层状半空间中单桩对任意入射地震波的响应

本文以任意入射地震波作为初始运动输入，采用层状半空间中显式表达形式的动力Ｇｒｅｅｎ函数形成阶－土相互作用分析所需的土介质柔度矩阵，用梁单元模拟桩的运动，在文献［５］的基础上，建立了层状半空间中单桩对任意入射地震波响应的实用计算模型，研究了层状半空间中单桩对不同角度入射ＳＨ波、ＳＶ波和Ｐ波的动力响应，得到了一些新的结果。     

层状半空间中单桩对任意入射地震波的响应

本文以任意入射地震波作为初始运动输入，采用层状半空间中显式表达形式的动力Ｇｒｅｅｎ函数形成桩－土相互作用分析所需的土介质柔度矩阵，用梁单元模拟桩的运动，在文献〔５〕的基础上，建立了层状半空间中单桩对任意入射地震波响应的实用计算模型，研究了层状半空间中单桩对不同角度入射ＳＨ波、ＳＶ波和Ｐ波的动力响应，得到了一些新的结果。     

分析层状半空间对入射地震波响应的改进模型

采用层内位移线性近似的薄层元及基岩半空间刚度的Ｔａｙｌｏｒ级数展开技术，利用基岩地震动三分量反算入射波振幅，建立了层状半空间场地地震波响应分析的一种改进模型，分析了层状半空间对倾斜入射ＳＨ，ＳＶ和Ｐ波的动力响应．结果表明，本文模型不仅具有较高精度，而且非常便于数值处理和计算机编程     

横观各向同性层状场地对入射SH波的响应分析

本文采用横观各向同性层状弹性模型模拟半空间之上的层状了，推导了在ＳＨ波入射时这种场地土的动力刚度矩阵及基岩输入运动时场地呼应的计算公式，算例表明，横观各向同性层状场地与各向同性层状了频谱特性有明显的区别，应当引起重视。     

层状地基中埋管地基阻抗函数的分析方法

本文首先利用波函数展开法推导了弹性半空间中埋管的地基轴向阻抗函数计算公式.然后采用层状地基中无限长线激振荷载薄层法基本位移解,结合容积法求解了层状地基中埋管的地基轴向、垂直及水平阻抗函数.分别用两种方法计算了弹性全空间、弹性半空间地基内埋管的地基轴向阻抗函数,两者的计算结果符合良好,验证了用薄层法求解的可行性.本文还利用薄层法分析了弹性半空间内埋管的埋深对地基水平、垂直及轴向阻抗函数的影响;计算了弹性半空间内埋管的轴向刚度系数并与我国及日本的相关规范对比分析;计算分析了上海典型层状地基内地铁隧道的地基阻抗函数.     

用二次形函数薄层法分析弹性层状地基中的动力问题

薄层法是分析和模拟弹性波在层状介质中传播的一种半解析半数值方法。本文在土层垂直方向离散中利用Galerkin加权残值法推导出二次形函数薄层元的计算公式。采用薄层单元模拟半空间上的层状场地,模型底面用阻尼器边界或傍轴边界代替半空间。利用点源简谐荷载作用下的土层反应与其它数值分析方法的对比讨论薄层模型的设置指标。并用一次和二次两种形函数离散方法计算了层状地基中的面波频散曲线、圆形均布简谐荷载作用下弹性半空间的位移反应和半无限地基中单桩的竖向阻抗函数,分别讨论其计算精度。     

用薄层法分析层状地基中各种基础的阻抗函数

薄层法是分析和模拟弹性波在层状介质中传播的一种半解析半数值方法.采用薄层单元和傍轴边界分别模拟层状地基和弹性半空间.利用薄层法位移基本解和容积法推导了层状地基中基础-地基动力相互作用方程及块式基础、桩基础和承台群桩基础阻抗函数的统一计算公式.通过计算半无限弹性地基中桩基础、块式基础和二层地基上基础的阻抗函数验证了方法的适用性.进而计算了某实际层状地基中承台群桩基础的阻抗函数,并与试验结果进行对比,两者吻合较好.本文方法可用于分析弹性层状地基中各种基础的阻抗函数.     

