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基于经典Winkler地基模型及Euler-Bernoulli梁理论,考虑梁的几何非线性效应,运用Newton第二定律建立了弹性地基上有限长梁的非线性运动方程。采用Galerkin方法对运动方程进行一阶模态截断,进而利用多尺度法求得了该系统自由振动的一阶近似解。揭示了两端简支梁的非线性自由振动特性,分析了弹性模量、长细比及地基刚度系数等参数对系统固有频率的影响。并通过该系统的位移时程曲线,分析了阻尼对弹性地基上梁运动特性的影响。
Based on the classical Winkler foundation model and the Euler-Bernoulli beam theory, considering the geometrical nonlinear effect of the beam, the nonlinear motion equation of the finite length beam on the elastic foundation is established by the Newton’s second law. First-order modal truncation of the equation of motion was performed by Galerkin method, and then the first-order approximate solution to the free vibration of the system was obtained by using the multi-scale method. The nonlinear free vibration characteristics of simply supported beams at both ends are revealed. The influence of elastic modulus, slenderness ratio and foundation stiffness coefficient on the natural frequency of the system is analyzed. The influence of damping on the motion characteristics of beam on elastic foundation is analyzed through the displacement history curve of the system.