任意形状埋置基础滑移振动复合集总参数模型

根据基础振动弹性半空间理论的最新发展成果推导出一个计算埋置基础滑移振动的复合集总参数模型。采用该模型对复杂形状的埋置块体基础在水平谐和扰力作用下的动力响应进行计算,并将振幅计算结果与采用弹性半空间理论所得到的埋置基础滑移振动刚度和阻尼系数公式(由大量试验、数值计算所证实)的振幅计算结果进行比较,结果表明:两者结果吻合,振幅误差为22.9%。利用该模型可以容易地计算在水平扰力作用下任意频率、任意泊松比和任意形状(不包括环型)的均质半空间上块体埋置基础的动力响应。     

空冷桥架风机随机扰力模型

分析不同转速下直接空冷风机桥架振动实测速度响应表明,传统简谐扰力作用的振动响应不能反映实测振幅、相位缓慢变化的窄带随机特性;采用载波理论建立的风机扰力模型可有效反映桥架振动的随机性。结合风机桥架振动时、频域分析结果,以速度响应功率谱为目标识别扰力模型参数。模拟结果表明,扰力模型标准差随风机转速增加而增大。     

基于格林函数法的封闭声腔的结构-声耦合分析

以封闭声腔为模型，在考虑流固耦合作用的基础上，结合流体格林函数和Helmholtz方程及其边界条件，导出了各阶声压模态对应的声压振幅响应公式；结合结构格林函数和板的振动方程及其边界条件，导出了各阶板模态对应的速度振幅响应公式。这两个公式物理意义明确，易于转化为矩阵形式直接进行数值仿真，可应用于任意几何形状的封闭声腔，为进一步研究封闭声腔的结构-声耦合问题提供了必要的理论基础。数值仿真部分首先对声压振幅和速度振幅的积分形式作了矩阵化。然后以长方体封闭声腔为模型，结合有限元法计算声压模态和弹性板的振动模态，合成耦合系数，并最终合成弹性板与声腔耦合作用下的的声压响应和弹性板的速度响应；将数值仿真结果与解析结果以及前人的试验结果进行比较，验证了本文在理论分析和数值仿真方面的正确性。最后将该方法应用于一个非规则封闭声腔模型，得到了结构-声耦合作用下的系统响应。     

相邻明置刚性条形基础的水平-摇摆耦合阻抗研究

基于弹性半空间理论研究两相邻明置条形基础的水平-摇摆耦合动力阻抗。推导了频域内水平、垂直简谐条形均布激振下弹性地基位移的格林函数,将基础与地基的接触面分割成若干个子单元,利用格林函数建立各子单元的耦合柔度方程。根据基础的刚体位移决定各子单元的位移,由叠加原理得到土与相邻明置条形基础的水平-摇摆动力耦合阻抗函数。通过收敛性研究并与其他数值计算及混合边值法的精细解进行比较,证明此方法具有计算简便和精度高的特点,可用于全频段阻抗函数的计算。最后分析了相邻条形基础距宽比对水平-摇摆耦合动力相互作用的影响,计算表明:当两明置条形基础距宽比S/L5.0时,应考虑其水平-摇摆的动力相互作用效应。     

基础对建筑结构振动的影响分析

基于基础振动弹性半空间理论和子结构法建立土-基础-结构动力相互作用模型,分析基础对于上部建筑结构水平向滑移、摆动以及竖向振动的影响。分析结果表明基础等效半径增加,可以增加地基对于上部结构的辐射阻尼、刚度以及附加振动质量,有效地减小地面环境微振动对上部结构的影响。建筑结构设计中,适当考虑基础形式和面积对环境微振动的衰减效应,是经济实用且效果较好的设计思路和减振措施。     

正压冲固平台波浪和海流作用下动力响应分析

针对正压冲固平台在波浪和海流作用下动力响应问题，应用Morison方程和Stokes五阶波理论计算波浪和海流合力；基于弹性半空间理论并采用三次样条函数双向插值方法求解基础的动刚度和阻尼；在此基础上采用有限元方法计算该平台的动力响应。此外采用6倍桩径法计算了平台的动力响应，对比二者结果，说明本文研究的计算方法可靠。     

基于Boer多孔介质理论的饱和半空间上刚性圆板基础竖向振动特性研究

针对饱和黏弹性半空间地基上刚性圆板基础竖向振动问题,基于Boer多孔介质动力控制方程组,应用Hankel积分变换技术并结合基础与地基土接触面混合边值条件,推导求解相关方程得到了饱和黏弹性半空间地基上刚性圆板基础的竖向动力阻抗以及振幅放大系数公式。在此基础上进一步通过数值算例对比分析探讨了液固耦合系数、基础质量比、地基土黏滞阻尼系数对所得基础竖向动力阻抗及振幅放大系数的影响规律。解析推导得出的对应竖向动力阻抗三维精确解不但丰富了基础振动理论,还可为相关工程实践提供参考和理论支持。     

