Impedance of pistons on a two-layer medium in a planar infinite rigid baffle

An integral transform technique is used to develop a general solution for the impedance of rigid pistons acting on a two-layer medium. The medium consists of a semi-infinite acoustic fluid on a viscoelastic thick plate in a rigid infinite baffle. The stresses acting on the planar baffle, as a result of piston motion, are determined using theory of linear elasticity and are therefore unrestricted in terms of applicable frequency range. The special case of a circular piston is considered and expressions for the self-and mutual impedances are developed and evaluated numerically. Numerical results are compared with classical piston impedance functions and finite-element model results. At low frequencies (k(0)a<1), the self-impedances vary significantly from the classical piston impedance functions due to the shear properties of the viscoelastic medium. In the midfrequency range (1相似文献   

Vibration of moderately thick square orthotropic stepped thickness plates

Numerous studies that address the vibration of stepped thickness plates are reported in the literature. Predominately, classical plate theory has been used to formulate studies for both isotropic and anisotropic stepped plates. Mindlin plate theory has been employed to obtain results for thick isotropic stepped thickness plates. Exact solutions, Rayleigh-Ritz, differential quadrature and finite element methods have been employed to compute results for frequency of vibration. Results for frequency of vibration for thick orthotropic stepped thickness plates are presented here using orthorhombic material properties of aragonite. The finite element method has been used to compute frequencies and determine mode shapes for simply supported and clamped square Mindlin plates.     

Nonlocal continuum-based modeling of a nanoplate subjected to a moving nanoparticle. Part I: Theoretical formulations

The potential applications of nanoplates in energy storage, chemical and biological sensors, solar cells, field emission, and transporting of nanocars have been attracted the attentions of the nanotechnology community to them during recent years. Herein, the later application of nanoplates from nonlocal elastodynamic point of view is of interest. To this end, dynamic response of a nanoplate subjected to a moving nanoparticle is examined within the context of nonlocal continuum theory of Eringen. The fully simply supported nanoplate is modeled based on the nonlocal Kirchhoff, Mindlin, and higher-order plate theories. The non-dimensional equations of motion of the nonlocal plate models are established. The effects of moving nanoparticle's weight and existing friction between the surfaces of the moving nanoparticle and nanoplate on the in-plane and out-of-plane vibrations of the nanoplate are incorporated into the formulations of the proposed models. The eigen function expansion and the Laplace transform methods are employed for discretization of the governing equations in the spatial and the time domains, respectively. The analytical expressions of the dynamic deformation field associated with each nonlocal plate theory are obtained when the moving nanoparticle traverses the nanoplate on an arbitrary straight path (an opened path) as well as an ellipse path (a closed path). The dynamic in-plane forces and moments of each nonlocal plate model are also derived. Furthermore, the critical velocity and the critical angular velocity of the moving nanoparticle for the proposed models are expressed analytically for the aforementioned paths. Part II of this work consists in a comprehensive parametric study where the effects of influential parameters on dynamic response of the proposed nonlocal plate models are scrutinized in some detail.     

Response of a cylindrical machine casing to oscillatory bearing forces

An analytical model is developed for the vibration response of a cylindrical machine casing excited by the force arising in a bearing that is assumed to support a rotating shaft. The casing system consists of a bearing housing mounted in a flat circular end cap that is built into a cylindrical casing. The housing is considered to be a rigid trunnion in the center of the end cap (which itself is modeled as a Mindlin plate). The development allows for arbitrary location of the center of mass of the housing and of the plane of action of the exciting force.     

Bending,vibration and buckling of simply supported thick multilayered orthotropic plates: An evaluation of a new displacement model

Based upon a piecewise linear displacement field which allows the contact conditions for the displacements and the transverse shearing stresses at the interfaces to be satisfied simultaneously, the non-linear (in the von Kármán sense) equations of motion for thick multilayered orthotropic plates are developed. Successively, the equations are specified to the linear boundary value problem of the bending and to the linear eigenvalue problems of the undamped vibration and buckling of rectangular plates. In order to assess the accuracy of the proposed theory, the sample problem of the bending, free undamped vibration and buckling of a three-layered, symmetric cross-ply, square plate simply supported on all edges is investigated. For purposes of comparison, numerical results from the exact elasticity theory, the classical lamination (Kirchhoff) theory and the shear deformation theory (Timoshenko and Mindlin) with three different values of the shear correction factor are also presented. It is found that the proposed approach is very efficient in predicting the global responses (deflection, natural frequencies and buckling loads) of thick multilayered plates and models effects, such as the distortion of the deformed normals, not attainable from the classical lamination theory, as well as the shear deformation theory.     

