中文摘要：

以参考文献[3]给定的运动微分方程为基础,使用一种更合理的方法对基础两端受简谐激励的铰支梁的最低阶主共振现象进行了研究,避免了直接采用线性自由振动模态的展开式来表示非线性方程的解。利用多尺度法求得方程的一次近似展开解,计算结果表明所采用的解的形式对于求解只考虑某一阶主共振且任意两模态间不存在内共振的情况比较简单,所研究的两端铰支梁的主共振曲线呈硬特性。

英文摘要：

Based on the non-linear governing equations given by reference [3],a more reasonable method which avoids using the expansion of linear free vibration mode to represent the solution of the nonlinear equation is adopted to research the first primary resonance of a simply supported slender beam under the harmonic excitation on both ends.A first-order uniform expansion of the equation is obtained by multi-scale approach,and the results indicate that the solution used in this paper for solving the primary resonance is simple in the case where only the nth mode is directly excited and thus it is assumed that there does not exist any internal resonance between two modes,and the non-linear dynamic instability behavior of the beam becomes hardening spring type.