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中文摘要：
基于Winkler地基模型及Euler-Bernoulli梁理论，建立了弹性地基上有限长梁的非线性运动方程．运用Galerkin方法对运动方程进行一阶模态截断，并利用多尺度法求得该系统主共振的一阶近似解．分析了长细比、地基刚度、外激励幅值和阻尼系数等参数对系统主共振幅频响应的影响，然后通过与非共振硬激励情况对比分析主共振对其动力响应的影响．结果表明：主共振幅频响应存在跳跃和滞后现象；阻尼对主共振响应有抑制作用；主共振显著增大系统稳态动力响应位移．
英文摘要：
The nonlinear vibration of finite-length beams on the Winkler foundation subjected to the lateral loads is investigated. Based on the Winkler foundation model and the Euler-Bernoulli beam theory, the nonlinear in-plane motion equation of the finite-length beam on the Winkler foundation is obtained. The approximate solution of the finite-length beam for the case of the primary resonance is obtained by the Gaierkin method and the method of multiple scales. To illustrate the characteristics of the primary resonance, the effects of major parameters on the frequency-response curves of the beam on the elastic foundation axe studied, such as, the slenderness ratio, the stiffness coefficient of the foundation, the amplitude of the excitation and the damping coefficient. Comparing with the non-resonant response of the beam, the effect of the primary resonance on the actual dynamic response is analyzed. The numerical results show that the frequency-response curves of the beam have jump and delay; the damping term plays a very important role in the primary resonance of the beam, the primary resonance significantly increases the amplitude of the steady state response.
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