基于能量泛函方法,建立了开口矩形板自由振动分析模型。计算了开口矩形板的固有频率和振型函数。在处理开口问题时,利用对称性和反对称性只研究四分之一块板,并将其分割成三个区域,通过位移连续条件建立区域之间的联系,并用梁函数模拟位移场,最终得到整体能量泛函。对其变分后得到广义特征值矩阵方程,求解方程可以求出各阶固有频率。结果对比表明本文方法的准确性,为在方案设计阶段快速分析开口矩形板振动及其相关问题提供了理论基础。

This article based on the energy functional method to establish a free vibration analysis model and calculate the natural frequency of rectangular plate with an opening. When considering the opening, only a quarter of the plate is available by using symmetry and antisymmetry conditions, which is divided into three regions. Then find connections between regions through continuity conditions of displacement. Displacement field is simulated by beam functions and get the overall energy function. After that, natural frequencies are obtained by solving dispersion characteristic equations yielding by variational method. The results show that the accuracy of the method by comparison. The method provides theoretical foundation on the issue of vibration of rectangular plate with opening and problem related.