三阶剪切变形板的振动特性研究

对于中厚板或层合板而言,横向剪切变形的影响是显著的,采用三阶剪切变形理论比采用经典薄板理论和一阶剪切变形理论能更好的满足精度的要求,而且能更好地描述板的剪切变形和剪应力沿厚度方向的分布情况.本文用解析的方法研究了简支、自由和固定三种边界条件的任意组合下三阶剪切变形板的自由振动问题.首先应用哈密顿原理建立自由振动方程,再通过引入中间变量使得原来耦合的自由振动方程得到解耦和简化,基于分离变量法,利用边界条件得到基函数的表达式,利用Rayleigh-Ritz法,求得三阶剪切变形板在任意边界条件下的固有频率和振型.本文得到的结果可以为厚板在工程中的应用提供理论依据,具有较高的工程实际应用价值.     

轴向运动梁横向非线性振动模型研究进展

综述了描述轴向运动梁横向非线性振动的两组数学模型的研究进展.在轴向运动梁径向和横向平面非线性振动耦合模型的基础上,总结了两组横向非线性振动模型的推导,以及在自由振动、受迫振动、参激振动工况下两组横向模型的近似解析比较的研究进展.在直接数值离散方法的基础上,总结了两组横向模型在各种工况下对平面耦合模型近似程度的研究进展.最后提出若干尚待深入研究的问题.     

纵横向耦合轴向运动梁的自由振动响应研究

研究轴向运动梁在纵向与横向振动耦合下的自由振动响应,尤其是在横向第1,2固有频率之比ω1/ω2接近1:3内共振条件下的系统响应.利用哈密顿原理建立非惯性参考系下轴向运动梁的振动微分方程,采用分离变量法分离时间变量和空间变量并利用Galerkin方法离散,得到了运动梁含有2次和3次非线性项的运动微分方程.利用增量谐波平衡法(IHB法)分析纵向与横向振动耦合时非线性振动复杂的频幅响应曲线,探讨了相互耦合下系统在横向前2阶固有频率附近没有横向外激励作用下的自由振动响应,揭示了很多复杂而有趣的非线性现象.     

轴向运动弦线横向振动控制的Lyapunov方法

研究轴向运动弦线和作动器组成的耦合系统的横向振动控制．此系统被作动器分成未控和受控两部分,通过作用在作动器上的控制力对受控部分进行主动控制．分析未控弦线的横向振动的有界性．采用Lyapunov方法获得控制规律,并证实受控弦线横向振动的指数稳定性．在初始扰动和激励力作用下,通过数值仿真证实控制规律的有效性．     

双参数弹性地基上板的自由振动

建立了双参数弹性地基上的正交异性矩形薄板自由振动位移函数微分方程,并得到其一般解．这可用以精确地求解板在任意边界条件下的自由振动问题．以四边固定的正方形板为例进行了分析,计算过程简单,便于实际应用．亦适用于求解单参数弹性地基和各向同性板情形。     

基于NURBS自由变形的腿部运动建模方法

如何建立人体各部分的数字模型是生物医学和计算机工程界较为关心的研究课题。利用基于ＮＵＲＢＳ的自由变形方法模拟膝关节变曲和股肉变形,并在二阶Ｂ样条基函数的基础上,依据关节的解剖结构,推导出了符合膝关节运动特点和肌肉特性的计算公式。     

基于修正变分法开孔板和加强板结构的自由振动分析

为研究船舶开孔板和加强板结构的振动特性,用1阶剪切变形板理论描述各向同性板的位移场,并采用修正变分原理和区域分解方法建立板的离散动力学模型.每一块子域板的位移和转角分量通过第一类切比雪夫正交多项式展开.针对加强板模型,将该方法获得的结果与已经发表的文献和有限元商用软件计算结果进行对比,验证该方法的收敛性和正确性.基于修正变分法探讨多种开孔和加强板模型的自由振动特性,充分说明该数理模型和半解析方法是一种适合处理复杂板结构问题的数值工具.     

