相对振型转换法求解具有多点限制连续体振动响应  

Non-linear dynamic response of a continuous system with multipoint constraints based on relative mode transfer method

作　　者：孔宪仁[1] 卫洪涛[1] 王本利[1] 张相盟[1] 

机构地区：[1]哈尔滨工业大学卫星技术研究所,哈尔滨150001

出　　处：《振动与冲击》2013年第3期12-17,共6页Journal of Vibration and Shock

基　　金：“微小型航天器系统技术”长江学者创新团队发展计划(IRT0520)

摘　　要：针对任意多处具有任意分段线性限制的连续体,通过变分原理,基于振型转换思想,在相对振型转换法(Relative Mode Transfer Method,RMTM)基础上得到一种广泛适用的求解该类问题非线性振动响应方法。用推导得到的方法研究两端固支中点带限制弹簧的梁系统非线性振动,处理接触振型及非接触振型之间的转换,算例结果表明,采用该方法求解时具有收敛性好,精度高等优点。通过梁上受限点振幅分岔图及时程图,讨论该算例代表的一类梁系统幅频响应特点,研究振型耦合、限制弹簧刚度对响应的影响。利用力积分法(Force Integration Method,FIM)对算例进行求解与相对振型转换法结果进行对比,印证新方法的正确性。The method proposed here was aimed at solving a problem of dynamic response of a continuous system with arbitrary discrete piecewise-linear constraints or a nonlinear constraint which could be converted to a piecewise-linear form. This method was deduced based on the mode transfer principle and the relative mode transfer method （RMTM）. An example of a clamped-clamped beam with a constraint at the middle point was studied with the new method. The transfer between contact modes and non-contact modes was performed with the new approach. The example results showed that is an efficient and higher precision method with good convergence in simulations. The distinct characteristics of the frequency response of a class of beam system represented by the numerical example were discussed, the effects of mode-coupling, a certain range of spring stiffness on the response were studied. The example was also solved adopting the force integration method （ FIM）, and the results were compared with those using RMTM, the correctness of the new method was verified.

关 键 词：模态分析 连续体 非线性振动 分段线性 相对振型转换法 

分 类 号：V414[航空宇航科学与技术—航空宇航推进理论与工程]