基于Zig-Zag变形假定的复合材料夹层板的自由振动

针对复合材料夹层板的实际变形特征，基于Zig-Zag变形假定和Mindlin一阶剪切理论，建立了复合材料夹层板自由振动的有限元模型，在该模型中分别对上、下面板和芯体建立了三个独立坐标系，使三部分的转角独立，为具有厚夹芯和软夹芯的复合材料夹层板的动力分析提供了一种更为准确的有限元模型；在此基础上推导了相应的刚度阵和质量阵，并采用子空间迭代法求解。夹层板的固有频率。通过典型考题证明了本模型的有效性。文中最后还通过参数讨论，研究了具有不同长厚比的复合材料夹层板基频的变化规律。     

复合材料的多层、夹层和加筋圆柱曲板的稳定和振动

本文在文献〔1,2〕的基础上,考虑了沿壳体厚度方向的剪切变形,探讨周边简支的纤维增强复合材料的正交各向异性的多层、夹层和加筋矩形圆柱曲板(与圆柱壳),在轴压、侧压和剪切(扭矩)作用下的临界载荷和横向振动固有频率的计算问题。在编成计算程序后,用一些算例将用文献〔1〕中的扁壳方程(Donnell壳体理论) 和文献〔3〕中的非扁壳方程(Love的壳体一阶近似理论) 算得的结果作了比较;将轴压下轴对称失稳和非轴对称失稳的临界载荷作了比较;将在轴压和侧压作用下失稳时外加筋曲板和内加筋曲板的临界载荷作了比较;将有薄膜力N_x~0和N_y~0同时和分别作用时与没有薄膜力作用时的横向振动固有频率作了比较;将按壳体的剪切变形理论和经典理论算得的临界载荷作了比较;将铺层情况对临界载荷的影响作了比较。     

直角坐标下厚圆柱扁壳弯曲的一般解

基于直角坐标下考虑横向剪切变形情况下厚圆柱扁壳的几何方程、物理方程、平衡微分方程,建立了以3个中面位移和2个中面转角为独立变量的中厚圆柱扁壳弯曲的位移型基本微分方程.因该方程可退化为薄圆柱扁壳弯曲的基本微分方程,说明了其推导过程的正确性及一般性.此外,厚圆柱扁壳的位移型基本微分方程是一个10阶微分方程,对其使用双重三角...     

三维编织复合材料圆柱壳在外压作用下的屈曲分析

提出一种三维四向编织复合材料圆柱壳的细观力学模型,宏观上基于Reddy高阶剪切变形理论和广义Kármán型方程,采用奇异摄动法求解在固支边界条件下三维四向编织复合材料圆柱壳在外压作用下的屈曲和后屈曲.分析中同时考虑非线性前屈曲、大挠度和初始几何缺陷的影响.讨论了纤维体积含量、壳体几何参数等因素对圆柱壳屈曲行为的影响.     

考虑横向剪切变形和旋转惯性的层合正交异性球壳的动态响应

本文建立了计及横向剪切变形的旋转惯性的复合材料轴对称层合圆柱正交异性球壳的运动方程。在此基础上，用有限差分法计算了球壳在轴对称动力载荷下的动态响应，并讨论了材料参数、结构参数和横向剪切变形的影响。     

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.     

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．     

基于径向基点插值法的旋转Mindlin板高次刚柔耦合动力学模型

将无网格径向基点插值法(radial point interpolation method,RPIM)用于中心刚体?旋转柔性板的动力学分析.基于浮动坐标系方法和一阶剪切变形理论即Mindlin板理论,考虑剪切变形的影响,并计入板面内变形的非线性耦合变形项,采用径向基点插值法描述板的变形场,保留动能中有关非线性耦合变形项...     

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.      

