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。     

横向磁场中矩形薄板在分布载荷作用下混沌分析

在应用Melnikov函数方法,给出受横向分布载荷作用下,矩形薄板的磁弹性耦合系统发生混沌运动的条件和混沌运动判据的基础上,建立了Duffing振动系统的微分方程,针对薄板的磁弹性耦合振动系统做了混沌运动分析.应用Matlab程序,对系统的混沌特性作了仿真实验分析,给出了不同γ值时的相图和位移波形图,并将本文(Ⅰ)中Melnikov函数法的判断条件与仿真结果作比较,两者的结果是一致的,而且仿真实验反映的混沌更具有丰富的数字特性.本文给出的方法可以推广到其他不同边界条件和不同外载荷条件下弹性薄板的磁弹性振动问题的研究.     

含几何缺陷的均质材料悬臂薄板的自由振动

以TC4钛合金均质材料悬臂薄板为研究对象.基于经典板壳理论,通过Rayleigh-Ritz法,根据悬臂板边界条件预设模态函数,求得包括全局、局部的函数型几何缺陷的悬臂板的前四阶固有频率.探究了悬臂板的缺陷类型、尺寸、位置等多种因素对自由振动的影响.     

轴向运动三阶剪切变形板自由振动的有限元模型及应用

采用三阶剪切变形理论,通过虚功原理建立轴向运动板的有限元方程,利用一种包含节点挠度及其斜率和截面转角的四节点四边形单元离散求解域,随后将离散式弹簧支承这一约束首次通过系统势能的形式引入系统有限元方程中.在算例应用部分,首先考虑不同边界条件以及不同支承刚度,与ANSYS计算结果进行对比,证明方法的有效性.接着在两种边界条件下针对轴向运动薄板分别研究运动速度和弹簧刚度与系统复频率实部和虚部的关系,结果显示高速易使板失稳,而高弹簧刚度会提高系统的振动频率.最后,给出板厚与系统复频率的关系,揭示了板厚对轴向运动三阶剪切变形板稳定性的影响.     

考虑关节柔性的模块机器人动力学参数辨识

提出了一种基于3维运动测量系统Optotrak3020的柔性关节模块机器人动力学模型参数辨识方法.首先将机器人的动力学模型参数化为不包括刚度力矩的线性形式,避免了参数矩阵的标定问题.激励轨迹基于有限的傅里叶级数函数,采用自适应遗传算法得出了优化的傅里叶级数系数.机器人每一关节单独跟随优化激励轨迹进行运动,同时电机位置、...     

基于板单元形函数的公路桥梁车桥耦合振动分析方法研究

为研究公路多片式梁桥的车桥耦合振动问题,提出一种基于矩形薄板形函数的车桥耦合振动分析方法.该方法以车轮与桥面接触点为界,将车桥耦合系统分为汽车与桥梁2个子系统,分别采用虚功原理与有限元法建立各自的运动方程,并通过车轮与桥面接触处的位移协调条件及车桥相互作用力的平衡关系相耦合,采用矩形薄板形函数实现车桥接触点位移与桥梁节点位移的联系以及车桥相互作用力的分配,通过迭代求解汽车和桥梁的运动方程得到其动力响应.根据分析方法的计算流程,编制了汽车 桥梁耦合系统的动力分析程序,并通过算例分析验证其可行性.研究结果表明,使用基于矩形薄板形函数的公路桥梁车桥耦合振动分析方法得到的车桥动力响应具有较好的精度,该方法具有广泛的适用性,可为多片式梁桥的车桥耦合振动分析提供一种新思路.     

带边角裂纹悬臂Mindlin 板的振动特性研究

本文基于Mindlin板理论,应用Ritz法研究带边角裂纹Mindlin板的振动特性,分析了不同裂纹参数如裂纹位置,裂纹长度,裂纹角度对悬臂Mindlin板的固有频率和模态的影响.利用Ritz法求解固有频率和模态函数,本文构造了一个特殊的模态函数,其模态函数由两部分构成,一部分是用梁函数组合法得到的无裂纹理想完整矩形板的振型,另一部分是利用裂纹尖端奇异性理论,构造描述裂纹附近位移和转角不连续的角函数.通过高精度的数值计算软件Maple得出结果,并与有限元软件ANSYS分析的结果进行对比,验证本文计算结果的准确性.     

