亚音速气流中复合材料悬臂板的非线性振动响应研究

随着材料科学的发展,越来越多的新型材料应用到了工程实践中.在气流激励的作用下,对于以航空航天工程为背景、采用复合材料的板壳结构的非线性动力学问题仍是动力学领域的研究热点.本文研究了复合材料悬臂板在亚音速气流条件下的非线性振动和响应.根据理想不可压缩流体的流动条件和Kutta–Joukowski升力定理,基于升力面理论,利用涡格法计算了三维有限长平板机翼上的亚音速气动升力.将亚音速气动力施加到复合材料悬臂板上,利用Hamilton原理,考虑Reddy三阶剪切变形理论并引入冯·卡门非线性应变位移关系,建立了有限长平板的非线性动力学微分方程.利用有限元方法考察了不同几何参数下层合板悬臂板的固有特性,通过比较不同材料和几何参数的线性系统的固有频率,得到不同比例的内共振关系.利用Galerkin方法将偏微分方程截断为两自由度非线性常微分方程,在这里考虑了1:2的内部共振关系并利用多尺度法进行了摄动分析.对应多个选取参数,得到了频率响应曲线.结果展示了硬化弹簧型行为和跳跃现象.     

亚音速气流中复合材料悬臂板的非线性振动响应研究

随着材料科学的发展,越来越多的新型材料应用到了工程实践中.在气流激励的作用下,对于以航空航天工程为背景、采用复合材料的板壳结构的非线性动力学问题仍是动力学领域的研究热点.本文研究了复合材料悬臂板在亚音速气流条件下的非线性振动和响应.根据理想不可压缩流体的流动条件和 Kutta--Joukowski升力定理,基于升力面理论,利用涡格法计算了三维有限长平板机翼上的亚音速气动升力.将亚音速气动力施加到复合材料悬臂板上,利用Hamilton原理,考虑Reddy三阶剪切变形理论并引入冯$\cdot$卡门非线性应变位移关系,建立了有限长平板的非线性动力学微分方程.利用有限元方法考察了不同几何参数下层合板悬臂板的固有特性,通过比较不同材料和几何参数的线性系统的固有频率,得到不同比例的内共振关系.利用Galerkin方法将偏微分方程截断为两自由度非线性常微分方程,在这里考虑了1:2的内部共振关系并利用多尺度法进行了摄动分析.对应多个选取参数,得到了频率响应曲线.结果展示了硬化弹簧型行为和跳跃现象.      

应用有限差分法的轴向流作用下叠层板的稳定性和模态分析

分析了轴向流作用下两端简支和固支叠层板的稳定性。基于势流理论建立轴向流作用下叠层板的流固耦合系统连续型运动方程,基于有限差分法建立了流场网格和结构网格统一的离散化格式,流场势函数用板的横向振动位移变量来表示,得到关于叠层板的横向振动位移变量的控制方程。求解控制方程的广义特征值,计算分析结果表明,两端简支和两端固支模型发生屈曲失稳,且得到了屈曲失稳临界速度与叠层板的层数和无量纲板间距的关系。此外,轴向流作用下叠层板的一阶模态并不是叠层板的同相弯曲模态。     

温度场作用下悬臂输流碳纳米管的颤振失稳分析

以非局部弹性理论为基础,采用欧拉-伯努利梁模型,考虑碳纳米管的小尺度效应,应用哈密顿原理获得了温度场作用下的悬臂输流单层碳纳米管(SWCNT)的振动控制方程以及边界条件,依靠微分变换法(DTM法)对此高阶偏微分方程进行求解,通过数值计算研究了温度场中悬臂单层输流碳纳米管的振动与颤振失稳问题.结果表明:管内流体流速、温度场中温度变化情况与小尺度参数都会对系统振动频率以及颤振失稳临界流速产生影响.其中,小尺度效应将会降低悬臂输流系统的稳定性,使系统更为柔软;而高温场与低温场对系统动态失稳的影响不同,低温场中随温度变化值的增加,系统的稳定性提高;高温场这一作用效果恰好与之相反.     

