微分变换法在动力学响应分析及系统边界参数识别中的应用研究

RESEARCH ON THE APPLICATION OF DIFFERENTIAL TRANSFORM METHOD IN RESPONSE ANALYSIS AND BOUNDARY CONDITION PARAMETERS IDENTIFICATION

引入求解非线性微分方程的微分变换法,将其推广为广义微分变换法。建立求解一般非线性振动微分方程的一般框架,将此方法用于求解著名的Vanderpol方程。并且将微分变换法推广到结构边界参数识别,以一个典型的悬臂梁边界参数识别为例,对其进行数值仿真和实验研究,并将此方法的实验研究识别结果与用实测频率响应函数法的识别结果作比较。说明该方法具有良好的工程应用价值。

A differential transform method is introduced to solve nonlinear differential equations and extended as a generalized differential transform method. Consequently, a procedure is established to solve nonlinear differential equations for general vibration problems, and to solve the famous Van der pol equation. Then, the proposed differential transform method（DTM） is generalized to identify boundary condition parameters. As an example, a typical cantilever beam is chosen to identify its elastic boundary condition parameters.The numeric simulation and experiment result, the result got by this method and FRF（frequency response function） identification are compared respectively. They prove the proposed method is effective.