Measurement of the scattering of a Lamb wave by a through hole in a plate

Flexural waves propagating in an aluminum plate containing a circular hole are studied. In the experiments the first antisymmetric Lamb wave mode A0 is excited selectively by a piezoelectric transducer. The scattered field around a circular cavity is measured pointwise using a heterodyne laser interferometer. The measurements are compared with theoretical calculations. Different approximate analytical approaches, employing Kirchhoff and Mindlin types of plate theories to describe the scattered field, are used. Good agreement between the experimental data and the analytical solutions is found within the ranges of validity of the different models. Introduction of a small imperfection, like a notch, at the boundary of the cavity changes the measured scattered field     

弯曲振动矩形板辐射阻抗的计算

本文推导了四边简支矩形板的辐射阻抗表达式, 利用高斯数值积分方法, 计算了其相对辐射阻抗的数值解. 由不同模态下相对辐射阻抗与频率以及不同长宽比对应的相对辐射阻抗与频率的关系可知, 在中低频段, 模态越低, 辐射阻抗越大, 也就意味着辐射声功率和同振质量越大; 对于一定面积和模态的矩形板, r (r=a/b, 长与宽之比)值越接近1, 即越接近正方形, 辐射阻和辐射抗越大. 本文的方法能对其他复杂边界条件下的、无振动解析解的矩形板的辐射阻抗数值量级大小提供一个参考, 也可由计算弯曲振动的阻抗自然地过渡到活塞振动阻抗的计算.     

Effects of a multi-layered poro-elastic ground on attenuation of acoustic waves and ground vibration

Ground conditions affect the propagation of outdoor sound and vibration. This paper focuses on the interaction between air pressure and porous ground at low frequencies- where mechanisms other than the rigid porous effects used in locally reacting models may be important. A 2-D analytical model has been developed in this study for the calculation of acoustic and acousto-seismic admittances in a multi-layered poro-elastic ground. The model can be used as a prediction tool both for the ground effect on the sound and the generation of ground vibration by the sound. The modelled acoustic admittance is validated successfully against established rigid frame admittance models over a frequency range of 1 Hz-3 kHz. Moreover, the acousto-seismic impedance is verified against full scale airblast field test data measured during the Norwegian Trials full scale field test program. For certain ground types, the predicted acoustic admittance illustrates a different behaviour compared with predictions from the traditional rigid frame acoustic impedance models. This emphasises the importance of including a deformable frame in the model to obtain realistic results for these conditions.     

Vibration of tapered Mindlin plates in terms of static Timoshenko beam functions

In this paper, the free vibrations of rectangular Mindlin plates with variable thickness in one or two directions are investigated. The thickness variation of the plate is continuous and can be represented by a power function of the rectangular co-ordinates. A wide range of tapered rectangular plates can be described by giving various index values to the power function. Two sets of new admissible functions are developed, respectively, to approximate the flexural displacement and the angle of rotation due to bending of the plate. The eigenfrequency equation is obtained by using the Rayleigh-Ritz method. The complete solutions of displacement and angle of rotation due to bending for a tapered Timoshenko beam (a strip taken from the tapered Mindlin plate in some direction) under a Taylor series of static load have been derived, which are used as the admissible functions of the rectangular Mindlin plates with taper thickness in one or two directions. Unlike conventional admissible functions which are independent of the thickness variation of the plate, the static Timoshenko beam functions presented in this paper are closely connected with the thickness variation of the plate so that higher accuracy and more rapid convergence can be expected. Some numerical results are furnished for both truncated Mindlin plates and sharp-ended Mindlin plates. On the basis of convergence study and comparison with available results in literature, it is shown that the first few eigenfrequencies can be obtained with quite satisfactory accuracy by using only a small number of terms of the static Timoshenko beam functions.     

