A study of hand vibration on chipping and grinding operators,part II: Four-degree-of-freedom lumped parameter model of the vibration response of the human hand

The results of the development of a four-degree-of-freedom, lumped parameter model of the vibration response characteristics of the human hand are presented. For this study dynamic compliance measurements were made on 75 foundry workers. Curve fitting techniques were then employed to identify the values of the model parameters that yielded empirically generated dynamic compliance curves that correlated well with the measured dynamic compliance values. The agreement was good between 20 Hz and 1000 Hz in the X- and Y-directions. The agreement was good between 20 Hz and 1000 Hz in the Z-direction.     

A note on the lumped parameter beam models based on mechanical impedance

Investigation of the three-parameter lumped mass model for a Bernoulli-Euler clamped-clamped beam has shown that the model is a universal model with respect to simple boundary conditions. Numerical results for the transient response due to a low frequency ground shock demonstrate the superiority of the beam model based on impedance methods.     

Electromechanical coupling factor of capacitive micromachined ultrasonic transducers

Recently, a linear, analytical distributed model for capacitive micromachined ultrasonic transducers (CMUTs) was presented, and an electromechanical equivalent circuit based on the theory reported was used to describe the behavior of the transducer [IEEE Trans. Ultrason. Ferroelectr. Freq. Control 49, 159-168 (2002)]. The distributed model is applied here to calculate the dynamic coupling factor k(w) of a lossless CMUT, based on a definition that involves the energies stored in a dynamic vibration cycle, and the results are compared with those obtained with a lumped model. A strong discrepancy is found between the two models as the bias voltage increases. The lumped model predicts an increasing dynamic k factor up to unity, whereas the distributed model predicts a more realistic saturation of this parameter to values substantially lower. It is demonstrated that the maximum value of k(w), corresponding to an operating point close to the diaphragm collapse, is 0.4 for a CMUT single cell with a circular membrane diaphragm and no parasitic capacitance (0.36 for a cell with a circular plate diaphragm). This means that the dynamic coupling factor of a CMUT is comparable to that of a piezoceramic plate oscillating in the thickness mode. Parasitic capacitance decreases the value of k(w), because it does not contribute to the energy conversion. The effective coupling factor k(eff) is also investigated, showing that this parameter coincides with k(w) within the lumped model approximation, but a quite different result is obtained if a computation is made with the more accurate distributed model. As a consequence, k(eff), which can be measured from the transducer electrical impedance, does not give a reliable value of the actual dynamic coupling factor.     

Suppression of brake squeal noise applying finite element brake and pad model enhanced by spectral-based assurance criteria

An enhanced dynamic finite element (FE) model with friction coupling is applied to analyze the design of disc brake pad structure for squeal noise reduction. The FE model is built-up from the individual brake component representations. Its interfacial structural connections and boundary conditions are determined by correlating to a set of measured frequency response functions using a spectral-based assurance criterion. The proposed friction coupling formulation produces an asymmetric system stiffness matrix that yields a set of complex conjugate eigenvalues. The analysis shows that eigenvalues possessing positive real parts tend to produce unstable modes with the propensity towards the generation of squeal noise. Using a proposed lumped parameter model and eigenvalue sensitivity study, beneficial pad design changes can be identified and implemented in the detailed FE model to determine the potential improvements in the dynamic stability of the system. Also, a selected set of parametric studies is performed to evaluate numerous design concepts using the proposed dynamic FE model. The best pad design attained, which produces the least amount of squeal response, is finally validated by comparison to a set of actual vehicle test results.     

