly amplified motion stroke. It is also observed that the parameters and performances optimized for vibration suppression are close to those optimized for energy harvesting, and the performance is not sensitive to the resistance of the charging circuit or electrical load.

Dynamic Features of a Planetary Gear System With Tooth Crack Under Different Sizes and Inclination Angles

Abstract: Planetary gears are widely used in the industry due to their advantages of compactness, high power-to-weight ratios, high efficiency, and so on However, planetary gears such as that in wind turbine transmissions always operate under dynamic conditions with internal and external load fluctuations, which accelerate the occurrence of gear failures, such as tooth crack, pitting, spalling, wear, scoring, scuffing, etc As one of these failure modes, gear tooth crack at the tooth root due to tooth bending fatigue or excessive load is investigated; how it influences the dynamic features of planetary gear system is studied The applied tooth root crack model can simulate the propagation process of the crack along tooth width and crack depth With this approach, the mesh stiffness of gear pairs in mesh is obtained and incorporated into a planetary gear dynamic model to investigate the effects of the tooth root crack on the planetary gear dynamic responses Tooth root cracks on the sun gear and on the planet gear are considered, respectively, with different crack sizes and inclination angles Finally, analysis regarding the influence of tooth root crack on the dynamic responses of the planetary gear system is performed in time and frequency domains, respectively Moreover, the differences in the dynamic features of the planetary gear between the cases that tooth root crack on the sun gear and on the planet gear are found

An Accurate Spatial Discretization and Substructure Method With Application to Moving Elevator Cable-Car Systems—Part I: Methodology

Abstract: A spatial discretization and substructure method is developed to accurately calculate dynamic responses of one-dimensional structural systems, which consist of length-variant distributed-parameter components, such as strings, rods, and beams, and lumped-parameter components, such as point masses and rigid bodies. The dependent variable of a distributed-parameter component is decomposed into boundary-induced terms and internal terms. The boundary-induced terms are interpolated from boundary motions, and the internal terms are approximated by an expansion of trial functions that satisfy the corresponding homogeneous boundary conditions. All the matching conditions at the interfaces of the components are satisfied, and the expansions of the dependent variables of the distributed-parameter components absolutely and uniformly converge if the dependent variables are smooth enough. Spatial derivatives of the dependent variables, which are related to internal forces/moments of the distributed-parameter components, such as axial forces, bending moments, and shear forces, can be accurately calculated. Combining component equations that are derived from Lagrange's equations and geometric matching conditions that arise from continuity relations leads to a system of differential algebraic equations (DAEs). When the geometric matching conditions are linear, the DAEs can be transformed to a system of ordinary differential equations (ODEs), which can be solved by an ODE solver. The methodology is applied to several moving elevator cable-car systems in Part II of this work.

Kirigami auxetic pyramidal core: Mechanical properties and wave propagation analysis in damped lattice

Abstract: The work describes the manufacturing, mechanical properties, and wave propagation characteristics of a pyramidal lattice made exhibiting an auxetic (negative Poisson's ratio) behavior. Contrary to similar lattice tessellations produced using metal cores, the pyramidal lattice described in this work is manufactured using a kirigami (origami pluscutting pattern) technique, which can be applied to a large variety of thermoset and thermoplastic composites. Due to the particular geometry created through this manufacturing technique, the kirigami pyramidal lattice shows an inversion between in-plane and out-of-plane mechanical properties compared to classical honeycomb configurations. Long wavelength approximations are used to calculate the slowness curves, showing unusual zero-curvature phononic properties in the transverse plane. A novel 2D wave propagation technique based on Bloch waves for damped structures is also applied to evaluate the dispersion behavior of composite (Kevlar/epoxy) lattices with intrinsic hysteretic loss. The 2D wave propagation analysis shows evanescence directivity at different frequency bandwidths and complex modal behavior due to unusual deformation mechanism of the lattice.

