简谐干扰力作用的弹性基础上压杆的横向振动与屈曲

The transverse vibration and buckling of a compressive bar on elastic foundation subjected to harmonic excitation

基于Hamilton原理,运用假设时间模态法,考虑横向简谐干扰力作用下弹性基础上的压杆,选取一端刚性固定另一端活动铰接为边界条件,建立了系统横向非线性振动与屈曲的位移型常微分控制方程及定解条件;采用打靶法得到了一阶结构频率、一阶屈曲荷载、主共振响应的数值结果。结果表明:随轴心压力增加,一阶结构频率减小;随弹性基础刚度增加,一阶结构频率与屈曲荷载均增加;当干扰力频率接近一阶结构频率时,会激发结构的主共振响应;当基础刚度增加时,共振区向干扰力频率增大的方向偏移;k为0、30、60时,系统具有硬弹簧特性。

Based on the Hamilton's principal, a compressive bar on elastic foundation subjected to transverse harmonic disturbing force is taken into account by selecting the end fixed and the other end movable simply supported boundary conditions. The ordinary differential governing equations of the transverse nonlinear vibration and buckling of system are obtained by using the method of 'assumed-time-mode'. The numerical results of the first-order structure frequency and the first-order buckling load and the primary resonance are obtained by employing the shooting method. Results obtained show that the structural frequencies decrease with the increase of axial compressive force. The structural frequencies and buckling load increase with the increase of foundation stiffness. When the disturbance frequency is close to the first-order structure frequency, the primary resonance response of structure may be stimulated. With the increase of the foundation stiffness, the resonance area shifts to the disturbance force frequency increases direction and the system reveals a hard spring property of nonlinear system.