Dynamic properties of the human head

Driving point mechanical impedance measurements were used to determine the dynamic response of the human head to sinusoidal vibration in the frequency range between 30 Hz and 5000 Hz at excitation levels of 0·98 m/s² and 3·4 m/s2. Because of the low excitation levels, the weight of the head was sufficient to couple the head to the vibration source.At 20 Hz the impedance magnitude was about 790 N-s/m but increased at approximately 6dB/octave to a peak near 3500 N-s/m at 70–90 Hz. Between 100 Hz and 2000 Hz impedance decreased by about two orders of magnitude while the apparent mass decreased by three orders of magnitude indicating good vibration isolation at higher frequencies. The impedance response contains the information for modelling the head as a dynamic system.The response of the head to vibration can be simulated by a two degree-of-freedom, mass-excited system consisting of a series connection of a small driving mass, a damper, a spring and damper in parallel and a large final mass. Parameter values, derived by computer techniques, suggest that the large mass represents the total head, the small mass the tissue in contact with the vibration input and the spring the skull stiffness.     

Coupled magneto-electro-mechanical lumped parameter model for a novel vibration-based magneto-electro-elastic energy harvesting systems

The objective of this paper is to present a coupled magneto-electro-mechanical (MEM) lumped parameter model for the response of the proposed magneto-electro-elastic (MEE) energy harvesting systems under base excitation. The proposed model can be used to create self-powering systems, which are not limited to a finite battery energy. As a novel approach, the MEE composites are used instead of the conventional piezoelectric materials in order to enhance the harvested electrical power. The considered structure consists of a MEE layer deposited on a layer of non-MEE material, in the framework of unimorph cantilever bars (longitudinal displacement) and beams (transverse displacement). To use the generated electrical potential, two electrodes are connected to the top and bottom surfaces of the MEE layer. Additionally, a stationary external coil is wrapped around the vibrating structure to induce a voltage in the coil by the magnetic field generated in the MEE layer. In order to simplify the design procedure of the proposed energy harvester and obtain closed form solutions, a lumped parameter model is prepared. As a first step in modeling process, the governing constitutive equations, Gauss's and Faraday's laws, are used to derive the coupled MEM differential equations. The derived equations are then solved analytically to obtain the dynamic behavior and the harvested voltages and powers of the proposed energy harvesting systems. Finally, the influences of the parameters that affect the performance of the MEE energy harvesters such as excitation frequency, external resistive loads and number of coil turns are discussed in detail. The results clearly show the benefit of the coil circuit implementation, whereby significant increases in the total useful harvested power as much as 38% and 36% are obtained for the beam and bar systems, respectively.     

Vibration of an excitation system supported flexibly on a viscoelastic sandwich beam at its mid-point

A vibration analysis of an excitation system supported flexibly on a three layer sandwich beam is presented in this paper. The flexibly supported excitation system, which is essentially the primary system, consists of a mass, a spring and a dash-pot. The beam is analyzed separately as a continuous system in a classical way and then its dynamic stiffness at the junction point is combined with that of the primary system to obtain the resultant dynamic stiffness, which in turn is used to develop the expressions for the response of the primary system and the transmissibility provided by the whole system. Both response and transmissibility are evaluated for different geometrical and physical parameters of the sandwich beam. The solution to this problem is also obtained by approximating the sandwich beam by a lumped mass supported on a spring and dash-pot. The results in the two cases are compared. Results obtained from an experimental test-rig substantiate the theoretical results.     

Middle-ear circuit model parameters based on a population of human ears

Middle-ear circuit model parameters are selected to produce overall magnitude and phase agreement with pressure to stapes velocity transfer function measurements made on 16 human temporal bones, up to approximately 12 kHz. The circuit model, which was previously used for the cat, represents the tympanic membrane (TM) as a distributed parameter acoustic transmission line, and ossicular chain and cochlea as a network of lumped circuit elements. For some ears the TM transmission line primarily affects the magnitude of the response, while for others it primarily affects the phase. Model responses also compare favorably with velocity ratio data between the umbo and stapes footplate as well as between the umbo and incus, and exhibit similar characteristics to three previous input impedance measurements, including two from living ears. Similarities are also shown between the model magnitude and adjusted pressure to stapes velocity measurements from living ears, suggesting that the model may suitably approximate the behavior of living ears. In addition to fitting individual measurements, a set of parameters is selected to produce agreement with the mean of the 16 measurements up to 10 kHz, to allow the main features of the ensemble to be reproduced from a single parameter set.     

