CAJ | 학술논문

基于理论计算有限元方法分析了四边固支矩形板结构的自由振动问题，求得了四边固支矩形板的振动固有频率和振型。利用双向梁函数构造了四边固支矩形板的振型函数，并根据位移变分原理求得了矩形板的固有振动特性。在板单元理论的基础上，利用有限元法推导了薄板振动的质量矩阵和刚度矩阵。由于工程实际中只关心板结构振动的横向位移幅值，利用静力凝聚法将质量矩阵和刚度矩阵中转动自由度上的质量和刚度凝聚到横向振动自由度上，以达到降低模型阶目的，为板结构振动主动控制奠定基础。
기우이론계산유한원방법분석료사변고지구형판결구적자유진동문제，구득료사변고지구형판적진동고유빈솔화진형。이용쌍향량함수구조료사변고지구형판적진형함수，병근거위이변분원리구득료구형판적고유진동특성。재판단원이론적기출상，이용유한원법추도료박판진동적질량구진화강도구진。유우공정실제중지관심판결구진동적횡향위이폭치，이용정력응취법장질량구진화강도구진중전동자유도상적질량화강도응취도횡향진동자유도상，이체도강저모형계목적，위판결구진동주동공제전정기출。
Finite element method based on theoretical calculation was used to analyze the free vibration of fully clamped rec-tangular plate structure,its natural frequencies and vibration mode were obtained,its vibration mode function was estab-lished using two-dimension beam function,and its natural vibration characteristics were obtained according to displacement variation principle.On the basis of the theory of plate element,the finite element method was employed to derive mass ma-trix and the stiffness matrix of the thin plate vibration.Due to the main concern is with the lateral displacement amplitude of the vibration of the plate structure in real practice,the study used static condensation method to condense the quality and stiffness at the rotational freedom of mass matrix and stiffness matrix onto the transverse vibration degrees of freedom,so as to achieve the purpose of reducing the model order,laying foundation for active vibration control of plate structure.