相对振型转换法求解具有多点限制连续体振动响应

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，在前文提出的相对振型转换法(Relative Mode Transfer Method, RMTM)的基础上得到了一种广泛适用的求解该类问题非线性振动响应的方法。利用推导得到的方法研究了一个两端固支中点带限制弹簧梁系统的非线性振动，利用新方法处理了接触振型及非接触振型之间的转换，从算例结果看，本文采用的方法求解时具有收敛性好，精度高等优点。通过梁上受限点振动幅值的分岔图及时程图，讨论了该算例所代表的一类梁系统的幅频响应特点，研究了振型耦合、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得到的结果进行了对比，印证了新方法的正确性。

Study on the Non-linear Dynamic Response of Continuous System with multipoint Constraints Based on Relative Mode Transfer Method

The method proposed here in this work is aimed at solving the problem of dynamic response of the forced vibration of continuous systems with arbitrary discrete piecewise-linear constraints or nonlinear constraint which can be converted to piecewise-linear form. This approach is deduced based on mode transfer principle and variation theory referring the previous fundamental work which is named Relative Mode Transfer Method(RMTM) put forward before. A study case of a clamped-clamped beam with a constraint at the middle point is studied to illustrate the new method. The transfer between contact modes and non-contact modes is dealt with the new approach. It can be seen from the simulation result that it is an efficient and high precision method with good convergence in the simulating process. The distinct characteristic of the frequency response of a class of beam system represented by the numerical example is discussed, the effects of modes coupling, stiffness of the stop spring to the response are studied. The study case is also solved adopting Force Integration Method(FIM), and the results are compared which corroborates the new method.