基于经验格林函数方法的爆破振动预测

通过单孔爆破振动监测实验,获取点振源的经验格林函数,利用单孔振源的格林函数来叠加合成群孔爆破振动时程。根据经验格林函数法原理建立了相应的爆破振动预测方法,编制了专用的预测分析软件。通过实例验证,若应用电子雷管精确控制起爆时差,预测目标点的群孔爆破振动波形与实测结果相当吻合。该方法获得的爆破振动预测准确度显著高于传统的回归统计分析法,不仅可以预报爆破振动峰值速度,也可对频率及持续振动时间进行预测.充分体现了爆破地震波的时频域信息,爆破振动的预测结果更全面。     

基于经验格林函数方法的爆破振动预测

通过单孔爆破振动监测实验,获取点振源的经验格林函数,利用单孔振源的格林函数来叠加合成群孔爆破振动时程。根据经验格林函数法原理建立了相应的爆破振动预测方法,编制了专用的预测分析软件。通过实例验证,若应用电子雷管精确控制起爆时差,预测目标点的群孔爆破振动波形与实测结果相当吻合。该方法获得的爆破振动预测准确度显著高于传统的回归统计分析法,不仅可以预报爆破振动峰值速度,也可对频率及持续振动时间进行预测.充分体现了爆破地震波的时频域信息,爆破振动的预测结果更全面。     

Computation of Dyadic Green's Functions for Electrodynamics in Quasi-Static Approximation with Tensor Conductivity

Homogeneous non-dispersive anisotropic materials, characterized by a positive constant permeability and a symmetric positive definite conductivity tensor, are considered in the paper. In these anisotropic materials, the electric and magnetic dyadic Green's functions are defined as electric and magnetic fields arising from impulsive current dipoles and satisfying the time-dependent Maxwell's equations in quasi-static approximation. A new method of deriving these dyadic Green's functions is suggested in the paper. This method consists of several steps: equations for electric and magnetic dyadic Green's functions are written in terms of the Fourier modes; explicit formulae for the Fourier modes of dyadic Green's functions are derived using the matrix transformations and solutions of some ordinary differential equations depending on the Fourier parameters; the inverse Fourier transform is applied to obtained formulae to find explicit formulae for dyadic Green's functions.     

变截面压电层合梁自由振动分析

考虑压电材料的质量效应和刚度效应,将表面粘贴或埋入式压电悬臂梁看作变截面梁,研究压电材料对智能结构固有特性的影响。基于一阶剪切变形理论导出压电层合梁的抗弯刚度和横向剪切刚度,计及梁的剪切变形和转动惯量,采用Timoshenko理论推导变截面压电层合梁的频率方程。给出了T300/970压电层合梁和硬铝压电层合梁的前3阶固有频率,并和有限元结果、等截面梁的计算结果进行比较。计算表明,压电材料对压电结构固有频率和固有振型的影响显著,在以振动控制为目标的压电结构动力学建模过程中,有必要考虑压电材料的质量和刚度。     

利用格林函数求解三阶两点边值问题

本文讨论了利用格林函数方法对一类三阶常微分方程的两点边值问题进行数值求解。由三阶微分算子引出了格林函数,再根据边界条件构造了特定的格林函数,然后用数值例子加以说明。     

箱形正交异性矩形板结构的自由振动分析

箱形正交异性矩形板结构为由四块板组成的结构。可以用一般解析解来求解这种结构的自由振动问题。这种解能用于求解板具有任意边界。对于每块板,其上边和下边具有边界条件,而在相连的两块板边则具有连续性条件。由四块板的全部条件方程式即可求解自然频率及其振型。为求解所有频率,可利用变形的对称和反对称条件,以矩形的和正方形的板结构为例进行了计算和分析。     

Nonlinear free vibration of a composite rectangular specially-orthotropic plate with variable fiber spacing

The geometrically nonlinear free vibration of a composite rectangular plate with variable fiber spacing is investigated. The investigation is limited to a single ply composite having straight and parallel fibers. The fibers are distributed more densely in the central region where high stiffness is needed than in other regions. The assumptions of von Karman’s nonlinear thin plate theory are made. The problem is solved numerically using the hierarchical finite element method. The nonlinear equations of free motion are mapped from the time domain to the frequency domain using the harmonic balance method. The resultant nonlinear equations are solved iteratively using the linearized updated mode method. Results for the fundamental linear and nonlinear frequencies are obtained for simply supported and clamped composite square plates with three variable distributions of E-Glass, Graphite, and Boron fibers in Epoxy matrices. The efficiency of the hierarchical finite element procedure is demonstrated through convergence and comparison with published data. The variable fiber spacing, fiber volume fraction, type of fiber material, and boundary conditions are shown to influence the hardening behavior.     

