附加多个集中质量加筋板的自由振动分析

摘要

Based on the method of variational energy function,the free vibration characteristics of discrete stiffened plates are studied in this paper. When assessing the deformation coordination constraints of boards and ribs,the vibration analysis problem of stiffened plates is transformed into a classical uncon-strained variational problem by introducing Lagrange multipliers. Through this method,a generalized char-acteristic value of matrix equations of stiffened plates are obtained,and solving the equation set yields the natural frequency of different order for the composite structure. By taking a discrete stiffened plate with four simple edge supported boundary conditions as an example,the characteristic values to determine its mode shape are obtained,and the simulation results are compared with those acquired from the multi-stiff-ened stiffness average method in order to validate the proposed method. Finally,this paper provides a new idea for solving this kind of engineering problems.%基于能量泛函变分的方法,研究附加多个集中质量纵横加筋板的自由振动特性.在处理板与筋条的变形协调约束条件时,通过引入拉格朗日乘子,把板、梁组合振动分析问题转化为处理一类无约束泛函变分问题,从而得到加筋板的广义特征值矩阵方程.通过集中质量点的形式引入板上装载设备质量.求解方程可以得到组合结构的各阶固有频率.以四边简支边界条件纵横离散加筋板为计算实例,通过特征值确定其振型并与仿真分析结果进行对比分析,表明其准确有效,可为此类工程问题的研究提供理论基础.