考虑损伤效应的粘弹性层合板的非线性动力响应分析

扩展了Ladeveze 的复合材料单层板的损伤模型, 使之可用于考虑剪切粘弹性的复合材料层合板的损伤分析, 基于Von Karman 方程, 建立了考虑损伤效应的粘弹性复合材料层合板的非线性动力学方程, 且应用有限差分法和迭代法进行求解。数值结果表明, 考虑结构的损伤和损伤演化时, 结构的非线性动力响应将发生显著的变化。     

粘弹性Timoshenko梁非线性动力学行为的微分求积分析

对有限变形条件下,Timoshenko粘弹性梁非线性分析的数学模型应用推广的微分求积方法进行空域的离散,得到了简洁的矩阵形式的非线性数值逼近公式,时域上引进新的变量,得到了简支粘弹性梁运动的简化模型.然后利用非线性动力学中数值方法,分析了粘弹性Timoshenko梁的动力学行为.同时,为表明该方法的可靠性和有效性,研究了DQ解的收敛性和精确性.并考察了梁的材料、几何等参数对非线性粘弹性梁的动力学特性的影响.     

非线性粘弹性桩耦合运动中的混沌分析

研究轴向周期载荷作用下非线性粘弹性桩纵横向耦合运动中的混沌运动。桩体材料满足Leaderman非线性粘弹性本构关系和近似的非线性几何关系，考虑桩体发生纵横向运动的耦合，得到的方程为耦合的非线性偏微分一积分方程；利用Galerkin方法将方程简化并进行数值计算，揭示非线性粘弹性桩的混沌运动和分岔等动力学行为。     

粘弹性复合材料层合板壳的动力稳定性分析

分析面内周期激励下粘弹性层合平板以及轴向周期荷载作用下粘弹性层合圆柱壳的动力稳定性。设粘弹性复合材料服从Boltzmann积分型本构关系，其松弛模量由Prony—Dirichlet级数表示，基于薄板与薄壳理论，分别得到对称正交铺设层合板与层合圆柱壳的微分-积分型动力学方程，并应用谐波平衡法直接求解，忽略积分运算所产生的衰减项，导出确定动力不稳定区域边界的特征方程。分析结果表明，主要动力不稳定区域的缩小与材料的粘性参数以及结构横向振动的基频密切相关。     

脉动流作用下粘弹性直管动力学特性分析

在Hamilton体系中应用精细积分法分析脉动流作用下粘弹性管道的动力学响应特性。首先建立了Hamilton体系下输送振荡流粘弹性直管的辛对偶正则方程组,接着推导了求解非线性运动方程的线性插值精细积分法,最后分析了不同流速、不同激振频率下输流直管非线性动力学特性。数值计算结果表明该方法能快速高效求解输流管道运动方程,计算精度令人满意。     

正弦型黏弹性拱的非线性动力学行为研究

利用分数导数的本构关系建立了粘弹性拱的控制方程,采用Galerkin方法简化了拱的数学模型。提出一种求解含分数算子的非线性方程的数值方法,并利用该方法对控制方程进行求解。考察载荷参数、材料参数对拱动力响应的影响。运用非线性动力学中各种经典的分析方法,如时程曲线、功率谱、相图、庞加莱截面等,判别并揭示了粘弹性拱的丰富的动力学行为。     

超音速流动中粘弹性圆柱壳的稳定性

基于薄壳的Karman-Donnell假设、空气动力学中的一阶活塞理论和粘弹性力学中的Boltzmann叠加原理,给出了超音速流动中粘弹性圆柱壳的数学模型。在空域上采用Galerkin方法,并在时域上通过引进新变量,将原来的积分－偏微分系统简化为高维微分系统。利用非线性动力学中的多种方法,考察了自由流动压对粘弹性圆柱壳稳定性的影响。发现气动粘弹性圆柱壳在径向周期激励下具有两种稳定的运动和两种不稳定的运动。     