板式轨道在高速列车作用下的动力响应分析

通过理论计算与现场试验研究高速列车与板式轨道的动力相互作用。提出了高速列车—板式轨道系统(简称此系统)空间振动分析方法:列车模型每节车辆考虑26个自由度;针对板式轨道结构特点,建立了32个自由度的板式轨道空间振动轨段单元新模型;基于弹性系统动力学总势能不变值原理及形成系统矩阵的"对号入座"法则,建立了此系统空间振动矩阵方程;采用Wilson-θ法求解。计算了板式轨道在高速列车作用下的位移以及车辆的脱轨系数、轮重减载率、横向轮轨力等动力响应,并与现场试验结果进行了对比。结果表明:理论计算结果与现场试验结果具有较好的一致性,由此说明文中提出的方法正确可靠。最后,还探讨了轨道刚度对此系统空间振动响应的影响规律。     

联合基础振动模型及动力特性的研究

提出一种刚体－－弹性体联合基础振动模型，用于大型动力机器联合基础的动力分析，对联合基础的自振频率，振型、减振效果以及在不同相拉扰力作用下的响应等动力特性进行了研究。     

基于指数摩擦力模型滑移隔震结构的动力特性

基于指数摩擦力模型,本文利用预估校正的数值积分方法计算滑移隔震结构的动力响应,分析了地面谐运动下结构的加速度传递率及基底滑移率随频率比的变化规律,并发现滑移隔振结构的振动有振幅跳跃、基底爬行等非线性动力特征。     

Direct boundary integral equations for elastodynamics in 3-D half-spaces

Vector boundary integral equations (BIE's) based on Somigliana's integral formula are presented with Stokes' (full-space) and Lamb's (half-space) fundamental tensors (Green's functions), for radiation and scattering of time-harmonic elastic waves by bodies embedded in or laying on the surface of a three-dimensional homogeneous, isotropic, linear-elastic half-space. Numerical work is based on BIEs free from principal-value integrals. Whereas the Stokes'-tensor BIE requires discretization of the infinite half-space surface, all discretization is confined to (finite) surfaces of the body when Lamb's tensors are used. The nonuniqueness of the integral equation solution at fictitious eigenfrequencies is addressed. Numerical results are presented for a rigid circular footing, a rigid hemispherical foundation and a fully embedded spherical cavity.     

Three‐dimensional vibration analysis of rectangular thick plates on Pasternak foundation

The free‐vibration characteristics of rectangular thick plates resting on elastic foundations have been studied, based on the three‐dimensional, linear and small strain elasticity theory. The foundation is described by the Pasternak (two‐parameter) model. The Ritz method is used to derive the eigenvalue equation of the rectangular plate by augmenting the strain energy of the plate with the potential energy of the elastic foundation. The Chebyshev polynomials multiplied by a boundary function are selected as the admissible functions of the displacement functions in each direction. The approach is suitable for rectangular plates with arbitrary boundary conditions. Convergence and comparison studies have been performed on square plates on elastic foundations with different boundary conditions. It is shown that the present method has a rapid convergent rate, stable numerical operation and very high accuracy. Parametric investigations on the dynamic behaviour of clamped square thick plates on elastic foundations have been carried out in detail, with respect to different thickness–span ratios and foundation parameters. Some results found for the first time have been given and some important conclusions have been drawn. Copyright © 2004 John Wiley & Sons, Ltd.     

无拉力弹性半空间地基上预应力四边自由中厚板的动力响应

基于Reissner-Mindlin一阶剪切变形板理论,讨论在预加面内机械荷载和温度场作用下,无拉力弹性半空间地基上四边自由中厚板在动荷载作用下的动力特性。把地基看作三维弹性半空间体,考虑地基变形衰减,用一组数学上完备的二元多项式作为位形函数,采用pb-2 Rayleigh-Rizt法求得四边自由中厚板的动力响应,并讨论了初应力对板的动挠度和动弯矩的影响。     

Dynamic response of finite sized elastic runways subjected to moving loads: A coupled BEM/FEM approach

The transient response of a finite elastic plate, resting on an elastic half-space, and subjected to moving loads is considered here. Both the cases of an elastic foundation alone, as well as a finite sized elastic plate resting on an elastic foundation are considered. The numerical methods employed are: (1) the time-domain boundary element method for the elastic foundation and (2) a combination of the time-domain boundary element method for the soil and the semi-discrete finite element method for the finite sized elastic plate. Both constant as well as linear-time-interpolation schemes are included in the BEM. The integration is carried out analytically in time. The analytical solution for a moving point load on an infinite elastic plate resting on an elastic half-space is derived here. This is used as a benchmark against which the present numerical solution is compared with. The accuracy of the numerical method is also verified by comparing the solutions with some existing numerical results; the comparison with the solutions based on a Winkler foundation model reveals the limitations of the applicability of such a model, especially in the cases of high velocities of the moving load. This is because neither the inertia of the foundation, nor the behaviour of the foundation as a continuum, can be properly accounted for in Winkler's model. A parametric study is conducted, and the influences of velocity of the moving load, load distribution, etc. on the dynamic response of the soil/runway system are investigated. Furthermore, the present computational method is applied to the problem of a transport airplane taxiing on a concrete pavement resting on a typical soil. The responses of pavements are presented for different taxiing velocities.     