具脱层的轴对称层合圆板的非线性振动分析

基于Von Karman板理论,应用三分区模型,建立了考虑横向剪切效应时具任意脱层的正交对称铺设轴对称层合圆板在径向压力荷载作用下的非线性运动微分方程。对未知变量在空间上采用Bessel函数,应用Galerkin法,得到无量纲的仅关于时间函数的运动微分方程,并应用谐波平衡法对此方程进行求解,算例中讨论了不同脱层半径、脱层深度对具脱层的正交对称铺设轴对称层合圆板非线性幅频响应的影响。     

温度场作用下输流悬臂碳纳米管的颤振失稳分析

以非局部弹性理论为基础,采用欧拉-伯努利梁模型,考虑碳纳米管的小尺度效应,应用哈密顿原理获得了温度场作用下的输流悬臂单层碳纳米管（SWCNT）的振动控制方程以及边界条件,依靠微分变换法（DTM法）对此高阶偏微分方程进行求解,通过数值计算研究了温度场中悬臂单层输流碳纳米管的振动与颤振失稳问题。结果表明：管内流体流速、温度场中温度变化情况与小尺度参数都会对系统振动频率以及颤振失稳临界流速产生影响。其中,小尺度效应将会降低悬臂输流系统的稳定性,使系统更为柔软;而高温场与低温场对系统动态失稳的影响不同,低温场中随温度变化值的增加,系统的稳定性提高;高温场这一作用效果恰好与之相反。     

粘弹性地基上粘弹性输流管道的稳定性分析

从Winkler假设和单轴线性粘弹性本构方程出发,推导了Kelvin-Voigt粘弹性地基上三参量固体模型输流管道的运动微分方程,采用改进的有限差分法,分析了管道和地基的粘弹性参数对输流管道无量纲复频率和无量纲流速之间的变化关系的影响。     

多场作用下输流单层碳纳米管的动力学特性

以非局部弹性理论为基础,采用欧拉-伯努利梁模型,考虑管型区域内滑移边界条件以及碳纳米管的小尺度效应,应用哈密顿原理获得了温度场与轴向磁场共同作用下的输流单层固支碳纳米管（SWCNT）的振动控制方程以及边界条件,依靠微分变换法（DTM法）对此高阶偏微分方程进行求解,通过数值计算研究了多场中单层固支输流碳纳米管的振动与失稳问题。结果表明：温度场、轴向磁场强度、Knudsen数及小尺度参数都会对系统振动频率以及失稳临界流速产生影响。     

三参量固体模型粘弹性输流管道的动力特性分析

推导了三参量固体模型粘弹性输流管道的振动微分方程 ,计算了在不同无量纲松弛系数和弹性常数比下管道的无量纲临界流速和无量纲自振复频率 ,并给出了前三阶复频率与流速的关系 .计算结果表明 ,质量比、无量纲松弛系数及无量纲弹性常数比对输流管道的动力特性均有影响 .     

磁场对不同温度场中输流悬臂碳纳米管动态特性的影响

本文在采用经典欧拉-伯努利梁模型的基础上,引入考虑小尺度效应的非局部弹性理论,着重研究不同温度场中输流悬臂单层碳纳米管系统（SWCNT）在外加纵向磁场作用下的颤振失稳问题。基于哈密顿原理获得了该流固耦合系统的振动控制方程及相应的边界条件,应用微分变换法（DTM法）求解此高阶偏微分方程,通过数值计算研究了不同温度场中施加纵向磁场对系统动力学特性的影响。结果表明：施加纵向磁场在不同温度场中都将增强输流悬臂碳纳米管的动态稳定性。然而,这种增强程度却与温度场的变化量有关,在不同温度变化量下,磁场对系统稳定性的增强程度有一个峰值,这意味着,实际应用中,为了提高这类流固耦合系统的动态稳定性,一味提高纵向磁场强度并不可取。     

弹性基础上对称叠层厚板的基本解

利用平面波分解法将弹性地基础上计入剪切变形的对称叠层厚板的偏微分方程组转化常微分方程组，然后利用Ｈ¨ｏｒｍａｎｄｅｒ算子法将常微分方程组转化为一个六阶的常微分方程，以定积分的形式提出了弹性基础上对称叠层厚板的基本解．     

四边简支矩形中厚板的弯曲

本文采用Reissner中厚板理论求解了四边简支矩形中厚板的弯曲问题。文中首先对Reissner中厚板理论的控制方程进行了适当的变更,使之成为非耦联的二阶偏微分方程组,然后利用有限积分变换法求解所得新的控制方程,得到了四边简支矩形中厚板受均布载荷作用下的解析解。文中所述方法可用以求解具有其它边界条件和载荷的矩形中厚板的弯曲问题,同时还可移植应用于其它中厚板理论。     

Unsymmetrical large deformation problem of orthotropic plates

Based upon the theory of ardsotropic plates, the unsymmetrical large deformation equations of orthotropic circular plates were derived. By using Fourier series, the partial differential equations of this problem can be transformed into sets of nonlinear differential equations . And the procedure to solve the problem using the iterative method is given .     

