弹性边界约束矩形板的振动特性分析:理论、有限元和实验

Vibration properties of rectangular plates with elastic boundary constraints:theory,finite element and experiments

提出一种有效的理论方法研究弹性边界约束矩形板的振动特性,并设计实验测试不同边界矩形板的固有频率。矩形板的弹性边界约束采用一系列的均布线性弹簧模拟,用特征正交多项式来表示矩形板的位移容许函数,并采用瑞利-里茨法获得弹性边界约束矩形板的固有频率和固有振型。通过改变边界弹簧的刚度即可模拟矩形板不同的边界条件,提高计算效率。基于理论方法计算获得结构固有频率并和有限元及实验结果进行对比,验证所提理论方法的正确性。此外,通过实验测试的方法分析弹性-简支、弹性-固支等不同边界组合条件下矩形板的振动特性,分析调整不同边界弹簧刚度对矩形板振动特性的影响。

An effective theoretical method is proposed to study the vibration characteristics of rectangular plates with elastic boundary constraints,and the natural frequencies of rectangular plates are obtained experimentally.The elastic boundaries of a plate are modelled by a set of distributed springs.By employing the characteristic polynomial series as the admissible functions,the Rayleigh-Ritz method is applied to obtain the natural frequencies and modes of a rectangular plate with elastic boundary constraints.By changing the stiffness of the boundary springs,different boundary conditions of the plate can be realized,and the calculation efficiency is obviously improved.The structural natural frequencies calculated from the present theoretical method are in good agreement with the finite element and experimental results,which demonstrates the effectiveness of our theoretical model.In addition,the vibration characteristics of a rectangular plate under different boundary conditions,such as elastic-simply supported and elasticclamped boundaries,are studied experimentally.The influence of spring stiffness on the vibration behaviors of the rectangular plate is analyzed in detail.