A FREQUENCY-DOMAIN METHOD OF STRUCTURAL DAMAGE IDENTIFICATION FORMULATED FROM THE DYNAMIC STIFFNESS EQUATION OF MOTION

This paper introduces a frequency-domain method of structural damage identification. It is formulated in a general form from the dynamic stiffness equation of motion for a structure and then applied to a beam structure. Only the dynamic stiffness matrix for the intact state appears in the final form of the damage identification algorithm as the structure model. The appealing features of the present damage identification method are: (1) it requires only the frequency response functions experimentally measured from the damaged structure as the input data, and (2) it can locate and quantify many local damages at the same time. The feasibility of the present damage identification method is tested through some numerically simulated damage identification analyses and then experimental verification is conducted for a cantilevered beam with damage caused by introducing three slots.     

THE DYNAMIC STIFFNESS MATRIX METHOD IN FORCED VIBRATION ANALYSIS OF MULTIPLE-CRACKED BEAM

The dynamic behaviour of a beam with numerous transverse cracks is studied. Based on the equivalent rotational spring model of crack and the transfer matrix for beam, the dynamic stiffness matrix method has been developed for spectral analysis of forced vibration of a multiple cracked beam. As a particular case, when the excitation frequency is close to zero, the solution for static response of beam with an arbitrary number of cracks has been obtained exactly in an analytical form. In general case, the effect of crack number and depth on the dynamic response of beam was analyzed numerically.     

电光调Q驱动电源与晶体之间的引线研究

分析了高重频电光调Q驱动电源与晶体之间的最佳引线。由于调Q晶体和引线都存在分布电容和电感,如果晶体两端阻抗不匹配,电压脉冲就会出现阻尼振荡,从而影响激光脉冲。针对这一问题,使用脉冲反射法和分布参数电路法,以平行导线作为引线,分析了脉冲在引线中的传输、晶体高压波形和引线所要求的驱动电源的最小功率。使用脉冲反射法,以同轴线作为引线,分析了简单连接晶体和阻抗匹配后连接晶体的两种情况,得出了晶体两端电压波形和同轴引线阻抗匹配后的电路对快速开关的要求。根据以上分析,得出了电光调Q中引线的选择原则。     

A simplified nonlinear dynamic model for the analysis of pipe structures with bolted flange joints

Bolted flange joints are widely used in engineering structures; however, the dynamic behavior of this connection is complex in nature. In this paper, a simplified nonlinear dynamic model with bi-linear springs is proposed and validated for pipe structures with bolted flange joints. First, static mechanical properties of the bolted flange joint are investigated. The analytical solution reveals that the axial stiffness of the bolted flange joint is different in tension and compression. Then, nonlinear springs with different stiffness in tension and compression are employed to represent the bolted flange joint. A special type of dynamic behavior, coupling vibration in the transverse and longitudinal directions, is observed in analytical derivation. Finally, relevant physical experiments and numerical simulations are performed. The physical experiments confirm the existence of the coupling vibration behavior. The relationship of longitudinal and transverse vibration frequencies is discussed. The numerical solutions reveal that the simplified nonlinear dynamic model better fits the physical response than conventional reduced linear beam model.     

Lumped parameter models representing impedance functions at the interface of a rod on a viscoelastic medium

In this study, a lumped parameter model that properly simulates the impedance characteristics at the extremity of a uniform, isotropic, homogeneous rod on a viscoelastic medium is proposed. The lumped parameter model consists of springs, dashpots, and so-called “gyro-mass elements”. The gyro-mass elements generate a reaction force proportional to the relative acceleration of the nodes between which they are placed. This model consists of units arranged in series, each unit consisting of a spring, a damper, and a gyro-mass element arranged in parallel. A formula is proposed for determining the properties of the elements in the units calculated from a closed-form solution based on a modal expansion. The impedance function simulated by the proposed model shows good agreement with the rigorous impedance function derived from the differential equation of motion of the rod. The results obtained by employing this model in some example applications show that the accuracy of the model is appreciably high when compared with conventional finite element models. A great advantage of this model is that a significant reduction of the number of degrees of freedom can be achieved for solving recent vibration problems with high-frequency excitations, such as ultrasonic vibrations.     

