摘要
基于Winkler地基模型、Euler梁理论和弹性地基的运动方程,建立了考虑土体质量影响的Winkler地基上有限长梁的非线性动力学模型。利用特征值分析和多尺度方法,分别求得梁的线性和非线性固有频率及模态构型。进而通过数值分析,研究了土体质量对Winkler地基上有限长梁线性和非线性自由振动的影响。研究结果表明:若将土体质量对梁动力响应的影响引入Winkler地基上有限长梁的动力学模型,梁的固有频率降低;土体质量对梁的高阶非线性模态构型影响显著。
Based on the Winkler model, Euler beam theory, and the motion equation of elastic foundation, the nonlinear dynamics model of a finite-length beam on Winkler foundation with a consideration of the effect of soil mass is obtained. Applying the eigenvalue analysis and the method of multiple scales, the linear and nonlinear natural frequencies and mode shapes of the beam are obtained. By means of the numerical calculation, the effect of soil mass on the linear and nonlinear free vibrations of the finite-length beam on Winkler foundation are explored. The numerical results show that: the natural frequencies of beam decrease, when the effect of soil mass on the dynamic response of the beam is included in the nonlinear dynamic model of the finite-length beam on Winkler foundation. Moreover, it is significant for the effect of soil mass on the high-order nonlinear mode shapes of the beam.
引文
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