CAJ | 학술논문

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。
이삼고문헌[3]급정적운동미분방정위기출,사용일충경합리적방법대기출량단수간해격려적교지량적최저계주공진현상진행료연구,피면료직접채용선성자유진동모태적전개식래표시비선성방정적해。이용다척도법구득방정적일차근사전개해,계산결과표명소채용적해적형식대우구해지고필모일계주공진차임의량모태간불존재내공진적정황비교간단,소연구적량단교지량적주공진곡선정경특성。
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.