复阻尼结构动力方程的高斯精细时程积分法

复阻尼振动系统的瞬态响应通常只能在频域内求解。该文根据复阻尼理论应遵循对偶复化的原则,结合精细积分指数矩阵和高斯积分的运算方法,通过理论推导,给出了复阻尼结构动力方程的高斯精细时程积分法。分别采用Newmark-法和高斯精细时程积分法计算了复阻尼多自由度系统地震时程响应,并与频域法（视为精确解）的计算结果进行比较。结果...     

弹性地基上自由边矩形板承受冲击荷载的动力响应解析解

利用双参变量的Stockes变换^[2],给出弹性地基上自由边矩形板承受冲击荷载的动力响应问题的cc型级数的解析解,并运用钟万勰^[7]提出的对线性定常结构动力系统的精细时程积分法,以弹性地基上自由边矩形板中心承受矩形波冲击荷载为例,给出瞬态时程的数值计算结果。     

粘弹性层状地基上板的动力响应及其参数识别方法

本文系统地研究了粘弹性层状地基上板的动力响应及其结构材料参数识别方法。在一次样条半解析法求解粘弹性地基动力柔度系数[1]的基础上,应用子结构法求解了粘弹性层状地基上板的动力响应。应用快速富利叶变换将落锤式弯沉仪(FWD)所记录的荷载和时程反应曲线转化为频域内的一系列稳态振动[2],[3]。进而利用系统识别技术在频率域内反演结构材料参数。数值分析结果表明,该方法能有效地识别结构参数,从而为进一步研究FWD在混凝土道面的无损检测和承载力评价提供了基础。     

基础隔震结构基于Clough-Penzien谱随机地震响应分析的复模态法

对多自由度基础隔震结构基于Clough-Penzien谱随机地震响应问题进行了系统研究。首先建立了运动方程，然后用第一振型将上部结构展开，针对所得方程为非经典阻尼、非对称质量和非对称刚度情况，用复模态法和扩阶法解耦，获得了以第一振型表示的结构随机地震响应的解析解，对单自由度隔震体系，此解即为结构响应的精确解，从而建立了两自由度体系在任意非经典阻尼、非对称质量和非对称刚度情况下基于Clough—Penzien谱随机地震响应解析解分析的一般方法。该方法也可用于带TMD、TLD结构、无损伤“加层减震”加固结构的随机地震响应分析及其基于动力可靠性约束的优化设计。     

竖向地震作用下充满液体管道的地震反应分析

用半解析法求解竖向地震作用下充满液体管道的弯曲振动反应。针对某些介质和结构参数，给出了一些数值结果，得出了管道内部液体压力对管道动力响应的影响及相对地震反应对其动力响应影响的若干初步结论。对地上充满液体管道的地震效应作了一些理论上的探讨。     

轨道结构在移动荷载作用下的周期解析解

为研究列车振动在地表的传播规律,推导了轨道结构在移动荷载作用下动力响应的解析解形式。文中首先以Duhamel积分为基础,应用动力互等定理,得到了移动荷载作用下,半无限弹性空间体上任意点的动力响应的一般表达式;然后在该式的基础上,针对轨道结构的周期性特点,将荷载沿钢轨的移动问题转化为拾振点以L为周期向反方向跳跃式移动与荷载只在一个轨枕间距L内移动的组合移动问题。以此,将一个从-∞到+∞的积分问题转化为了任意点频域周期解析的叠加问题,从而得到了轨道结构在移动荷载作用下动力响应的新的解析解形式。     

爆炸荷载作用下地下拱结构动力分析

为了准确分析爆炸作用下地下拱结构的动力响应,利用阻尼系数来表达土介质与结构的动力相互作用,建立结构运动方程。由于结构动态响应方程的复杂性,在计算中对结构进行了简化,忽略了结构剪切力、转动惯性矩以及切向力的影响,并且假设拱结构在切线方向是不可延展的。利用振型分解法获得了两端固支拱结构在爆炸荷载作用下的动态响应的解析解。对圆心角为120°的拱结构单元进行了计算,得出了位移、速度和加速度时程响应曲线,探讨了参数响应的最大值与比例爆距之间的关系,得到了最大值与比例爆距之间的关系曲线。利用解析计算得到了结构弯矩的包络图。     

一种多自由度阻尼体系动力问题的高阶分析方法

传统动力时程直接积分法多采用低阶数值格式,需要选择非常小的时间步距才能获得满足精度要求的动力分析结果.该文将结构动力时程分析的积分求微法推广至多自由度情形,发展了一种具有较高计算效率的多自由度阻尼体系的动力时程高阶分析方法.将相邻的ρ个时步组成一个待求解时段,基于多自由度体系动力响应积分解,以精细积分法结合秦九韶算法计...     