舰船海底地震波形成机理的理论分析

航行舰船是一个很大的振动和噪声源,其振动和噪声引起的压力波经由流体介质传播到海底,引起海底岩层振动,产生弹性波并向远处传播,这种航行舰船在海底引起的弹性波称为舰船海底地震波。舰船海底地震波可用于识别舰船目标,作为水中武器的目标探测信号。基于波动理论,得到了舰船引起海底地震波的波动方程和有限元数值计算模型。利用该模型,对二维半无限空间层状海洋环境在水压场和极低频点声源作用下的海底地震波信号进行了数值模拟,得到了远场海底表面处加速度和水压的时域频域信号。结果表明,在二维半无限空间层状海洋环境条件下,舰船远场海底地震波主要由舰船极低频的噪声辐射引起,主要频率范围在1-7Hz。     

移动荷载下路面板-层状多相弹性地基的稳态响应

考虑路面板和地基的相互作用,将路面板作为三维弹性体,建立路面板-层状多相弹性地基动力响应的三维多相层状弹性半空间体模型,分析了移动荷载作用下路面板-多相弹性地基系统的动力响应.将移动单元法引入到两相饱和弹性介质的半解析方法中,构造了随荷载按照相同速度运动的移动层单元,基于移动坐标下两相饱和弹性介质的动力控制方程和边界条件,应用加权残数法建立了两相弹性介质移动层单元动力方程,该方程可退化为单相弹性介质移动层单元动力方程,基于此,建立了移动荷载下多相弹性地基与路面板系统的三维动态响应的统一的半解析方程.并以两相饱和弹性半空间地基-单相弹性地基-路面板所形成的路面结构为例,数值分析了荷载速度、饱和层渗透系数、弹性层厚度等参数对路面板位移和土体孔压响应的影响.研究结果表明移动单元法是研究移动荷载下路面结构动态响应的一种有效的方法.     

一种用于层状结构模型的先进计算方法

提出一种针对层状结构模型的先进计算方法。研究的层状结构通常为水平层状板或者层状半空间,结构由横观各向同性（TI）材料组成,材料对称轴指向分层方向。本文方法可以考虑材料的多场耦合特性,即热弹性、多孔弹性和磁电弹性耦合。基于最近提出的傅立叶-贝塞尔级数（FBS）向量函数系和双变量/位置（DVP）方法,建立了本文的先进计算方法。DVP能够无条件稳定地将层矩阵从一层传播到下一层。FBS向量函数系具有以下特点,（1）反映了具有明确类型的广义变形/波,（2）将展开系数预先计算为Love数,然后将其用于涉及问题的模拟。层状地球中的断层（或位错）作用、土-结构相互作用以及近地表地球剖面中的瞬态波等三个典型算例,证明了提出方法的准确性和有效性。     

The numerical solutions of Green's functions for transversely isotropic elastic strata

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Vibration of a transversely isotropic,simply supported and layered rectangular plate

The propagator matrix method is used in this paper to study the vibration of a transversely isotropic, simply supported and layered rectangular plate. A new system of vector functions is constructed to deal with general surface loading, and general solutions and layer matrices of exact closed form are obtained in this system. The particular solution for forced vibration, and the characteristic equations for free vibration of various surface conditions are then obtained by simple multiplication of layer matrices. These results are presented in such a way that the dilatational and distortional modes of vibration are separated. As a special case of the layered plate, results for the corresponding homogeneous thick plate are also derived. They are presented in a very simple form, and contain the previous results for the static transversely isotropic and the dynamic isotropic plates.     

Free vibration of a FGPM circular plate placed in a uniform magnetic field

In this paper, free vibration of a circular plate composed of a transversely isotropic functionally graded piezoelectric material (FGPM) placed in a uniform magnetic field is investigated. Material properties are assumed to depend on the thickness of the circular plate and they are expressed as the same exponential function of h. The problem of free vibration for the transversely isotropic FGPM circular plate with clamped and simply supported boundary conditions is solved by means of the state space method. Numerical examples and some useful discussions are given to demonstrate the significant influence of material inhomogeneity, and adopting a certain value of the graded index can optimize structures of the circular plate. This will be of particular importance in modern engineering design.     