损伤粘弹性桩基的非线性动力学行为

在有限变形的假设下，将孔洞作为一种分布损伤建立了粘弹性地基上具有损伤的粘弹性Timoshenko梁的静／动力学行为的初边值问题，并用此来模拟土中具有损伤的桩基非线性动力学行为，其中，本构模型是用具有孔洞的粘弹性固体的卷积方法所表示的，并且地震激励等价于一种横向力的作用。利用Galerkin方法对数学模型进行了简化，得到了一阶和二阶简化系统。非线性动力学中的数值方法被用来求解简化系统，数值上得到了系统的时程曲线、功率谱、相平面图、Poincare截面和分叉图等，讨论了地基和桩基材料参数与载荷参数对桩基动力学行为的影响，也考察了损伤对动力学行为的影响。可以看到，具有损伤的粘弹性桩基构成的动力学系统具有丰富的动力学行为。     

非线性不对称弹性支承车辆-基础系统动力学建模

研究软支承下的车辆-基础系统动力学建模问题.将基础模拟为具有多个非线性、不对称弹性支承和阻尼器约束的Euler Beinoulli梁,利用分段线性化方法描述弹性支承的非线性刚度和阻尼特性,根据Hamilton原理和假设振型方法建立系统的运动方程,基于Newmark直接积分方法编制MATLAB二次开发函数,数值求解系统动力学响应,分析了支承约束非线性对系统动力学特性的影响.     

粘弹性层状半空间上刚体的垂直振动

本文较深入地研究了层状粘弹性半空间上刚性圆形基础的垂直振动问题。首先作者采用独创的方法求解弹性动力学基本方程，并借助于Ｔｈｏｍｓｏｎ Ｈａｓｋｅｌ的传递矩阵方法得出层状地基表面位移的Ｈａｎｋｅｌ变换式。然后按弹性力学混合边值问题建立层状粘弹性地基上刚体垂直振动的对偶积分方程，并化为第二类Ｆｒｅｄｈｏｌｍ积分方程。文末给出了数值算例。     

Creep buckling and post-buckling analyses for a hybrid laminated viscoelastic FGM cylindrical shell under in-plane loading

In this paper, creep buckling and post-buckling of a hybrid laminated viscoelastic functionally graded material (FGM) cylindrical shell under in-plane loading are investigated. Considering the high-order transverse shear deformation and geometric nonlinear theory, the von Karman geometric relation of the hybrid laminated viscoelastic FGM cylindrical shell with initial deflection is established. Based on the Donnell theory, elastic piezoelectric theory and Boltzmann superposition principle, nonlinear creep governing equations of the hybrid laminated viscoelastic FGM cylindrical shell under in-plane loading are derived. By means of the finite difference method and the Newton–Newmark method, the problem for creep buckling and post-buckling of the laminated shell’s structure is solved. Numerical results are presented to show effects of geometric parameters, power law index and loading on creep buckling and post-buckling of the hybrid laminated viscoelastic FGM cylindrical shell.     

Analysis of the nonlinear dynamic response of viscoelastic symmetric cross-ply laminated plates with transverse matrix crack

Based on the Schapery’s 3-D constitutive relationship and the Von Karman’s plate theory, the constitutive equations and the nonlinear dynamic governing equations for viscoelastic symmetric cross-ply laminated plates with transverse matrix cracks are derived. By using the finite difference method and Newmark-β scheme, the unknown functions are separated and these equations are iterated to seek solutions. Numerical calculating results show that the effect of damage on the nonlinear dynamic responses of structures is significant.     

Viscoelastic damped response of cross-ply laminated shallow spherical shells subjected to various impulsive loads

In this paper, the viscoelastic damped response of cross-ply laminated shallow spherical shells is investigated numerically in a transformed Laplace space. In the proposed approach, the governing differential equations of cross-ply laminated shallow spherical shell are derived using the dynamic version of the principle of virtual displacements. Following this, the Laplace transform is employed in the transient analysis of viscoelastic laminated shell problem. Also, damping can be incorporated with ease in the transformed domain. The transformed time-independent equations in spatial coordinate are solved numerically by Gauss elimination. Numerical inverse transformation of the results into the real domain are operated by the modified Durbin transform method. Verification of the presented method is carried out by comparing the results with those obtained by the Newmark method and ANSYS finite element software. Furthermore, the developed solution approach is applied to problems with several impulsive loads. The novelty of the present study lies in the fact that a combination of the Navier method and Laplace transform is employed in the analysis of cross-ply laminated shallow spherical viscoelastic shells. The numerical sample results have proved that the presented method constitutes a highly accurate and efficient solution, which can be easily applied to the laminated viscoelastic shell problems.     