输入具有齿隙非线性特性的周期系统的自适应控制

针对一类输入含齿隙非线性动态特性的周期时变系统, 在周期不确定性可时变参数化的条件下设计自适应控制器. 对周期时变参数进行傅里叶级数展开, 并采用微分自适应律估计未知傅里叶系数和齿隙动态特性参数, 通过鲁棒方法消除截断误差和齿隙模型的有界误差项对系统性能的影响. 采用双曲函数替代符号函数确保控制器可微, 同时能有效抑制颤振. 引入Δ函数, 避免参数估计发散, 并保证系统输出渐近跟踪理想轨迹. 理论分析与仿真结果表明, 闭环系统所有信号有界.     

作大范围运动FGM矩形薄板的动力学特性研究

对作大范围运动功能梯度材料矩形薄板的刚柔耦合动力学问题进行了研究.以连续介质力学为基础,在柔性薄板面内变形中考虑了传统建模方法忽略的二次耦合变形量,采用假设模态法对薄板变形位移进行离散,运用拉格朗日方程推导了大范围运动功能梯度材料板的刚柔耦合动力学方程.对旋转运动下取不同功能梯度指数的悬臂功能梯度板的动力学行为进行仿真,比较了本文建立的一次近似耦合模型和传统不计耦合变形项的零次近似模型.结果表明,随着转速的提高,传统零次模型发散,而本文模型收敛,能够较好地描述系统动力学行为.利用本文建立的一次近似模型,研究了功能梯度指数对转动功能梯度板变形的影响,研究表明,随着功能梯度指数的增大,板的横向变形也增大.通过求解旋转FGM板在恒定转速下的固有频率,进一步分析了功能梯度板材料组分变化对板振动特性的影响.     

样条有限点法在圆柱薄壳中的应用

对于弹性薄板的静力、自由振动和稳定问题,文献[1,2]已表明,利用样条有限点法比有限条法,有限元法及样条有限元法计算工作量都少,而精度高,特别是解动力和稳定问题其优点更加显著。样条有限点法究其实质是以梁的振型函数和样条函数作为位移函数,以样条结点参数作为未知参数的瑞利——里兹法,这种方法不但可应用于薄板问题,而且     

A three-dimensional free vibration analysis of cross-ply laminated rectangular plates with clamped edges

On the basis of three-dimensional elasticity, this paper presents a free vibration analysis of cross-ply laminated rectangular plates with clamped boundaries. The analysis is based on a recursive solution suitable for three-dimensional vibration analysis of simply supported plates. Clamped boundary conditions are imposed by suppressing the edge displacements of a number of planes which are parallel to the mid-plane. This is achieved by coupling a number of different vibration modes of the corresponding simply supported plate using a Lagrange multiplier method. A satisfactory solution can be obtained by choosing suitably larger numbers of the coupled vibration modes and the fixed planes across the thickness of the plate. Numerical results are presented to show the convergence of the solution. Results are also obtained for either isotropic or cross-ply laminated plates having different combinations of simply supported and clamped boundaries.     

Flexural vibration of shear deformable circular and annular plates on ring supports

This paper presents an analysis of free flexural vibration of circular and annular Mindlin plates lying on multiple internal concentric ring supports. The Rayleigh-Ritz method with an admissible displacement function expressed in terms of a set of simple polynomials is used to obtain the governing eigenvalue equation. The natural frequencies of circular and annular Mindlin plates with one or two ring supports having inner and outer peripheries with different combinations of free, simply supported and clamped conditions are determined. A comprehensive set of vibration results is presented and, where possible, these have been verified with existing solutions published in the open literature. No previous theoretical results for thick annular plates supported with internal rings are known to exist. Thus the study should be useful and valuable to engineers and researchers.     

Vibration studies on skew plates: Treatment of internal line supports

A comprehensive literature survey on the vibration of thin skew plates is presented and a few virgin areas on this subject are identified. As an initial part of a research plan to fill these gaps, the paper focuses on vibrating skew plates with internal line supports. For analysis, the pb-2 Rayleigh-Ritz method is used. The Ritz function is defined by the product of (1) a two-dimensional polynomial function, (2) the equations of the boundaries with each equation raised to the power of 0, 1, or 2 corresponding to a free, simply supported or clamped edge and (3) the equations of the internal line supports. Since the pb-2 Ritz function satisfies the kinematic boundary conditions at the outset, the analyst need not be inconvenient by having to search for the appropriate function; especially when dealing with any arbitrary shaped plate of various combinations of supporting edge conditions. Based on this simple and accurate pb-2 Rayleigh-Ritz method, tabulated vibration solutions are presented for skew plates with different edge conditions, skew angles, aspect ratios and internal line support positions.     

