桩基非线性轴向受迫振动稳态幅频响应分析

STUDY ON STEADY-STATE FREQUENCY-RESPONSE OF NONLINEAR AXIAL FORCED VIBRATION OF PILES

用多时间尺度法得到了一端固定、另一端自由的桩基非线性轴向受迫振动系统主共振时的稳态幅频响应曲线。研究表明:桩基非线性轴向受迫振动的幅频响应曲线不仅与派生线性振动系统的固有频率、土刚度和阻尼系数有关,而且也与振幅、相位和非线性特征量有关。幅频响应曲线中会出现一种典型的振幅跳跃的非线性现象,当激励频率接近线性系统固有频率时,系统产生共振从而响应幅值增大,而且同一激励频率可能会对应于振幅的多个不同值,运动状态具有不稳定性。随着非线性系数的增大,响应曲线峰值侧向弯曲;粘性阻尼会抑制响应振幅的增大;激励振幅增大会导致响应振幅增大。

The steady-state amplitude-frequency response curve for the primary resonances of the nonlinear axial forced vibration of a pile fixed at one end and free at the other end is presented by the method of multiple time scales. Results show that the amplitude-frequency response curve for the nonlinear axial forced vibration of the pile is related to not only the natural frequency of the derivational linear vibration system, soil rigidity, and damping coefficient, but also the amplitude, phase and nonlinear eigenvector. A kind of typical nonlinear phenomenon of amplitude skipping is appeared on the amplitude-frequency response curve. When the exciting frequency approachs to the natural frequency of linear system, the system produce resonance so as to increase the response amplitude, and one exciting frequency is corresponding to several different values, and the motion state has instability. As the nonlinear coefficient increases, the peak of response curve bends to the left; viscous damping could restrain the accretion of responding amplitude; the accretion of incentive amplitude results in the accretion of responding amplitude.