Active Acoustic Metamaterial With Simultaneously Programmable Density and Bulk Modulus

Abstract: Acoustic metamaterials are those structurally engineered materials that are composed of periodic cells designed in such a fashion to yield specific material properties (density and bulk modulus) that would affect the wave propagation pattern within in a specific way. All the currently exerted efforts are focused on studying passive metamaterials with fixed material properties. In this paper, the emphasis is placed on the development of a new class of composite one-dimensional active acoustic metamaterials (CAAMM) with effective densities and bulk moduli that are programmed to vary according to any prescribed patterns along its volume. A cylindrical water-filled cylinder coupled to two piezoelectric elements form a composite cell to act as a base unit for a periodic metamaterial structure. Two different configurations are considered. In the first configuration, a piezoelectric panel is flash-mounted to the face of the cylinder, while the other is side-mounted to the cylinder wall, introducing a variable stiffness along the wave propagation path. In the second configuration, the face-mounted piezoelectric panel remains unchanged, while the side-mounted panel is replaced with an active Helmholtz resonator with piezoelectric base panel. A detailed theoretical lumped-parameter model for the two configurations is present, from which the stiffness of both active elements is controlled via charge feedback control to yield arbitrary homogenized effective bulk modulus and density over a very wide frequency range. Numerical examples are presented to demonstrate the performance characteristics of the proposed. The CAAMM presents a viable approach to the development of effective domains with a controllable wave propagation pattern to suit many applications.

Gas-Filled Encapsulated Thermal-Acoustic Transducer

Abstract: A new model for a gas-filled encapsulated thermal-acoustic transducer, which uses newly devised carbon nanotube (CNT) thin film is developed and the exact and approximate solutions are derived. A comparison between theoretical prediction and experimental data is presented and excellent agreement is reported. The frequency response for this acoustic transducer is investigated and the acoustic response of as a function of window–thin-film distance of the encapsulated transducer is discussed. An optimal distance between window and thin film is successfully derived and used in some practical examples. Resonance takes place for a suitable input frequency, and thus such transducers can be used to either generate acoustic waves of specific frequency or to filter specific resonant frequencies from a wide spectrum of signals. This kind of transducer can be immersed in different liquid media. A gaseous medium shows better performance at lower frequency while it is otherwise for a liquid medium. The conclusions derived in this work could be regarded as effective guidelines and information for enhancing thermal-acoustics efficiency conversion, as well as for the optimal design of a thermal-acoustic transducer.

Phononic Band Gap Systems in Structural Mechanics: Finite Slender Elastic Structures and Infinite Periodic Waveguides

Abstract: The paper presents a novel spectral approach, accompanied by an asymptotic model and numerical simulations for slender elastic systems such as long bridges or tall buildings. The focus is on asymptotic approximations of solutions by Bloch waves, which may propagate in a infinite periodic waveguide. Although the notion of passive mass dampers is conventional in the engineering literature, it is not obvious that an infinite waveguide problem is adequate for analysis of long but finite slender elastic systems. The formal mathematical treatment of a Bloch wave would reduce to a spectral analysis of equations of motion on an elementary cell of a periodic structure, with Bloch–Floquet quasi-periodicity conditions imposed on the boundary of the cell. Frequencies of some classes of standing waves can be estimated analytically. One of the applications discussed in the paper is the “dancing bridge” across the river Volga in Volgograd.

Tuning of Acoustic Bandgaps in Phononic Crystals With Helmholtz Resonators

Abstract: In this paper, acoustic wave propagation in a two- or three-dimensional phononic crystal consisting of Helmholtz resonators embedded in a fluid matrix is studied. The band structures are calculated to discuss the influence of the geometry topology of Helmholtz resonators on the bandgap characteristics. It is shown that a narrow bandgap will appear in the lower frequency range due to the resonance of the Helmholtz resonators. The width and position of this resonance bandgap can be tuned by adjusting the geometrical parameters of the Helmholtz resonator. The position of the resonance bandgap can be evaluated by the resonance frequency of the Helmholtz resonator. A decrease in the size of the opening generally results in a lower position and a smaller width of the bandgap. The system with one opening exhibits a wider bandgap in a lower position than the system with two openings.

Zero-Energy Active Suspension System for Automobiles With Adaptive Sky-Hook Damping

Abstract: Previous research has shown that a semiactive automotive suspension system can provide significant benefits compared to a passive suspension but cannot quite match the performance of a fully active system. The advantage of the semiactive system over an active system is that it consumes almost zero energy by utilizing a variable damper whose damping coefficient is changed in real time, while a fully active suspension consumes significant power for its operation. This paper explores a new zero-energy active suspension system that combines the advantages of semiactive and active suspensions by providing the performance of the active system at zero energy cost. Unlike a semiactive system in which the energy is always dissipated, the proposed system harvests and recycles energy to achieve active operation. An electrical motor-generator is used as the zero-energy actuator and a controller and energy management system are developed. An energy adaptive sky-hook gain is proposed to prevent the system from running out of energy, thereby eliminating the need to switch between passive and active systems. The results show that the system performs at least as well as a passive system for all frequencies, and is equivalent to an active system for a broad range of frequencies including both resonant frequencies.