复合材料层合开顶扁球壳的非线性动态屈曲

研究了复合材料层合开顶扁球壳的非线性动态屈曲问题。建立了对称层合圆柱正交异性开顶扁球壳考虑横向剪切的非线性振动微分方程,根据突变理论建立了该壳体动态屈曲的突变模型,得到了动态屈曲的临界方程。     

Elasticity solution for free vibration analysis of four-parameter functionally graded fiber orientation cylindrical panels using differential quadrature method

In this paper, three-dimensional free vibrations analysis of a four-parameter functionally graded fiber orientation cylindrical panel is presented. The panel is simply supported at the edges and assumed to have an arbitrary variation of fiber orientation in the radial direction. A generalization of the power-law distribution presented in literature is proposed. Symmetric and asymmetric fiber orientation profiles are studied in this paper. Suitable displacement functions that identically satisfy the boundary conditions at the simply supported edges are used to reduce the equilibrium equations to a set of coupled ordinary differential equations with variable coefficients, which can be solved by differential quadrature method to obtain the natural frequency. The main contribution of this work is to illustrate the influence of the power-law exponent, of the power-law distribution choice and of the choice of the four parameters on the natural frequencies of continuous grading fiber orientation cylindrical panels. Numerical results are presented for a cylindrical panel with arbitrary variation of fiber orientation in the shell’s thickness and compared with discrete laminates composite panels. It is shown maximum natural frequencies will be obtained by using symmetric fiber orientation profiles.     

Nonlinear flutter of viscoelastic rectangular plates and cylindrical panels of a composite with a concentrated masses

The problem of flutter of viscoelastic rectangular plates and cylindrical panels with concentrated masses is studied in a geometrically nonlinear formulation. In the equation of motion of the plate and panel, the effect of concentrated masses is accounted for using the δ-Dirac function. The problem is reduced to a system of nonlinear ordinary integrodifferential equations by using the Bubnov-Galerkin method. The resulting system with a weakly singular Koltunov-Rzhanitsyn kernel is solved by employing a numerical method based on quadrature formulas. The behavior of viscoelastic rectangular plates and cylindrical panels is studied and the critical flow velocities are determined for real composite materials over wide ranges of physicomechanical and geometrical parameters.     

复合材料层合板1:1参数共振的分岔研究

针对复合材料对称铺设各向异性矩形层合板的物理模型,在同时考虑了材料、阻尼和几何等非线性因素后,建立了二自由度非线性参数振动系统动力学控制方程,并应用多尺度法求得基本参数共振下的近似解析解,利用数值模拟分析了系统的分岔和混沌运动.指出了伽辽金截断对系统动力学分析的影响,以及系统进入混沌的途径.     

Three-dimensional free vibration analysis of four-parameter continuous grading fiber reinforced cylindrical panels resting on Pasternak foundations

This research investigates three-dimensional free vibration analysis of four-parameter continuous grading fiber reinforced (CGFR) cylindrical panels resting on Pasternak foundations by using generalized power-law distribution. The functionally graded orthotropic panel is simply supported at the edges, and it is assumed to have an arbitrary variation of matrix volume fraction in the radial direction. A four-parameter power-law distribution presented in literature is proposed. Symmetric and asymmetric volume fraction profiles are presented. Suitable displacement functions that identically satisfy the boundary conditions at the simply supported edges are used to reduce the equilibrium equations to a set of coupled ordinary differential equations with variable coefficients, which are solved by generalized differential quadrature method, and natural frequency is obtained. The fast rate of convergence of the method is demonstrated, and to validate the results, comparisons are made with the available solutions for functionally graded isotropic shells with/without elastic foundations. The effect of the elastic foundation stiffness parameters and various geometrical parameters on the vibration behavior of the CGFR cylindrical panels is investigated. This work mainly contributes to illustrate the influence of the four parameters of power-law distributions on the vibration behavior of functionally graded orthotropic cylindrical panels resting on elastic foundation. This paper is also supposed to present useful results for continuous grading of matrix volume fraction in the thickness direction of a cylindrical panel on elastic foundation and comparison with similar discrete laminated composite cylindrical panel.     

碳纳米管增强复合材料圆锥薄壳非线性自由振动

考虑碳纳米管复合材料作为功能梯度材料的不均匀性,基于连续介质理论以及哈密尔顿变分原理,建立了功能梯度碳纳米管增强复合材料开口圆锥薄壳结构的非线性运动偏微分控制方程,然后利用Galerkin法,将非线性偏微分控制方程转化为常微分控制方程,进而采用谐波平衡法求解了开口圆锥壳的非线性自由振动问题,并探讨了圆锥薄壳几何参数、碳纳米管参数对结构非线性自由振动的影响．数值研究表明结构的无量纲非线性自由振动频率与线性自由振动频率的比值随圆锥薄壳长厚比的增大而变小、并随圆锥角的增大而变大．     

