相对振型转换法求解分段线性边界条件连续体振动响应的优点

摘要

为了研究航天领域关注的非线性连接结构对整体结构振动响应的影响,文章利用变分原理,重新推导了基于振型转换的求解具有任意分段线性及可以转换为分段线性边界条件的连续体振动响应的方法——相对振型转换法,并与文献[10]中的混合方法的推导过程进行了对比,印证了相对振型转换法的正确性及其优点.针对一个施加均布载荷的端点单侧带阻挡的悬臂梁算例,分别应用相对振型转换法及力积分法进行了求解,通过悬臂梁端点的分岔响应研究了系统的非线性响应,讨论了两种方法得到的结果.%Based on the variational principle, the Relative Mode Transfer Method (RMTM), that we previously proposed, is deduced again in the present paper, for solving the vibration problems of continuous systems with arbitrary piece-linear boundary conditions and nonlinear boundary conditions that can be transformed into piece-linear boundary conditions.The derivations in this paper and reference [10] are compared in order to verify the validity of the RMTM and its advantages are discussed.A cantilever with a stop at the end and excited by a uniform distributed force is considered and the responses are obtained both by the RMTM and the Force Integration Method(FIM).The nonlinear vibration of the typical system is studied through the bifurcation response and the time history at the end, and the results are discussed.