折线型非线性振动响应计算的时域有限元分段求解

本文研究折线型非线性振动系统响应的求解，按分段线性性质建立了分段线性的时域有限元离散模型。在求解中先计算当前段的振动响应，根据转折条件判断是否存在转折点。当存在多个转折点时，以最早出现的转折点作为下一段的起始点，否则以本时间段终点作为下一段的起始点，然后进入下一段的计算。本文方法能在每一段较精确地求出转折点，并同时给出该转折点之前各结点的响应解。较有效地解决了这类问题的数值求解。文中算例给出了相当精确的计算结果，验证了本文方法的有效性。

Time-domain finite element technique for response calculation of nonlinear vibration system with fold linearity

A study on solving the response of nonlinear vibration system with fold linearity is presented in this paper. A finite element model in time domain is developed basded on its fold linearity. When all nodal responses in one time segment have been solved, the conditions of turning point are used to determine whether there exist turning points in this time segment. If such turning points appear in this region, the smallest one is taken as the initial time of the next segment, otherwise the last time node is considered as the initial time of the next segment. Then the response of next time segment will be calculated. Both the turning point and the responses before this point in current seggment can be relatively exactly solved by presented method. Some results with high precision are got from some numerical examples in the paper, which verify that the method presented is very effective and useful.