板厚对无障薄板声辐射特性影响的分析

分析无障薄板的声辐射特性时通常忽略板厚对格林函数的影响而采用双层势计算.本文考虑板厚引起的声辐射阻抗,采用混合势计算结构表面声压与振速,并分析板厚对声辐射参数的影响。根据交界相容性条件,采用边界积分方程分别表示平板上下表面的声压和振速,并合并同类项.进一步将结构的动力方程代入混合势形式的振速方程中,离散声压差值和板的位移为振动模态叠加的形式,获得二重积分形式的声辐射阻抗,从而求解振动模态系数,确定声辐射特性参数.以水下简支矩形板为例计算对比了声辐射参数,并讨论了其对板厚的敏感性。结果表明:板厚引起的声辐射阻抗对声辐射参数的大小影响较小,但随着频率的增加致使共振频率发生较大偏移;在相同阶数的共振频率范围内,板厚度越大,采用双层势计算的误差越大。      

Further study on the characteristic impedance of a new transmission line of round conductor and parallel plane with a slit

A conformal transformation for the analysis of a transmission line consisting of a cylindrical conductor placed opposite a slit in an infinite flat plate is developed. The approximate and exact expressions in closed- form of the characteristic impedance for the proposed line based on assuming only a quasi-TEM mode propagating in the line are as exact as the conventional one cited.     

Sound insulation provided by single and double panel walls—a comparison of analytical solutions versus experimental results

The predicted values for acoustic insulation of single and double panel walls, using analytical models previously developed by the authors, are compared with experimental findings. The analytical method used fully takes into account the coupling between the air and the solid panels, and there is no restriction on their thickness, as the Kirchhoff or Mindlin approaches require. The laboratory experiments involved placing test specimens between standard chambers. Results are presented for panels made of glass, concrete and steel. From the results we can conclude that the predictive analytical solutions are in good agreement with the experimental results, except when the area of the panels is very small and the frequencies are very low. At low frequencies, the experimental results appear to be significantly affected by the resonance effects associated with the creation of stationary waves within the acoustic chambers, and the vibration modes introduced into the dynamic system by the restriction on the movement of the panel along its boundary.     

旋转超声磨削平行砂轮复合变幅器设计与试验

为了获得大负载平行砂轮复合变幅器的设计方法,将复合变幅器简化为复合变幅杆与多阶环盘组成.利用Mindlin中厚板理论,求解了各振动环盘的位移、转角、弯矩和剪力解析表达式,通过复合变幅杆各振动单元间的力、位移的边界条件和连续条件,以及复合变幅杆和环盘两者结构间力与位移的耦合条件,建立了复合变幅器的数学模型和频率方程.针对...     

Evaluation of mutual radiation impedances between circular pistons by impulse response and asymptotic methods

A general approach is presented to evaluate the mutual radiation impedance between circular pistons of arbitrary size and spacing in an infinite rigid planar baffle. The impedance is expressed as a Fourier transform of a generalized impulse response which is defined by an integral relationship. Although the integral must, in general, be numerically evaluated, several special cases of interest can readily be evaluated by using asymptotic techniques. Several asymptotic expressions for the mutual radiation impedance are developed and their limitations are noted. Numerical results are then presented for the generalized impulse response and mutual radiation impedance corresponding to pistons of equal size and arbitrary spacing. The time domain characteristics of the generalized impulse responses as a function of spacing are noted and related to the frequency characteristics of the mutual radiation impedances as a function of spacing. In addition, the accuracy of a simple closed form expression for the mutual radiation impedance is presented as a function of normalized frequency and spacing.     

On the Generalized Thermoelasticity Problem for an Infinite Fibre-Reinforced Thick Plate under Initial Stress

In this paper, the generalized thermoelasticity problem for an infinite fiber-reinforced transversely-isotropic thick plate subjected to initial stress is solved. The lower surface of the plate rests on a rigid foundation and temperature while the upper surface is thermally insulated with prescribed surface loading. The normal mode analysis is used to obtain the analytical expressions for the displacements, stresses and temperature distributions. The problem has been solved analytically using the generalized thermoelasticity theory of dual-phase-lags. Effect of phase-lags, reinforcement and initial stress on the field quantities is shown graphically. The results due to the coupled thermoelasticity theory, Lord and Shulman's theory, and Green and Naghdi's theory have been derived as limiting cases. The graphs illustrated that the initial stress, the reinforcement and phase-lags have great effects on the distributions of the field quantities.     