Green's functions for Kirchhoff plates of irregular shape

A method is proposed for the construction of Green's functions for the Sophie Germain equation in regions of irregular shape with mixed boundary conditions imposed. The method is based on the boundary integral equation approach where a kernel vector function B satisfies the biharmonic equation inside the region. This leads to a regular boundary integral equation where the compensating loads and moments are applied to the boundary. Green's function is consequently expressed in terms of the kernel vector function B, the fundamental solution function of the biharmonic equation, and kernel functions of the inverse regular integral operators. To compute moments and forces, the kernel functions are differentiated under the integral sign. The proposed method appears highly effective in computing both displacements and stress components.     

Evaluation of the three-dimensional elastic Green's function in anisotropic cubic media

By using the Fourier transforms method, the three-dimensional Green's function solution for a unit force applied in an infinite cubic material is evaluated in this paper. Although the elastic behavior of a cubic material can be characterized by only three elastic constants, the explicit solutions of Green's function for a cubic material are not available in the literatures. The central problem for explicitly solving the elastic Green's function of anisotropic materials depends upon the roots of a sextic algebraic equation, which results from the inverse Fourier transforms and is composed of the material constants and position vector parameters. The close form expression of Green's function is presented here in terms of roots of the sextic equation. The sextic equation for an anisotropic cubic material is discussed thoroughly and specific results are given for possible explicit solutions.     

轴向运动黏弹性夹层板的多模态耦合横向振动

基于薄板小挠度理论和Kelvin-Voigt黏弹性本构方程, 建立了轴向运动黏弹性夹层板横向振动控制方程, 研究了其横向振动特性。采用一阶和二阶Galerkin截断得到夹层板横向振动的特征方程, 讨论了两种夹心层所占总厚度比率下轴向运动速度对其横向振动特性的影响。研究表明: 在未超过临界速度前, 无论一阶还是二阶截断, 在定性描述系统特征上二者相同, 但一阶截断不适合描述轴向运动速度超过临界速度的情形; 对四边简支黏弹性夹层板, 临界速度和发生耦合模态颤振的速度随着夹心层比率的减少逐渐增大。     

基于解析法的非均匀张力作用下运动薄膜的稳定性

目的针对高速印刷运动薄膜在传输制备过程中由于相邻导纸辊等支撑副的平行度误差,料膜沿宽度方向张力分布易出现不均匀性问题,研究提高印刷设备的工作稳定性的方法。方法根据D’Alembert原理建立运动薄膜的横向振动微分方程,引入无量纲量,将微分方程转化为无量纲形式,利用解析法求解运动薄膜的复频率方程。结果得到不同参数下无量纲复频率与无量纲速度的变化曲线,当增大张力系数、张力比,或者减小长宽比时,薄膜系统达到发散失稳的临界无量纲速度增大,运动薄膜系统越稳定。结论获得了在不同张力比、张力系数、长宽比等参数下薄膜系统达到发散失稳的临界无量纲速度。     

Green''s function method solution of the Reissner''s plate problem

Green's functions can play a significant role in the development of numerical procedures based on the BEM. For that reason the construction of Green's functions and matrices is of great practical importance. In this study, the extension of the Green's function formalism is introduced to Reissner's plate theory, which accounts for the effect of transverse normal stress and transverse shear deformation. The development of Green's matrix for the governing boundary value problem is described based on the separation of variables. The explicit expressions for the entries of Green's matrix are derived. The algorithm is developed for computation of the stress-strain for a rectangular plate. A validation example is presented, illustrating an equal level of accuracy attained for both displacement and stress.     

圆形薄膜自由振动的理论解

本文研究圆形薄膜的自由振动。首先根据哈密顿原理建立薄膜横向振动的动力学方程,然后采用分离变量法,导出时间t\、径向坐标r和环向坐标 变量分离的2个二阶常微分方程和1个贝塞尔方程并分别求解,求得周边固定圆形薄膜、扇形薄膜自由振动的理论解,从而得到固有频率及其振型的解析表达式。最后,应用ANSYS有限元计算软件计算上述几种类型自由振动的频率及其模态并与理论解比较。ANSYS有限元数值解与理论解二者十分接近,理论解是有限元数值解的下限。     

Benchmark solutions of stationary random vibration for rectangular thin plate based on discrete analytical method

This paper aims to accurately and efficiently achieve the benchmark solutions of stationary stochastic responses for rectangular thin plate. Firstly, the exact solutions of free vibration for thin plate with SSSS, SSSC, SCSC, SFSF, SSSF and SCSF boundary conditions are introduced to random vibration analysis. Based on pseudo excitation method (PEM), the analytical power spectral density (PSD) functions of the transverse deflection, velocity, acceleration and stress responses for thin plate under random base acceleration excitation are derived. Subsequently, to enhance computational efficiency, the discrete analytical method (DAM) that realizes the discretization for the modal coordinates and frequency domain is proposed. Finally, the efficiency of DAM and the accuracy of benchmark solutions are scrutinized by comparison with the analytical solutions and finite element solutions.     