Non-axisymmetrical vibration of elastic circular plate on layered transversely isotropic saturated ground

The non-axisymmetrical vibration of elastic circular plate resting on a layered transversely isotropic saturated ground was studied.First,the 3-d dynamic equations in cylindrical coordinate for transversely isotropic saturated soils were transformed into a group of governing differential equations with 1-order by the technique of Fourier ex- panding with respect to azimuth,and the state equation is established by Hankel integral transform method,furthermore the transfer matrixes within layered media are derived based on the solutions of the state equation.Secondly,by the transfer matrixes,the general solutions of dynamic response for layered transversely isotropic saturated ground excited by an arbitrary harmonic force were established under the boundary conditions, drainage conditions on the surface of.ground as well as the contact conditions.Thirdly, the problem was led to a pair of dual integral equations describing the mixed boundary- value problem which can be reduced to the Fredholm integral equations of the second kind solved by numerical procedure easily.At the end of this paper,a numerical result concerning vertical and radical displacements both the surface of saturated ground and plate is evaluated.     

压电板壳自由振动的三维精确分析

本文简要评述了压电材料板壳结构的研究现状,着重介绍了近年来我们在压电板壳三维分析方面所做的工作：（1）四边简支横观各向同性压电矩形板的状态空间分析方法：（2）横观各向同性压电圆板和环板的状态空间分析方法;（3）横观各向同性压电圆柱壳和球面各向同性压电球壳耦合振动的精确分析。这些工作都直接从压电弹性力学三维基本方程出发,不引进任何变形假设,因此可作为二维简化理论和数值计算方法的校核标准。文末对今后压电材料板壳的研究方向也作了展望。     

Non-linear vibrations of transversely isotropic rectangular'' plates

The large amplitude free flexural vibration of transversely isotropic rectangular plate, incorporating the effects of transverse shear and rotatory inertia, is studied using the von Karman field equations. A mode shape, consisting of three generalised-coordinates together with the Galerkin technique, results in a system of three non-linear simultaneous ordinary differential equations which govern the motion of the plate. These equations are integrated using a fourth-order Runge-Kutta method to obtain the period for each amplitude of vibration. The non-linear period vs amplitude behaviour is of the hardening type and it is also found that transverse shear and rotary inertia effects increase the period and that this increase is quite significant even for thin transversely isotropic plates. The results are compared with earlier results which were based on a one-term or one generalised coordinate solution and using the Berger approximation or the von Karman field equations.     

Exact solutions for free vibration of transversely isotropic piezoelectric circular plates

By employing the general solution for coupled three-dimensional equations of a transversely isotropic piezoelectric body, this paper investigates the free vibration of a circular plate made of piezoelectric material. Three-dimensional exact solutions are then obtained under two specified boundary conditions, which can be used for both axisymmetric and non-axisymmetric cases. Numerical results are finally presented. The project supported by the National Natural Science Foundation of China (No. 19872060)     

On the boundary conditions for transversely isotropic piezoelectric plates

By invoking the theorem of work reciprocity for piezoelectric media, necessary conditions, which the prescribed edge data of the plate must fulfill in order that it should generate a decaying state within the plate, are established through generalizing the method proposed by Gregory and Wan. These decaying state conditions for the case of axisymmetric deformation of a transversely isotropic piezoelectric circular plate when stress and electric displacement conditions are imposed on the plate edge are derived explicitly, which are then used for the formulation of boundary conditions for the plate theory solution (or the interior solution). Also an analytical solution of the axisymmetric decaying state of transversely isotropic piezoelectric circular plates is derived. Furthermore, the corresponding necessary conditions for the axisymmetric deformation of elastic circular plates are indeed reproduced directly.     

An exact closed-form procedure for free vibration analysis of laminated spherical shell panels based on Sanders theory

This paper deals with closed-form solutions for in-plane and out-of-plane free vibration of moderately thick laminated transversely isotropic spherical shell panels on the basis of Sanders theory without any usage of approximate methods. The governing equations of motion and the boundary conditions are derived using Hamilton’s principle. The highly coupled governing equations are recast to some uncoupled equations by introducing four potential functions. Also, some relations were presented for the unknowns of the original set of equations in terms of the unknowns of the uncoupled equations. According to the proposed analytical approach, both Navier and Lévy-type explicit solutions are developed for moderately thick laminated spherical shell panels. The efficiency and high accuracy of the present approach are investigated by comparing some of the present study with the available results in the literature and the results of 3D finite element method. The effects of various shell parameters like shear modulus ratio of transversely isotropic materials and curvature ratio on the natural frequencies are studied. Clearly, the proposed solutions can accurately predict the in-plane and out-of-plane natural frequencies of moderately thick transversely isotropic spherical shell panels.