Power flow through machine isolators to resonant and non-resonant beams

The parameters controlling power transmission from a vibrating machine to the seating structure, via spring-like vibration isolators, are investigated. The low frequency range is considered where the machine moves as a rigid body. It is shown that the finite seating structure can be modelled by an equivalent structure of infinite extent for frequency averaged power transmission calculations. Power transmission to a finite and an infinite beam via a mass and spring in series is measured experimentally and compared with theoretical predictions. The power transmission is measured by two proposed methods; the first involves the real component of the seating impedance, and the second the transfer impedance of the isolator.     

The determination of electrical parameters of quartz crystal resonators with the consideration of dissipation

Recently, as the dissipation of quartz crystal through material viscosity is being considered in vibrations of piezoelectric plates, we have the opportunity to obtain electrical parameters from vibration solutions of a crystal plate representing an ideal resonator. Since the solutions are readily available with complex elastic constants from Mindlin plate equations for thickness-shear vibrations, the calculation of resistance and other parameters related to both mechanical deformation and electrical potential is straightforward. We start with the first-order Mindlin plate equations of a piezoelectric plate for the thickness-shear vibration analysis of a simple resonator model. The electrical parameters are derived with emphasis on the resistance that is related to the imaginary part of complex elastic constants, or the viscosity. All the electrical parameters are frequency dependent, enabling the study of the frequency behavior of crystal resonators with a direct formulation. Through the full consideration of complications like partial electrodes and supporting structures, we should be able obtain electrical parameters for practical applications in resonator design.     

Finite element analysis of the axisymmetric vibrations of cylinders

A finite element analysis is developed for finite and infinite solid or hollow cylinders in axisymmetric vibration. The elements themselves are solid or annular cylinders, and have 16 degrees of freedom. Results are given for the propagation constants of solid and hollow infinite cylinders, and excellent agreement is found with those from the exact Pochhammer theory and Mindlin and McNiven's three-mode theory. Frequency spectra are presented for the symmetric and antisymmetric modes of solid and hollow finite rods. Excellent agreement is found with experimental results, and this suggests that some of the results obtained from the three-mode theory by McNiven et al., and in particular the frequency of the end mode, are in error by more than 10%. Details of the finite element inertia and stiffness matrices appear in an appendix.     

Acoustic impedance of rectangular panels

The modal radiation impedance of a rectangular panel simply supported in an infinite baffle in the presence of an inviscid, uniform, subsonic flow is determined. The analysis is based on an expansion in normal modes of the transverse vibration displacement field of the panel and the use of wavenumber-frequency transforms. Integral expressions for the modal radiation impedance and the cross-modal coupling impedance are formulated. A Gaussian quadrature with reusable abscissas is developed to evaluate these modal radiation impedances. Changes with respect to flow speed in modal radiation damping of a rectangular membrane are measured. For the first observable low order mode the change is significant and agrees with the theory. For higher order modes non-significant changes are predicted and measured. The computed modal radiation reactances of the membrane are compared with the best available experiments. Significant discrepancies exist. Their causes are discussed.     

Free vibration of size-dependent Mindlin microplates based on the modified couple stress theory

This paper develops a Mindlin microplate model based on the modified couple stress theory for the free vibration analysis of microplates. This non-classical plate model contains an internal material length scale parameter related to the material microstructures and is capable of interpreting the size effect that the classical Mindlin plate model is unable to describe. The higher-order governing equations of motion and boundary conditions are derived using the Hamilton principle. The p-version Ritz method is employed to determine the natural frequencies of the microplate with different boundary conditions. A detailed parametric study is conducted to study the influences of the length scale parameter, side-to-thickness ratio and aspect ratio on the free vibration characteristics of the microplate. It is found that the size effect is significant when the thickness of microplate is close to the material length scale parameter.