Detection of Damage in Space Frame Structures With L-Shaped Beams and Bolted Joints Using Changes in Natural Frequencies

Abstract: It is difficult to use conventional non-destructive testing methods to detect damage, such as loosening of bolted connections, in a space frame structure due to the complexity of the structure and the nature of the possible damage. A vibration-based method that uses changes in the natural frequencies of a structure to detect the locations and extent of damage in it has the advantage of being able to detect various types of damage in the structure. Since the vibration-based method is model-based, applying it to a space frame structure with L-shaped beams and bolted joints will face challenges ranging from the development of accurate dynamic models for the structures to that of a robust damage detection algorithm for severely under-determined, nonlinear least-square problems under the effects of relatively large modeling error and measurement noise.With the development of the modeling techniques for fillets in thin-walled beams (He and Zhu, 2009, “Modeling of Fillets in Thin-Walled Beams Using Shell/Plate and Beam Finite Elements,” ASME J. Vibr. Acoust., 131(5), p. 051002) and bolted joints (He and Zhu, “Finite Element Modeling of Structures with L-shaped Beams and Bolted Joints,” ASME J. Vibr. Acoust., in press) by the authors, accurate physics-based models of space frame structures can be developed with a reasonable model size. A new damage detection algorithm that uses a trust-region search strategy combined with a logistic function transformation is developed to improve the robustness of the vibration-based damage detection method. The new algorithm can ensure global convergence of the iterations and minimize the effects of modeling error and measurement noise. The damage detection method developed is experimentally validated on an aluminum three-bay space frame structure with L-shaped beams and bolted joints. Three types of introduced damage, including joint damage, member damage, and boundary damage, were successfully detected. In the numerical simulation where there is no modeling error and measurement noise, the almost exact locations and extent of damage can be detected.

Characterization of Dynamic Response of Structures With Uncertainty by Using Gaussian Processes

Abstract: Characterizing dynamic characteristics of structures with uncertainty is an important task that provides critical predictive information for structural design, assessment, and control. In practical applications, sampling is the fundamental approach to uncertainty analysis but has to be conducted under various constraints. To address the frequently encountered data scarcity issue, in the present paper Gaussian processes are employed to predict and quantify structural dynamic responses, especially responses under uncertainty. A self-contained description of Gaussian processes is presented within the Bayesian framework with implementation details, and then a series of case studies are carried out using a cyclically symmetric structure that is highly sensitive to uncertainties. Structural frequency responses are predicted with data sparsely sampled within the full frequency range. Based on the inferred credible intervals, a measure is defined to quantify the potential risk of response maxima. Gaussian process emulation is proposed for Monte Carlo uncertainty analysis to reduce data acquisition costs. It is shown that Gaussian processes can be an efficient data-based tool for analyzing structural dynamic responses in the presence of uncertainty. Meanwhile, some technical challenges in the implementation of Gaussian processes are discussed.

Flexoelectric Responses of Circular Rings

Abstract: Dynamic sensing is essential to effective closed-loop control of precision structures. In a centrosymmetric crystal subjected to inhomogeneous deformation, when piezoelectricity is absent, only the strain gradient contributes to the polarization known as the “flexoelectricity.” In this study, a flexoelectric layer is laminated on a circular ring shell to monitor the natural modal signal distributions. Due to the strain gradient characteristic, only the bending strain component contributes to the output signal. The total flexoelectric signal consists of two components respectively induced by the transverse modal oscillation and the circumferential modal oscillation. Analog to the signal analysis, the flexoelectric sensitivity is also studied in two forms: a transverse sensitivity induced by the transverse modal oscillation and a transverse sensitivity induced by the circumferential modal oscillation. Analysis data suggest that the transverse modal oscillation dominates the flexoelectric signal generation and its magnitude/distribution shows nearly the same as the total signal. Furthermore, voltage signals and signal sensitivities are evaluated with respect to ring mode, sensor segment size, ring thickness, and ring radius in case studies. The total signal increases with mode numbers and sensor thicknesses, decreases with sensor segment size and ring radii, and remains the same with different ring thicknesses.