铁镓单晶Janus-Helmholtz换能器

针对深水、低频、宽带换能器的技术需求,结合Janus-Helmholtz换能器的结构特点和铁镓单晶材料低场应变大及机械强度高的特性,提出了铁镓单晶Janus-Helmholtz换能器设计方案。采用永磁偏磁场和环形闭合磁路,建立了一系列铁镓单晶磁致伸缩换能器理论分析模型,包括对磁致伸缩材料参数进行线性化处理,设计了换能器最佳工作点,结合静态磁场和动态磁场分布情况分段细化换能器驱动等效参数,以及利用全阻抗模型通过电感损耗等效计算换能器静态阻抗,然后通过二维有限元分析等效模型,优化分析了换能器的结构参数与电声性能。最后制作了换能器样机,并进行了测试与分析。对比仿真和测试结果表明:全阻抗模型得到的阻抗曲线与样机测试结果相一致,有限元等效模型计算的发送电流响应与样机测试结果良好吻合。换能器样机水中谐振基频为1000 Hz,谐振频率下发送电流响应176.4 dB;在875～2300 Hz频率范围内,发送电流响应起伏不大于6 dB;增加驱动电流有效值到16.2 A,最大声源级可以达到196.2 dB。     

Finite element analysis and experimental study on dynamic properties of a composite beam with viscoelastic damping

This paper investigates the frequency dependent viscoelastic dynamics of a multifunctional composite structure from finite element analysis and experimental validation. The frequency-dependent behavior of the stiffness and damping of a viscoelastic material directly affects the system's modal frequencies and damping, and results in complex vibration modes and differences in the relative phase of vibration. A second order three parameter Golla–Hughes–McTavish (GHM) method and a second order three fields Anelastic Displacement Fields (ADF) approach are used to implement the viscoelastic material model, enabling the straightforward development of time domain and frequency domain finite elements, and describing the frequency dependent viscoelastic behavior. Considering the parameter identification a strategy to estimate the fractional order of the time derivative and the relaxation time is outlined. Agreement between the curve fits using both the GHM and ADF and experiment is within 0.001 percent error. Continuing efforts are addressing the material modulus comparison of the GHM and the ADF model. There may be a theoretical difference between viscoelastic degrees of freedom at nodes and elements, but their numerical results are very close to each other in the specific frequency range of interest. With identified model parameters, numerical simulation is carried out to predict the damping behavior in its first two vibration modes. The experimental testing on the layered composite beam validates the numerical predication. Experimental results also show that elastic modulus measured from dynamic response yields more accurate results than static measurement, such as tensile testing, especially for elastomers.     

Numerical study on reducing the vibration of spur gear pairs with phasing

A new method of reducing gear vibration was analyzed using a simple spur gear pair with phasing. This new method is based on reducing the variation in mesh stiffness by adding another pair of gears with half-pitch phasing. This reduces the variation in the mesh stiffness of the final (phasing) gear, because each gear compensates for the variation in the other's mesh stiffness. A single gear pair model with a time-varying rectangular-type mesh stiffness function and backlash was used, and the dynamic response over a wide range of speeds was obtained by numerical integration. Because of the reduced variation in mesh stiffness and the double frequency, the phasing gear greatly reduced the dynamic response and nonlinear behavior of the normal gears. The results of the analysis indicate the possibility of reducing vibration of spur gear pairs using the proposed method.     