Nonlinear static/dynamic analysis for elasto-plastic laminated plates with interfacial damage evolution

A new analysis model, which includes the effects of interfacial damage, geometrical nonlinearity and material nonlinearity, is presented for elasto-plastic laminated plates. Based on the model, the nonlinear equilibrium differential equations for elasto-plastic laminated plates with interfacial damage are established. The finite difference method and iteration method are adopted to solve these equations. The nonlinear static and dynamic behaviors for the elasto-plastic laminated plates under the action of transverse loads are analyzed. Effects of interfacial damage on the stress and displacement distribution and nonlinear dynamic response are discussed in the numerical examples together with the comparison of nonlinear mechanical behaviors between the elastic and elasto-plastic laminated plates. Numerical results show that both the interfacial damage and plastic deformation put obvious influence on the mechanical properties of structures.     

Smart damping of geometrically nonlinear vibrations of composite shells using fractional order derivative viscoelastic constitutive relations

In this article, a three-dimensional fractional order derivative model has been developed for the constrained viscoelastic layer of the active constrained layer damping (ACLD) treatment of laminated composite shells undergoing geometrically nonlinear vibrations. The constraining layer of the ACLD treatment is made of vertically/obliquely reinforced 1–3 piezoelectric composites and acts as the distributed actuator. A three-dimensional smart nonlinear finite element model has been developed. Several numerical results are presented to check the accuracy of the present three-dimensional fractional derivative model of the constrained viscoelastic layer for smart damping of geometrically nonlinear vibrations of laminated composite shells.     

复合材料层合开顶扁球壳在集中冲击下的非线性动力屈曲

研究了具有刚性中心的复合材料层合开顶扁球壳在中心集中冲击载荷作用下的非线性动力屈曲问题。通过增加横向转动惯量项得到中心集中冲击下复合材料层合开顶扁球壳非线性稳定性的控制方程，采用Galerkin方法得到以刚性中心位移表达的冲击动力响应方程，并用Runge-Kutta方法进行数值求解，应用Budiansky-Roth准则（简称B—R准则）确定冲击屈曲的临界荷载；讨论了壳体几何尺寸对复合材料层合开顶扁球壳冲击屈曲的影响。     

Nonlinear dynamic response of laminated plates resting on nonlinear elastic foundations by the discrete singular convolution-differential quadrature coupled approaches

In this paper, nonlinear dynamic response of rectangular laminated composite plate resting on nonlinear Pasternak type elastic foundations is investigated. First-order shear deformation theory (FSDT) is used for modeling of moderately thick plates. The plate formulation is based on the von Karman nonlinear equation. The resulting nonlinear governing equations for transient analysis of laminated plates on elastic foundation are integrated using the discrete singular convolution-differential quadrature coupled approaches. The nonlinear governing equations of motion of plate are discretized in space and time domains using the discrete singular convolution and the differential quadrature methods, respectively. The validity of the present method is demonstrated by comparing the present results with those available in the open literature. The effects of the foundation parameters, boundary conditions and geometric parameters of plates on nonlinear dynamic response of laminated thick plates are investigated.     

粘弹性圆柱壳在轴向恒压下的动力稳定性

基于Timoshenko-Mindlin假设,得到考虑粘弹性的各向同性圆柱壳及纤维增强正交铺设层合圆柱壳在轴向恒压下的动力学方程。文中对两端简支的圆柱壳进行了分析,依Laplace变换,导出动力稳定的特征方程,由Routh-Hurwitz判据建立动力稳定性条件,对两类圆柱壳讨论了横向剪切变形的影响。