系列移动荷载下周期性弹性支撑连续梁的共振及消振效应

基于Fourier变换、系列Fourier变换及传递矩阵方法,研究了移动荷载列作用下周期性弹性支撑连续梁的共振及消振效应。通过Fourier变换和系列Fourier变换,把单个移动载荷所引起的动力响应表示为响应函数沿代表跨的积分。利用梁和弹性支撑处的传递矩阵,建立了周期性弹性支撑连续梁的响应函数和特征方程。根据叠加原理并利用单个移动载荷的解,得出了等间距移动载荷列作用下周期性弹性支撑连续梁的动力响应表达式。根据单个移动载荷引起梁的频域响应,建立了周期性弹性支撑连续梁在等间距移动载荷列作用下的共振和消振条件。计算结果表明:当移动载荷列的速度及间距符合共振条件时,将会发生共振效应;当符合消振条件时,将会发生消振效应。

Resonance and cancellation effects of periodically elastically supported continuous beam under a series of moving loads

Based on the Fourier and Fourier sequence transforms, and the transfer matrix method, the resonance of a periodically elastically supported continuous beam produced by a series of moving loads and its cancellation effects were investigated. By using the Fourier and Fourier sequence transforms, the dynamic response produced by single moving loads was represented by the integral of the response function over the representative span. The response function and eigenvalue equation of the periodically elastically supported continuous beam were obtained using the transfer matrices between the beam and its elastic supporting points. According to the superposition principle and the expression of the dynamic response of the beam under single moving loads, the dynamic response of the beam under a series of equidistant moving loads was obtained. Using the frequency domain dynamic response of the beam under single moving loads, the resonance and cancellation conditions of the periodically elastically supported continuous beam subject to a series of equidistant moving loads were established. Numerical results show that, when the loading velocity and distance satisfy the resonance condition, resonance will occur; when the condition for resonance cancellation is fulfilled, the effect of resonance cancellation will occur.