基于波函数法的附加弹簧阻尼薄板的振动研究

Vibration analysis of plates with spring-damper by using wave based method

基于Kirchhoff薄板弯曲振动理论和波函数法Wave Based Method（WBM）理论,推导了运用WBM将附加弹簧阻尼结构转化为点激励的方法,构建了基于WBM计算含弹簧阻尼支承薄板振动响应的系统矩阵,得到了含弹簧阻尼支承的薄板弯曲振动响应。以四边简支矩形板为例,计算了50~600 Hz频段内参考点的振动响应,并与解析法和有限元法的计算结果进行了对比。运用该方法对比计算了添加不同弹簧阻尼结构数与无弹簧阻尼结构时薄板在120 Hz的弯曲振动响应。结果表明：通过将弹簧阻尼结构转换成点激励的方法,能有效的将WBM应用于附加弹簧阻尼支承薄板弯曲振动响应的仿真计算,与有限元法相比,有着更高精度和收敛速度。

A wave based prediction technique for spring-damper plates was proposed based on the theory of Kirchhoff and wave based method（ WBM） via converting the additional spring-damper structure into a point force with modified frequency and amplitude of displacement. The system matrix of plates with spring-damper was constructed by using WBM to solve the bending vibration response of plates. Taking a four edges simply supported rectangular plate as an example,the method was verified via comparing the vibration response at a reference point in 50- 600 Hz frequency band implemented by the method with those by the analytic method and finite element method respectively. The vibration responses of plates with different number of spring-damper were computed to find the effect of the adding structure. The analysis results indicates that WBM is valid in the prediction of vibration responses of spring-damper plates. Contrasting with the FEM,the WBM can achieve higher accuracy and converging rate in the calculation of mid-frequency bending vibration responses of spring-damper plates.