轴向运动梁横向非线性振动研究

应用增量谐波平衡法(IHB法)研究轴向运动梁横向非线性振动的内部共振．根据哈密顿原理建立非惯性参考系下轴向运动梁的横向振动微分方程,采用分离变量法分离时间变量和空间变量并利用Galerkin方法离散运动方程,再应用IHB法进行非线性振动分析,研究了在固有频率之比ω20／ω10接近于3：1情况下,外激励频率ω在ω10,ω20附近的具有内部共振的基谐波和次谐波响应．数值结果表明了IHB法是一个求解轴向运动体系非线性振动的非常有效的半解析、半数值的方法。     

粘弹性夹层圆板自由振动的理论解

研究了粘弹性夹层圆板的自由振动特性.基于经典弹性薄板理论和Kelvin-Voigt粘弹性本构方程,建立了粘弹性夹层圆板振动控制方程.采用分离变量法导出了粘弹性夹层圆板的自然频率及振型解析表达式,计算了固支和简支粘弹性夹层圆板的自然频率,并与有限元计算结果进行比较;讨论了粘弹性夹层圆板的夹心层比率对自然频率及衰减系数的影响.研究表明：（1）随着夹心层厚度的增大,系统频率先增大后减小,高阶时该趋势表现更为明显;（2）随着夹心层厚度的增大,衰减系数一直增大,高阶时该趋势表现更为明显.     

轴向运动复合材料薄壁梁的横向振动分析

研究可轴向运动复合材料薄壁梁的动力学特性.基于VAM（变分渐进法）复合材料薄壁梁理论,采用Euler Bernoulli梁模型并根据Hamilton原理来建立复合材料薄壁梁的动力学方程.应用假设模态法对薄壁梁进行自由振动分析,通过比较研究验证了该建模方法的正确性,并分析了几何参数和物理参数对薄壁梁固有频率的影响.推导了轴向运动复合材料薄壁梁的横向振动方程,借助四阶Runge-Kutta法进行数值计算,研究了不同纤维铺层方式和不同匀速度大小对可轴向运动复合材料薄壁梁横向振动末端位移响应的影响.     

Finite element free vibration of eccentrically stiffened plates

An isoparametric stiffened plate element is introduced for the free vibration analysis of eccentrically stiffened plates. The element has the ability to accommodate irregular boundaries. Moreover, the formulation considers shear deformation, hence, the formulation is applicable to both thick and thin plates. In the present formulation, the stiffeners can be placed anywhere within the plate element and they need not necessarily follow the nodal lines. In addition, the effects of lumped and consistent mass matrices on natural frequencies of stiffened plates are investigated. The effects of several parameters of the stiffener—eccentricity, shape, torsional stiffness etc.—on the natural frequencies of the stiffened plates are studied.     

Finite element free vibration analysis of eccentrically stiffened plates

A new finite element model is proposed for free vibration analysis of eccentrically stiffened plates. The formulation allows the placement of any number of arbitrarily oriented stiffeners within a plate element without disturbing their individual properties. A plate-bending element consistent with the Reissner-Mindlin thick plate theory is employed to model the behaviour of the plating. A stiffener element, consistent with the plate element, is introduced to model the contributions of the stiffeners. The applied plate-bending and stiffener elements are based on mixed interpolation of tensorial components (MITC), to avoid spurious shear locking and to guarantee good convergence behaviour. Several numerical examples using both uniform and distorted meshes are given to demonstrate the excellent predictive capability of this approach.     

A finite element method for the free vibration of plates allowing for transverse shear deformation

An isoparametric quadrilateral plate bending element is introduced and its use for the free vibration analysis of both thick and thin plates is examined. Plates of rectangular planform and of orthotropic materials are analysed and excellent results are obtained. The element performance is assessed by comparison with well established analytical and numerical solutions based on Mindlin's thick plate theory, three dimensional elasticity solutions and solutions based on thin plate theory. The ease with which the element may be implemented is stressed. The use of an eigenvalue economiser which produces considerable economy in the computer solution is demonstrated. Various mass lumping schemes and numerical integration rules used in the construction of the element mass matrix are also examined.     