Natural convection flow of a couple stress fluid between two vertical parallel plates with Hall and ion-slip effects

The Hall and ion-slip effects on fully developed electrically conducting couple stress fluid flow between vertical parallel plates in the presence of a temperature dependent heat source are investigated. The governing non-linear partial differential equations are transformed into a system of ordinary differential equations using similarity transformations. The resulting equations are then solved using the homotopy analysis method (HAM). The effects of the magnetic parameter, Hall parameter, ion-slip parameter and couple stress fluid parameter on velocity and temperature are discussed and shown graphically.     

Karman型正交异性矩形薄板非线性弯曲的统一求解方法

本文对Karman型四边支承正交异性薄板在5种不同边界条件下的几何非线性弯曲进行了统一分析。所设的位移函数均为梁振动函数。它们精确地满足边界条件，利用Galerkin方法和位移函数的正交属性，转换控制方程为非线性代数方程。用“稳定化双共轭梯度法”求解稀疏矩阵线性方程组以及“可调节参数的修正迭代法”求解非线性代数方程组，最后给出了相应的数值结果。     

Analysis of cantilever plates by the line-solution technique

Summary The application of the line-solution technique to the analysis of uniformly loaded cantilever plates is described in this paper. In this method, the two-dimensional partial differential equation of plate theory is reduced to a set of ordinary linear differential equations by replacing the derivatives in one direction by their finite-difference equivalents. The resulting equations are solved numerically by the matrix-progression technique.Three different approaches are suggested for the elimination of the corner forces which arise as a result of using Kirchhoff's boundary conditions. Numerical results are presented and compared with those of previous theoretical and experimental investigations.     

On heat and mass transfer in the unsteady squeezing flow between parallel plates

This paper reports the heat and mass transfer characteristics in a viscous fluid which is squeezed between parallel plates. The governing partial differential equations for unsteady two-dimensional flow with heat and mass transfer of a viscous fluid are reduced to ordinary differential equations by similarity transformations. Homotopy analysis method (HAM) is employed to construct the series solution of the problem. Physical interpretation to various embedding parameters is assigned through graphs for temperature and concentration profiles and tables for skin friction coefficient, local Nusselt number and local Sherwood number.     

Nonlinear Oscillations of Viscoelastic Rectangular Plates

Nonlinear oscillations of viscoelastic simply supported rectangular plates are studied by assuming the Voigt–Kelvin constitutive model. Using Hamilton's principle in conjunction with the kinematics associated with Kirchhoff's plate model, the governing equations of motion including the effect of damping are represented in terms of the transversal deflection and a stress function. Utilizing the Bubnov–Galerkin method, the nonlinear partial differential equations are reduced to an ordinary differential equation which is studied geometrically by approximate construction of the Poincaré maps. Explicit expressions are given for periodic solutions.     

Large deflections of heterogeneous anisotropic rectangular plates

An approximate solution is presented for large deflections of clamped, uniformly loaded, unsymmetrically laminated, anisotropic, rectangular plates. Expressing the load and displacements in the form of series, the von Karman-type nonlinear differential equations and immovable boundary conditions are reduced to a series of linear partial differential equations and boundary conditions. The solution obtained by successive approximations can reduce to some existing solutions for large deflections of homogeneous plates. Numerical results based on the first three terms of the truncated series are graphically presented for unsymmetrical cross-ply and angle-ply plates having various values of fiber-reinforced material, number of layers, and aspect ratio. The results in small deflections of coupled laminates are compared with available data.     

A strong formulation finite element method (SFEM) based on RBF and GDQ techniques for the static and dynamic analyses of laminated plates of arbitrary shape

This paper deals with the static and dynamic analyses of multi-layered plates with discontinuities. The two-dimensional first-order shear deformation theory is used to derive the fundamental system of equations in terms of generalized displacements. The fundamental set, with its boundary conditions, is solved in its strong form. A new method termed strong formulation finite element method is considered in the present paper to solve this kind of plates. This numerical methodology is the cohesion of derivative evaluation of partial differential systems of equations and a domain sub-division. The numerical results in terms of natural frequencies and maximum deflections are compared to literature and to the same results obtained with a finite element code. The stability, accuracy and reliability of the present methodology is shown through several numerical applications.