弹性基础上压杆的横向非线性自由振动与屈曲

THE TRANSVERSE NONLINEAR FREE VIBRATION AND THE BUCKLING OF A COMPRESSIVE BAR ON AN ELASTIC FOUNDATION

基于Hamilton原理,运用假设时间模态法,得到了弹性基础上压杆的横向非线性自由振动与屈曲的位移型常微分控制方程.考虑一端固定另一端可移简支边界条件,采用打靶法得到了结构第一至第三阶结构频率与一阶屈曲载荷的数值结果.结果表明:随轴心压力增加,结构频率减小;随弹性基础刚度增加,结构频率与屈曲载荷均增加;弹性基础刚度对结构频率的影响随振型阶数增加在减小;在小振幅的情形下,不同振型对一阶屈曲载荷的影响很小.

Based on Hamilton＇s principal, the ordinary differential control equations for the transverse nonlinear free vibration and the buckling of a compressive bar on an elastic foundation are obtained by using the method of ＂assumed-time-mode＂. With one end fixed and the other end movable simply supported, the numerical results of the first to third order structural frequencies and the first order buckling load are obtained by employing the shooting method.The results show that the structural frequencies decrease with the increase of the axial compressive force. The structural frequencies and the buckling load increase with the increase of the elastic foundation＇s stiffness. The effect of the stiffness of the elastic foundation on high order structural frequencies is reduced with the increase of the order number of the vibration modes. The effect of different vibration modes on the first order buckling load is negligible as far as a small amplitude is concerned.