具有曲率和惯性非线性以及材料内阻的旋转复合材料轴的主共振

旋转复合材料轴作为一类典型的转子动力学系统,在先进直升机和汽车动力驱动系统中有着广阔的应用前景.研究旋转复合材料轴的非线性振动特性具有重要的理论与实用价值.然而,目前有关旋转轴的非线性振动研究仅限于各向同性金属材料轴,很少考虑材料内阻的影响.本文研究具有材料内阻的旋转非线性复合材料轴的主共振.非线性来源于不可伸长复合材料轴的大变形引起的非线性曲率和非线性惯性,材料内阻来源于复合材料的黏弹性.动力学建模计入转动惯量和陀螺效应.基于扩展的Hamilton原理,导出具有偏心激励的旋转复合材料轴的弯-弯耦合非线性振动偏微分方程组.采用Galerkin法将偏微分方程离散化为常微分方程,采用多尺度法对常微分方程进行摄动分析,导出主共振响应的解析表达式.对内阻、外阻、铺层角、长径比、铺层方式和偏心距进行数值分析,研究上述参数对旋转非线性复合材料轴的稳态受迫振动响应行为的影响.研究发现,角铺设复合材料轴的内阻系数随着铺层角的增大而增大;内阻对主共振响应特性的影响主要体现在对抑制振幅和改变频率响应的稳定性方面;发生在正进动固有频率附近的主共振响应具有典型的硬弹簧非线性特性.本文提出的模型能够用于描述旋转复合材料轴的主共振特性,是对不可伸长旋转金属轴非线性动力学模型的重要推广.     

Nonlinear Random Response of Cylindrical Panels to Acoustic Excitations Using Finite Element Modal Method

This paper investigates large amplitude multi-mode free vibration andrandom response of thin cylindrical panels of rectangular planform usinga finite element modal formulation. A thin laminated composite doublycurved element is developed. The system equation in structural nodal DOFis transformed into the modal coordinates by the using the modes of theunderlying linear system. The nonlinear stiffness matrices are alsotransformed into nonlinear modal stiffness matrices. Numericalintegration is employed to determine free vibration and random response.Single-mode free vibration results are compared with existing classicalanalytical solutions to validate the nonlinear modal formulation.Nonlinear random analysis results for cylindrical panels have shown thatthe root mean square of panel deflections could be larger than thoseobtained using the linear structure theory. Time histories, probabilitydistribution functions, power spectral densities, and phase plane plotsare also presented.     

Torsional buckling of cross-ply laminated orthotropic composite cylindrical shells subject to dynamic loading

This study considers torsional buckling of cross-ply laminated orthotropic composite cylindrical thin shells under loads, which is a power function of time. The modified Donnell type dynamic stability and compatibility equations are obtained first. These equations are subsequently reduced to a time dependent differential equation with variable coefficients by using Galerkin's method. The critical parameters are found analytically by applying the Ritz type variational method. According to theoretical solutions, numerical analyses are done.     

Chaotic Analysis of Nonlinear Viscoelastic Panel Flutter in Supersonic Flow

In this paper chaotic behavior of nonlinear viscoelastic panels in asupersonic flow is investigated. The governing equations, based on vonKàarmàn's large deflection theory of isotropic flat plates, areconsidered with viscoelastic structural damping of Kelvin's modelincluded. Quasi-steady aerodynamic panel loadings are determined usingpiston theory. The effect of constant axial loading in the panel middlesurface and static pressure differential have also been included in thegoverning equation. The panel nonlinear partial differential equation istransformed into a set of nonlinear ordinary differential equationsthrough a Galerkin approach. The resulting system of equations is solvedthrough the fourth and fifth-order Runge–Kutta–Fehlberg (RKF-45)integration method. Static (divergence) and Hopf (flutter) bifurcationboundaries are presented for various levels of viscoelastic structuraldamping. Despite the deterministic nature of the system of equations,the dynamic panel response can become random-like. Chaotic analysis isperformed using several conventional criteria. Results are indicative ofthe important influence of structural damping on the domain of chaoticregion.     

Nonlinear Theory of Dynamic Stability for Laminated Composite Cylindrical Shells

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