两种求解连续体撞振响应方法对比研究

力积分法和振型转换法是处理连续体撞振问题的常用方法。虽然作者已在前期提出了相对振型转换法,进一步扩展了传统振型转换法的适用范围,但尚未对其与力积分法求解结果差异进行深入研究。文章分别采用力积分法和相对振型转换法对基于工程背景的实际算例进行了数值求解,进而通过一种差异指标研究了刚度、阻尼对求解结果差异的影响。将上述两种方法与现有实验数据进行对比,结果表明,刚度增大与阻尼减小均会导致两种方法的分析结果差异增大,尤其当刚度提高到一定程度,即撞振为刚性撞击时,需要与实验结果对比确定仿真的正确性。对比两种方法数值求解过程可以发现,力积分法易于数值实现,而相对振型转换法具有计算效率高、收敛性好等优点。

A comparative study of two methods for determining the vibration response of vibro-impact continuum

The force integration method(FIM) and the mode transfer method(MTM) are two kinds of frequently-used methods to solve the vibro-impact problem of continuum. In a previous paper, the authors put forward the method of the relative mode transfer method(RMTM), and expanded the application scope of MTM, but the differences of numerical results obtained from the FIM and the RMTM remain to be explored. With an example of practical engineering background, the numerical results are obtained both through the FIM and the RMTM. An index for evaluating the difference of the results is proposed, and the effects of the stiffness and the damping ratio on the index are discussed. Finally the results are compared with the experimental data from literature, and it is indicated that the increase of the stiffness and the damping ratio leads to the increase of the difference index. The correctness of the simulation result using the two methods is determined by comparing with experimental data when the stiffness is increased to a certain degree which makes the impact become a rigid impact. By comparing the numerical process of the two methods, it is shown that FIM is more convenient to obtain the results but RMTM enjoys a better convergence and a higher calculation efficiency.