阻尼矩阵选取对核电厂结构地震响应的影响分析

已有研究表明时程动力法中阻尼矩阵的确定对复杂结构工程的地震响应有明显的影响,而核电厂安全相关结构在抗震分析时通常采用时程动力法。为研究阻尼矩阵的选取对核电厂结构的地震响应的影响,从比例阻尼拟合的精度出发,基于结构不同振型对结构产生的影响程度入手,建立更为精确的结构阻尼模型,即等效比例阻尼,并进一步考虑结构自振特性以加权最小二乘法拟合确定等效比例阻尼系数,提出了核电厂结构地震响应分析相应的计算方法。计算结果表明,该方法较传统比例阻尼的方法更接近精确解,是核电工程抗震分析的一个实用参考应用。     

索穹顶结构风振响应时程分析

采用改进的AR法和相应自编程序,模拟出索穹顶屋盖结构各节点的脉动风速时程,将流固耦合作用引入结构的动力平衡方程,进行了结构风振响应时程分析。通过结构典型节点处的位移响应和关键构件的内力响应计算结果的分析,给出结构的位移风振系数和内力风振系数,并与结构风振响应频域分析结果加以对比,得到一些有意义的结果和结论。     

Buckling analysis of moderately thick FG carbon nanotube reinforced composite conical shells under axial compression by DQM

A semi-analytical method is presented to study the buckling of moderately thick carbon nanotube reinforced composite conical shells under axial compression. Material properties are assumed to be graded across the shell thickness. In order to derive the equilibrium equations of the shell, first-order shear deformation theory is used. Then, the partial differential equations are transformed to algebraic type by using the differential quadrature method. To validate the results obtained in this study, comparisons are made with the outcomes of previous studies. Finally, the effects of the geometry of the shell, circumferential mode number, volume fraction of the carbon nanotube, and boundary conditions are studied.     

Frequency domain analysis of elastic bounded domains using a new semi-analytical method

In this paper, a new semi-analytical method is developed for solving two-dimensional elastodynamic problems in the frequency domain, employing Fast Fourier Transform. Using specific non-isoparametric elements, the boundary of the problem’s domain is discretized. By employing higher-order Chebyshev mapping functions, special shape functions, Clenshaw–Curtis quadrature, and implementing a weak form of weighted residual method, coefficient matrices of equation system become diagonal. This fact results in a set of decoupled Bessel differential equations to be used for solving the whole system. This means that the governing Bessel differential equation for each degree of freedom (DOF) becomes independent from other DOFs of the domain. For each DOF, the Bessel differential equation is solved for a specific frequency. Finally, the time history of responses may be obtained by using Inverse Fast Fourier Transform. Three numerical examples are presented to demonstrate the accuracy of the present new method.     

Free vibration analysis of functionally graded annular plates by state-space based differential quadrature method and comparative modeling by ANN

This paper deals with three-dimensional analysis of functionally graded annular plates through using state-space based differential quadrature method (SSDQM) and comparative behavior modeling by artificial neural network (ANN) for different boundary conditions. The material properties are assumed to have an exponent-law variation along the thickness. A semi-analytical approach which makes use of state-space method in thickness direction and one-dimensional differential quadrature method in radial direction is used to obtain the vibration frequencies. The state variables include a combination of three displacement parameters and three stress parameters. Numerical results are given to demonstrate the convergency and accuracy of the present method. Once the semi-analytical method is validated, an optimal ANN is selected, trained and tested by the obtained numerical results. In addition to the quantitative input parameters, support type is also considered as a qualitative input in NN modeling. Eventually the results of SSDQM and ANN are compared and the influence of thickness of the annular plate, material property graded index and circumferential wave number on the non-dimensional natural frequency of annular functionally graded material (FGM) plates with different boundary conditions are investigated. The results show that ANN can acceptably model the behavior of FG annular plates with different boundary conditions.     

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.     