Construction of Green's function using null-field integral approach for Laplace problems with circular boundaries

A null-field approach is employed to derive the Green's function for boundary value problems stated for the Laplace equation with circular boundaries. The kernel function and boundary density are expanded by using the degenerate kernel and Fourier series, respectively. Series-form Green's function for interior and exterior problems of circular boundary are derived and plotted in a good agreement with the closed-form solution. The Poisson integral formula is extended to an annular case from a circle. Not only an eccentric ring but also a half-plane problem with an aperture are demonstrated to see the validity of the present approach. Besides, a half-plane problem with a circular hole subject to Dirichlet and Robin boundary conditions and a half-plane problem with a circular hole and a semi-circular inclusion are solved. Good agreement is made after comparing with the Melnikov's results.     

Thin plate spline radial basis function for the free vibration analysis of laminated composite shells

In this paper, the free vibration characteristics of laminated composite cylindrical and spherical shells are analyzed by the first-order shear deformation theory and a meshless global collocation method based on thin plate spline radial basis function. The singularity of thin plate spline radial basis function is eliminated by adding infinitesimal to the zero distance. Several numerical examples are used to show convergence of the present method and choose the proper shape parameter. It is found that the natural frequencies computed by thin plate spline radial basis function with shape parameter m = 4 converge most rapidly. In the comparison study, the present results are in good agreement with the results of Reddy and Liu [8] and Ferreira et al. [21].     

聚乙烯醇复合膜的制备

以亲水性的聚乙烯醇为原料，采用机械涂敷法制备复合纳滤膜．考查了基膜、聚乙烯醇的浓度、交联剂的浓度及配比、涂层厚度、交联时间以及热处理等对膜分离性能的影响，确定了最终制备条件．在一定的温度和湿度条件下，在截留相对分子质量为100000的基膜上，通过5％的聚乙烯醇溶液与1％的戊二醛的交联反应，研制了截留相对分子质量为600的PVA复合纳滤膜。     

随从力作用下运动薄膜的非线性强迫振动特性研究

研究随从力作用下运动印刷薄膜的非线性强迫振动特性。基于Von Karman薄板理论推导出轴向运动薄膜的非线性振动方程,应用Galerkin方法对振动偏微分方程组进行离散,利用4阶龙格-库塔法对微分方程进行求解,得出薄膜非线性振动的时程图、相图、Poincare截面图和分岔图。分析了初始条件、随从力和长宽比对薄膜振动特性的影响。研究结果得出了薄膜稳定工作区间和发散失稳区间。     

Static and free vibration analyses of rectangular plates by the new version of the differential quadrature element method

A new version of the differential quadrature method is presented in this paper to overcome the difficulty existing in the ordinary differential quadrature method for applying multi‐boundary conditions in two‐dimensional problems. Since the weighting coefficients of the first derivative are the same as for the ordinary differential quadrature method even with the introduction of multi‐degree‐of‐freedom at the boundary points, the method is easier to extend to two‐ or three‐dimensional problems. A new version of the differential quadrature plate element has been established for demonstration. The essential difference from the existing old version of the differential quadrature plate element is the way the weighting coefficients are determined. The methodology is worked out in detail and some numerical examples are given to show the efficiency of the present method. Copyright © 2004 John Wiley & Sons, Ltd.     

基于Chebyshev-变分法的复杂开口形状矩形薄板弯曲振动特性分析

针对复杂开口形状的矩形薄板弯曲振动问题,提出一种基于Chebyshev-变分原理的建模方法,建立弹性边界条件下不同开口形状矩形薄板弯曲振动模型。采用边界约束因子模拟弹性边界条件,视开口部分为一种物理属性为零的特殊薄膜。将板的横向位移展开成双重Chebyshev多项式级数形式,建立薄板的拉格朗日泛函,利用变分法推导薄板的特征方程并求得固有频率及对应振型。开展开口薄板模态试验研究,对比理论计算结果与试验结果及有限元结果,验证该方法及模型的准确性和有效性。研究边界约束和开口形状对弯曲振动特性的影响。结果表明:开口形状对结构低阶固有频率影响较小,对高阶固有频率影响较大;开口形状的改变对结构奇数阶固有频率的影响大于对偶数阶固有频率的影响。