Torsional Vibration Analysis of Carbon Nanotubes Based on the Strain Gradient Theory and Molecular Dynamic Simulations

Abstract: In the current study, the torsional vibration of carbon nanotubes is examined using the strain gradient theory and molecular dynamic simulations. The model developed based on this gradient theory enables us to interpret size effect through introducing material length scale parameters. The model accommodates the modified couple stress and classical models when two or all material length scale parameters are set to zero, respectively. Using Hamilton's principle, the governing equation and higher-order boundary conditions of carbon nanotubes are obtained. The generalized differential quadrature method is utilized to discretize the governing differential equation of the present model along with two boundary conditions. Then, molecular dynamic simulations are performed for a series of carbon nanotubes with different aspect ratios and boundary conditions, the results of which are matched with those of the present strain gradient model to extract the appropriate value of the length scale parameter. It is found that the present model with properly calibrated value of length scale parameter has a good capability to predict the torsional vibration behavior of carbon nanotubes.

Natural Frequency Clusters in Planetary Gear Vibration

Abstract: This paper investigates how the natural frequencies of planetary gears tend to gather into clusters (or groups) This behavior is observed experimentally and analyzed in further detail by numerical analysis There are three natural frequency clusters at relatively high frequencies The modes at these natural frequencies are marked by planet gear motion and contain strain energy in the tooth meshes and planet bearings Each cluster contains one rotational, one translational, and one planet mode type discussed in previous research The clustering phenomenon is robust, continuing through parameter variations of several orders of magnitude The natural frequency clusters move together as a group when planet parameters change They never intersect, but when the natural frequencies clusters approach each other, they exchange modal properties and veer away When central member parameters are varied, the clusters remain nearly constant except for regions in which natural frequencies simultaneously shift to different cluster groups There are two conditions that disrupt the clustering effect or diminish its prominence One is when the planet parameters are similar to those of the other components, and the other is when there are large differences in mass, moment of inertia, bearing stiffness, or mesh stiffness among the planet gears The clusters remain grouped together with arbitrary planet spacing

Free Vibration Analysis of thin-walled cylinders reinforced with longitudinal and transversal stiffeners

Abstract: This paper deals with the dynamic analysis of reinforced thin-walled structures by means of refined one-dimensional models. Complex reinforced structures are considered which are built by using different components: skin, ribs, and stringers. Higher-order one-dimensional model based on the Carrera unified formulation (CUF) are used to model panels, stringer, and ribs by referring to a unique model. The finite element method (FEM) is used to provide a solution that deals with any boundary condition configuration. The structure is geometrically linear and the materials are isotropic and elastic. The dynamic behavior of a number of reinforced thin-walled cylindrical structures have been analyzed. The effects of the reinforcements (ribs and stringers) are investigated in terms of natural frequencies and modal-shapes. The results show a good agreement with those from commercial codes by reducing the computational costs in terms of degrees of freedom (DOFs).

Wave Based Method for Free Vibration Analysis of Cylindrical Shells With Nonuniform Stiffener Distribution

Abstract: Wave based method (WBM) is presented to analysis the free vibration characteristics of cylindrical shells with nonuniform stiffener distributions for arbitrary boundary conditions. The stiffeners are treated as discrete elements. The equations of motion of annular circular plate are used to describe the motion of stiffeners. Instead of expanding the dynamic field variables in terms of polynomial approximation in element based method (finite element method etc), the ring-stiffened cylindrical shell is divided into several substructures and the dynamic field variables in each substructure are expressed as wave function expansions. Boundary conditions and continuity conditions between adjacent substructures are used to form the final matrix to be solved. Natural frequencies of cylindrical shells with uniform rings spacing and eccentricity distributions for shear diaphragm-shear diaphragm boundary conditions have been calculated by WBM model which shows good agreement with the experimental results and the analytical results of other researchers. Natural frequencies of cylindrical shells with other boundary conditions have also been calculated and the results are compared with the finite element method which also shows good agreement. Effects of the nonuniform rings spacing and nonuniform eccentricity and effects of boundary conditions on the fundamental frequencies and the beam mode frequencies have been studied. Different stiffener distributions are needed to increase the fundamental frequencies and beam mode frequencies for different boundary conditions. WBM model presented in this paper can be recognized as a semianalytical and seminumerical method which is quite useful in analyzing the vibration characteristics of cylindrical shells with nonuniform rings spacing and eccentricity distributions.