Stability analysis of skew orthotropic plates by the finite strip method

A stability analysis based on the Finite Strip Method is presented for skew orthotropic plates subjected to in-plane loadings. The straight sides of the plate are simply supported and the other two skewed sides are supported with any combination of fixed, free and simply supported boundaries. The plate is divided into strips, in contradistinction to elements in the Finite Element Method, and the displacement function is so chosen that it satisfies the boundary conditions and also the inter-strip compatibility conditions of an elemental strip. The energy expressions required to formulate the stiffness and stability coefficient matrices are formulated using smalldeflection theory. The buckling load intensity factor is evaluated for different aspect ratios of isotropic and orthotropic skew plates and the results of certain rectangular isotropic cases are compared with earlier investigations.     

Analysis of plate resting on elastic supports and elastic foundation by finite strip method

A procedure incorporating the finite strip method together with spring systems is proposed in this paper for treating plates on elastic supports. The spring systems can simulate different elastic supports, such as elastic foundation, line and point elastic supports, and also mixed boundary conditions. To illustrate the application of this procedure, two numerical examples are presented. A three-span simply supported plate is first considered and the effects of support stiffness on the static and free vibration responses and on the critical buckling stress are discussed. A plate resting on Winkler elastic foundation is next studied and the effects of dimension ratio on the static and free vibration responses are discussed. Numerical results show that the spring system can successfully simulate different kinds of elastic supports.     

Optimal locations of point supports in plates for maximum fundamental frequency

This paper investigates the optimal locations of rigid point supports to maximize the fundamental frequency of free vibration of plates. The computational method uses the Rayleigh-Ritz method for the vibration analysis and the simplex method of Nelder and Mead for the optimization search of support locations. Optimal results have been obtained for various common shapes of plates with a few point supports. The results show that the frequency of the plate is sensitive to the locations of the point supports. Moreover, these new optimal results provide useful information to designers seeking to exploit the position of point supports in their plate designs. It has been found that multiple solutions are a common feature of this plate optimization problem.     

Free vibration analysis of plates using least-square-based finite difference method

In this paper, we apply the two-dimensional least-square-based finite difference (LSFD) method for solving free vibration problems of isotropic, thin, arbitrarily shaped plates with simply supported and clamped edges. Using the chain rule, we show how the fourth-order derivatives of the plate governing equation can be discretized in two or three steps as well as how the boundary conditions can be implemented directly into the governing equation. By analyzing vibrating plates of various shapes and comparing the solutions obtained against existing results, we clearly demonstrate the effectiveness of LSFD as a mesh-free method for computing vibration frequencies of generally shaped plates accurately.     

In-plane vibration of plates by continuous mass matrix method

The continuous mass matrix method derived for frameworks is extended to the analysis of in-plane vibration of plates. A continuous mass distribution which is the same as the actual mass distribution of the plate is considered over each rectangular finite element. Taking into account that the rigid body movement produces inertial forces in dynamic analysis for a rectangular plate element eight independent conditions are provided to satisfy eight independent freedoms. Each condition is obtained from an independent displacement distribution satisfying the equations of motion at any point of the element and not only at the nodes of the rectangle. The dynamic element stiffness matrix thus obtained is a function of the natural circular frequency. The limit of the dynamic element stiffness matrix when the value of the natural circular frequency tends to zero is the static, stress compatible element stiffness matrix. The analysis of plates under forcing forces is performed by modal analysis after the natural circular frequencies and the corresponding modal shapes have been obtained from the free vibrations, for all the forcing forces are assumed to be function of the same time variation. Otherwise one must recur to a numerical analysis. The effect of the sizes, number of the meshes, the additional static load on the plate and the rigidity of the boundaries on the vibration of the plate is discussed. Few example problems are solved in order to illustrate the above mentioned effects. The numerical results obtained by continuous mass matrix method are compared with those of consistent mass matrix method. The convergence in terms of the sizes of meshes and the limit of convergence are examined.     

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.