轴向运动薄板非线性振动及其稳定性研究

应用增量谐波平衡法(IHB法)研究轴向运动薄板横向非线性振动特性及其稳定性.通过Hamilton原理推导出了非惯性参考系下四边简支轴向运动薄板的横向振动微分方程,然后利用Galerkin方法离散运动方程.对离散后的非线性方程组应用IHB法进行非线性振动分析,研究了在固有频率之比ω20/ω10接近于3:1情况下,外激励频率ω在ω10附近的具有内部共振的基谐波响应.最后用多元Floquet理论分析了系统周期解的稳定性,其中采用Hsu方法来计算转移矩阵.通过对具体例子的数值计算,分别得到了自由振动和不同外激励下的频幅相应曲线,通过对比运动梁模型和运动薄板模型的计算结果,分析了各种模型的适用范围.     

Finite element analysis of eccentrically stiffened plates in free vibration

A compound finite element model is developed to investigate eccentrically stiffened plates in free vibration. The plate elements and beam elements are treated as integral parts of a compound section, and not as independent bending components. The derivation is based on the assumptions of small deflection theory. In the orthogonally stiffened directions of the compound section, the neutral surfaces may not coincide. They lie between the middle surface of the plate and the centroidal axes of the stiffeners. The results of this study are compared with existing ones and with those of the orthotropic plate approximation. Modifications to the existing equivalent orthotropic rigidities are proposed.     

Finite element free flexural vibration analysis of plates having various shapes and varying rigidities

Natural frequencies of skew, curved and tapered plates have been determined using the isoparametric quadratic plate bending element. Plates having linearly varying thickness in one direction and also those having parabolically varying thickness in orthogonal directions have been analysed. A simple stepped plate approach for a linearly tapered plate has also been considered to compare the results. Two approaches have been adopted for the solution of skew plates. In one case, the boundary conditions have been exactly satisfied by transforming the rotational displacements at the boundary nodes along and normal to the edge. In the other case, only the vertical deflection was locked. A curved plate has also been analysed by the first method. Results thus obtained from both cases have been compared.     

Finite element free vibration analysis of conoidal shells

Doubly curved conoidal shells are increasingly used for various industrial structures. Conoidal shells are aesthetically appealing and, being ruled surfaces, provide ease of casting. The variation of curvature is the difficulty enountered in the analysis of these shells. The finite element method is used here for the analysis of generalized doubly curved shells and is applied to truncated and full conoids of different boundary conditions, aspect ratios and degrees of truncation. An eight-noded isoparametric finite element with five degrees of freedom per node, including three translations and two rotations, is utilized. The accuracy is checked by comparing the results obtained by the present analysis with those existing in the literature. Results are presented for different conoidal shells and a set of conclusions are arrived at based on a parametric study.     

Modal spectral element formulation for axially moving plates subjected to in-plane axial tension

The use of frequency-dependent spectral element matrix (or dynamic stiffness matrix) in structural dynamics is known to provide very accurate solutions, while reducing the number of degrees-of-freedom to resolve the computational and cost problems. Thus, in the present paper, the modal spectral element is formulated for thin plates moving with constant speed under a uniform in-plane axial tension. The concept of the Kantorovich method is used to formulate the modal spectral element matrix in the frequency-domain. The present modal spectral element is then evaluated by comparing its solutions with exact analytical solutions as well as with FEM solutions. The effects of the moving speed and the in-plane tension on the dynamic characteristics of a moving plate are investigated numerically.     

Finite element free vibration analysis of damped stiffened panels

Free vibration characleristics of a damped stiffened panel with applied viscoelastic damping on the flanges of the stiffeners are studied using finite element method. The complex nature of the rotational and transverse stiffnesses of the stringers is taken into consideration while deriving the stiffness and mass matrices of the damped stiffener element. The finite element method consists of representing the panel by rectangular plate elements of 12 d.o.f. and the stiffeners by beam elements of 8 d.o.f. which allow for bending, torsional and warping effects. Numerical results showing the effect of the geometric and material properties of the damping layer treatment on the resonant frequencies and loss factors of the composite panel are presented.