时滞效应对弹性地基上梁主共振响应影响分析

Effect of Time Delay on Primary Resonant Response of Beam on Elastic Foundation

本文研究了弹性地基上梁主共振响应的时滞效应.基于Hamilton原理,建立了时滞影响下弹性地基上梁的非线性运动微分方程,采用多尺度法,求得了时滞效应下主共振响应调制方程以及稳定性条件.通过数值算例,分析了时滞和调谐参数影响下主共振响应的峰值及幅频响应特性.结果表明,地基反力中的时滞效应对主共振响应影响较大,会导致共振域偏移,在一定区间内,响应幅值随时滞变化先减小再增大,呈现出周期性,并导致幅频曲线弯曲程度增大.

In this study,the time delay effect of the primary resonance response of beams on elastic foundations is considered.Based on Hamilton’s principle,the differential equation of nonlinear motion of the beam on the elastic foundation considering the time delay effect is established,and the modulation equation of the main resonance response and the stability conditions under the effect of time delay are obtained by using the multi-scale method.Through numerical examples,the peak and the amplitudefrequency characteristics of the primary resonance response under the influences of time delay and tuning parameters are analyzed.The results show that the time delay effect in the reaction force of the foundation has a great impact on the primary resonance response,and will probably cause the shift of the resonance range.Within a certain range,the response amplitude first decreases and then increases with the change of time delay,showing a periodic character,and leading to an increase in the bending degree of the amplitude-frequency curve.