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

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,在以前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,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。

The method proposed here was aimed at solving dynamic response of a continuous system with arbitrary piecewise-linear constraints or a nonlinear constraint converted into piecewise-linear constraints. This approach was deduced based on the mode transfer principle, the variational principle and the Relative Mode Transfer Method （RMTM） presented by the authors in the past. An example of a clamped-clamped beam with a constraint at the middle point was studied to illustrate the new method. The transfer between contact modes and non-contact modes was investigated with the new approach. It was shown from the example results that the proposed method is an efficient and high precision method with good convergence in simulations. The characteristics of the frequency response for a class of beam systems represented by the numerical example were discussed, the effects of modes coupling, stiffness of the constraint spring on the response were studied. The example was also solved with the Force Integration Method （FIM）, its results were compared with those using the new method, the correctness of the proposed method was verified.