Nonlinear model and system identification of a capacitive dual-backplate MEMS microphone

This paper presents the nonlinear identification of a capacitive dual-backplate microelectromechanical systems (MEMS) microphone. First, a nonlinear lumped element model of the coupled electromechanical microphone dynamics is developed. Nonlinear finite element analyses are performed to verify the accuracy of the lumped linear and cubic stiffnesses of the diaphragm. In order to experimentally extract the system parameters, an approximate solution using the second-order multiple scales method is synthesized for a nonlinear microphone model, subject to an electrical step input. A nonlinear least-squares technique is then implemented to extract system parameters from laser vibrometry data of the diaphragm motion. The results indicate that the theoretical fundamental resonant frequency, damping ratio and nonlinear stiffness parameter agree with the corresponding extracted experimental parameters with 95% confidence interval estimates.     

An approach for including the stiffness and damping of elastohydrodynamic point contacts in deep groove ball bearing equilibrium models

This work presents a methodology for including the Elastohydrodynamic (EHD) film effects to a lateral vibration model of a deep groove ball bearing by using a novel approximation for the EHD contacts by a set of equivalent nonlinear spring and viscous damper. The fitting of the equivalent contact model used the results of a transient multi-level finite difference EHD algorithm to adjust the dynamic parameters. The comparison between the approximated model and the finite difference simulated results showed a suitable representation of the stationary and dynamic contact behaviors. The linear damping hypothesis could be shown as a rough representation of the actual hysteretic behavior of the EHD contact. Nevertheless, the overall accuracy of the model was not impaired by the use of such approximation. Further on, the inclusion of the equivalent EHD contact model is equated for both the restoring and the dissipative components of the bearing?s lateral dynamics. The derived model was used to investigate the effects of the rolling element bearing lubrication on the vibration response of a rotor?s lumped parameter model. The fluid film stiffening effect, previously only observable by experimentation, could be quantified using the proposed model, as well as the portion of the bearing damping provided by the EHD fluid film. Results from a laboratory rotor–bearing test rig were used to indirectly validate the proposed contact approximation. A finite element model of the rotor accounting for the lubricated bearing formulation adequately portrayed the frequency content of the bearing orbits observed on the test rig.     

Reaction network reduction for distributed systems by model training in lumped reactors: Application to bifurcations in combustion

A new methodology is presented to derive reduced reaction mechanisms for distributed reacting flows by model training in a lumped parameter system (a continuous-stirred tank reactor). The method identifies the relevant transport time scales in the reaction zone of a distributed system along with the local composition vector, over a range of operation conditions. A training box in the parameter space of pressure-transport time scale-composition is then identified. Sensitivity and principal component analyses are subsequently performed at bifurcation points in a lumped parameter system at representative conditions of the training box. The most inclusive chemistry derived in the lumped system captures the proper transport-chemistry coupling and is suitable for the distributed reactor. Application to ignition of hydrogen/air and methane/air mixtures is presented and validated for premixed and diffusion flames in a stagnation flow geometry. (c) 1999 American Institute of Physics.     

Wave propagation in a periodic elastic-piezoelectric axial-bending coupled beam

The wave propagation in a periodic elastic-piezoelectric axial-bending coupled beam is investigated in this paper by considering the mechanical–electrical coupling behavior. The strain energy and kinetic energy of each sub-cell are first formulated to extract the dynamic stiffness matrices, and then the compatibility and continuity conditions at the interface between the adjacent cells are utilized to derive the transfer matrix that governs the propagation of the wave along the periodic piezoelectric beam. By employing the Lyapunov exponent method, the dynamic behaviors of the periodic beam structure are evaluated with different base beam materials, dimension ratios, piezoelectric constants and elastic stiffness. The results indicate that regardless of the length ratio, there exist certain frequency intervals, where the width and magnitude of the prominent stop band of the aluminum beam with periodic piezoelectric patches are always broader and larger than those of the steel base system. In addition, as the thickness ratio decreases, the location of the stop band tends to move toward a higher frequency. Numerical studies also demonstrate that different piezoelectric constants and elastic stiffness affect the characteristics of wave propagation in completely different fashions. The investigation in the present study provides basic guidelines to design periodic elastic-piezoelectric laminate structures in order to achieve desired filtering characteristics.