SH波作用下层状土层随机波动分析

提出了SH波作用下层状土层地震反应分析的随机波动分析方法。在这一方法中,将波动理论和随机振动理论结合起来,求解波动方程和土层地震反应的统计参数,可以准确而又方便地综合考虑地震波斜入射及基岩弹性刚度对土层地震反应的影响。随后进一步通过算例分析,讨论了基岩弹性刚度及SH波入射角度对半空间上均匀土层地震反应的影响及其规律,为工程中进行复杂土层的地震反应分析提供参考。     

3-D Free vibration analysis of thick functionally graded annular plates on Pasternak elastic foundation via differential quadrature method (DQM)

In this paper, the free vibration of functionally graded annular plates on elastic foundations, based on the three-dimensional theory of elasticity, using the differential quadrature method for different boundary conditions including simply supported–clamped, clamped–clamped and free–clamped ends is investigated. The foundation is described by the Pasternak or two-parameter model. A semi-analytical approach composed of differential quadrature method (DQM) and series solution are adopted to solve the equations of motions. The material properties change continuously through the thickness of the plate, which can vary according to power law, exponentially or any other formulations in this direction. The fast rate of convergence of the method is demonstrated, and comparison studies are carried out to establish its very high accuracy and versatility. Some new results for the natural frequencies of the plate are prepared, which include the effects of elastic coefficients of foundation, boundary conditions, material and geometrical parameters. The new results can be used as benchmark solutions for future researches.     

Free vibration analysis of continuous grading fiber reinforced plates on elastic foundation

The free vibration characteristics of rectangular continuous grading fiber reinforced (CGFR) plates resting on elastic foundations have been studied, based on the three-dimensional, linear and small strain elasticity theory. The foundation is described by the Pasternak or two-parameter model. The CGFR plate is simply supported at the edges and is assumed to have an arbitrary variation of fiber volume fraction in the thickness direction. Suitable displacement functions that identically satisfy the simply supported boundary conditions are used to reduce the equilibrium equations to a set of coupled ordinary differential equations with variable coefficients, which can be solved by differential quadrature method (DQM) to obtain natural frequencies. Convergence studies have been performed on CGFR plates on the elastic foundations. It is shown that the present method has a rapid convergent rate, stable numerical operation and very high accuracy. Besides results for CGFR plate with arbitrary variation of fiber volume fraction in the plate’s thickness are compared with discrete laminated composite plate. The main contribution of this work is to present useful results for continuous grading of fiber reinforcement in the thickness direction of a plate on elastic foundation and comparison with similar discrete laminate composite plate. Results indicate the advantages of using CGFR plate with graded fiber volume fractions over traditional discretely laminated plates.     

Application of the generalized rays to transient waves in an elastic half-space due to a buried line source

Summary The aim of this investigation is to study by means of the generalized rays the effects of a free surface on the propagation of elastic transient waves emanating from a line source of explosion, which varies with time as the Heaviside step function with rounded shoulders. This is accomplished by the numerical evaluation and analysis of the exact solutions provided by this theory. Graphs are obtained which show displacements and stresses as functions of time at three different receivers in the interior of an infinite medium and at the free surface of a homogeneous half-space. The character of surface responses, for short observation times, is the same as in the infinite medium, with the difference that they are all amplified (surface receiver effect). The late time surface responses are characterized by the presence of a smooth pulse representing the Rayleigh surface wave. The Rayleigh pulse in the non-vanishing surface stress takes its ultimate shape already close to the epicentre, while the Rayleigh pulse in the surface displacements developes fully at the remote distance from the epicentre.With 6 Figures     

Nonlinear dynamic response and vibration of imperfect shear deformable functionally graded plates subjected to blast and thermal loads

Based on Reddy's higher-order shear deformation plate theory, this article presents an analysis of the nonlinear dynamic response and vibration of imperfect functionally graded material (FGM) thick plates subjected to blast and thermal loads resting on elastic foundations. The material properties are assumed to be temperature-dependent and graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. Numerical results for the dynamic response and vibration of the FGM plates with two cases of boundary conditions are obtained by the Galerkin method and fourth-order Runge–Kutta method. The results show the effects of geometrical parameters, material properties, imperfections, temperature increment, elastic foundations, and boundary conditions on the nonlinear dynamic response and vibration of FGM plates.     

Nonlinear thermo-elastic bending of functionally graded carbon nanotube-reinforced composite plates resting on elastic foundations by dynamic relaxation method

In this study, the nonlinear thermo-elastic bending analysis of a functionally graded carbon nanotube-reinforced composite plate resting on two parameter elastic foundations is investigated. The material properties of the carbon nanotube-reinforced composite plates are assumed to be temperature dependent and graded in the thickness direction. The nonlinear formulations are based on a first-order shear deformation plate theory and large deflection von Karman equations. A dynamic relaxation method is employed to solve the plate nonlinear partial differential equations. The effects of volume fraction of carbon nanotubes, thermal gradient, temperature dependency, elastic foundation, boundary conditions, plate width-to-thickness ratio, aspect ratio, and carbon nanotubes distribution are studied in detail.