速度作用下非线性弹性地基上矩形薄板主共振

本文基于非线性弹性地基模型及弹性理论,建立了非线性弹性地基上矩形薄板在移动车辆荷载作用下的非线性动力方程,运用Galerkin方法及多尺度法求得该系统主共振的幅频响应方程,以行车速度为调谐参数,分析阻尼系数、车辆荷载、板厚及相位差等参数对非线性弹性地基上矩形薄板在移动车辆荷载作用下主共振幅频响应的影响。结果表明:非线性弹性地基上矩形薄板在行车速度作用下主共振系统的非线性特点不明显,振幅-速度响应曲线接近对称,改变阻尼系数、车辆荷载等参数时对共振区间影响不大。在正常取值范围内,随着阻尼系数值增大振幅-速度响应曲线峰值减小;随着车辆荷载、板厚及相位差的增大振幅-速度响应曲线峰值增大。

The Main Resonance of Rectangular Thin Plate on Nonlinear Elastic Foundation with the Effect of Velocity

Based on the model of the nonlinear elastic foundation and the elastic theory, this paper establishes the nonlinear dynamic equation of rectangular thin plate on the nonlinear elastic foundation under the load of moving vehicles. Using the Galerkin method and the method of multiple scales, the amplitude frequency response equation of the main resonance in this system can be obtained. Taking the driving speed as the turning parameter, this paper analyzes the impact of the damping coefifcient, vehicle load, the plate thickness and phase difference. The result indicates that on the nonlinear elastic foundation, with the effect of driving speed, the nonlinear characteristics of the main resonance system of the rectangular thin plate are not obvious; the amplitude-velocity response curve is close to the symmetry; and the impact of the changes of damping coefifcient and vehicle load on the resonance range is small. In addition, in the normal range, with the increase of the damping coefficient, the peak of the amplitude -velocity response curve decreases; and with the increase of the vehicle load, the plate thickness and the phase difference, the peak of the amplitude-velocity response curve also increases.