3-D free vibration analysis of thick functionally graded annular sector plates on Pasternak elastic foundation via 2-D differential quadrature method

Early studies on annular sector plate vibrations were focused on two-dimensional theories, such as the classical plate theory and the first- and the higher-order shear deformation plate theories. These plate theories neglect transverse normal deformations and generally assume that a plane stress state of deformation prevails in the plate. These assumptions may be appropriate for thin plates. In this paper, free vibration of thick functionally graded annular sector plates with simply supported radial edges on a two-parameter elastic foundation, based on the three-dimensional theory of elasticity, using differential quadrature method for different circular edge conditions including simply supported-clamped, clamped–clamped, and free-clamped is investigated. A semi-analytical approach composed of differential quadrature method and series solution is adopted to solve the equations of motion. The material properties change continuously through the thickness of the plate, which can vary according to a power law, exponentially, or any other formulations in this direction. 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 research.     

Solution of anisotropic nonuniform plate problems by the differential quadrature finite difference method

The differential quadrature finite difference method (DQFDM) has been proposed by the author. The finite difference operators are derived by the differential quadrature (DQ). They can be obtained by using the weighting coefficients for DQ discretizations. The derivation is straight and easy. By using different orders or the same order but different grid DQ discretizations for the same derivative or partial derivative, various finite difference operators for the same differential or partial differential operator can be obtained. Finite difference operators for unequally spaced and irregular grids can also be generated through the use of generic differential quadrature (GDQ). The derivation of higher order finite difference operators is also easy. The DQFDM is used to solve anisotropic nonuniform plate problems. Numerical results are presented. They demonstrate the DQFDM. Received: 11 January 2000     

Semi-analytical solution for orthotropic piezoelectric laminates in cylindrical bending with interfacial imperfections

The static and dynamic problems of an imperfectly bonded, orthotropic, piezoelectric laminate in cylindrical bending are investigated based on the equations of piezoelasticity. A general spring layer is adopted to model the bonding imperfection at the interfaces of the laminate. A recently proposed semi-analytical approach, which makes a hybrid use of the state-space method (SSM) and the differential quadrature method (DQM), is employed. This approach allows us to efficiently analyze the laminate with a large number of plies and with arbitrary boundary conditions at the two ends. Numerical examples are considered and discussed to show the efficiency of the present semi-analytical solution and the effects of relevant parameters on the behavior of the laminate.     

摄动DQ法分析板的大挠度热弯曲

本文给出了求解板的大挠度热弯曲问题的摄动DQ法。该方法由二阶摄动得到板的大挠度热弯曲问题的一组线性摄动方程后运用DQ法进行求解,具有良好的计算精度和计算效率。     

The 3-D thermoelastic boundary element method: semi-analytical integration for subparametric triangular elements

In this paper a semi-analytical integration scheme is described which is designed to reduce the errors that can result with the numerical evaluation of integrals with singular integrands. The semi-analytical scheme can be applied to quadratic subparametric triangular elements for use in thermoelastic problems. Established analytical solutions for linear isoparametric triangular elements are combined with standard quadrature techniques to provide an accurate integration scheme for quadratic subparametric triangular elements. The use of subparametric elements provides an efficient means for coupling thermal and elastostatic analyses. It is possible for the same mesh to be employed, with linear isoparametric elements used for thermal analysis and quadratic subparametric elements used for deformation analysis. Numerical tests are performed on simple test problems to demonstrate the advantages of the semi-analytical approach which is shown to be orders of magnitude more accurate than standard quadrature techniques. Moreover, the expected increased accuracy with subparametric elements is also demonstrated. © 1998 John Wiley & Sons, Ltd.     

Boundary reduction technique and triangular differential quadrature domain decomposition method for polygonal region

The differential quadrature method (DQM) is an attractive numerical method with high efficiency and accuracy. But the conventional DQM is limited in its application to regular regions by using functional values along a mesh line to approximate derivatives. To deal with problems on irregular geometric domains, coordinate transformation has to be conducted. The triangular differential quadrature method (TDQM) proposed by Zhong [Zhong H. Triangular differential quadrature. Commun Numer Meth Eng 2000; 16:401–8; Zhong H. Triangular differential quadrature and its application to elastostatic analysis of Reissner plates. Int J Solids Struct 2001; 38:2821–32], avoid the coordinate transformation. In this paper, the domain decomposition method (DDM) is used for the elliptical boundary problems on a pentagonal region. In every sub-domain, we solve the partial differential equations with TDQM. With boundary reduction technique, the functional values on internal points can be eliminated. The system of equations, which satisfied by the boundary points, can be obtained. Numerical results show that triangular differential quadrature domain decomposition method (TDQDDM) is easy and effective for treating the problems on irregular region.