薄板弯曲自由振动问题的高精度近似解析解及改进研究

发布时间：2018-06-30 00:23

本文选题：Hamilton体系 + 薄板　；参考：《应用数学和力学》2016年11期

【摘要】：对于薄板弯曲自由振动问题,已有如下方法:在Hamilton(哈密顿)体系下基于分离变量法得到挠度的解析形式,并建立自振频率联立方程组,给出求解振动频率和振型函数的方法.笔者指出该方法中所用挠度函数的解析式实际上是一种满足位移边界条件的高精度近似解,基于Rayleigh-Ritz(瑞利-里茨)法再次求近似频率后发现,原方法的近似解的精度很高.另外,对于含有固支、简支等不同的边界形式,恰当地选取不同位置作为坐标系的原点,得到含有频率的方程组的统一形式,且较为简洁.这些形式可基于四边固支、四边简支等边界条件的矩形板研究,依照板变形的对称性可验证频率方程组形式的正确性,并得到不同边界条件下频率方程形式之间的联系与转化.
[Abstract]:For the bending free vibration of thin plates, the following methods have been developed: based on the method of separating variables, the analytical form of deflection is obtained in Hamilton system, and the simultaneous equations of natural vibration frequency are established, and the method to solve the vibration frequency and mode function is given. The author points out that the analytical formula of deflection function used in this method is in fact a high precision approximate solution which satisfies the displacement boundary condition. Based on Rayleigh-Ritz (Rayleigh-Ritz) method to calculate the approximate frequency again, it is found that the accuracy of the approximate solution of the original method is very high. In addition, for different boundary forms, such as fixed support and simple support, different positions are properly selected as the origin of the coordinate system, and the unified form of the equations with frequency is obtained, which is more concise. These forms can be studied on rectangular plates with quadrilateral fixed and simply supported quadripartite boundary conditions. According to the symmetry of plate deformation, the correctness of frequency equations can be verified, and the relations and transformations between the forms of frequency equations under different boundary conditions are obtained.
【作者单位】：苏州科技学院土木工程学院工程力学系;西北工业大学工程力学系;
【基金】：国家自然科学基金(11202146) 江苏省青蓝工程基金~~
【分类号】：O327;O302

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