【摘要】 基于Winkler地基模型及Euler-Bernoulli梁理论,建立了Winkler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,得到离散的非线性振动方程,利用多尺度法求得该系统1/3次亚谐共振的一阶近似解。分析了长细比、弹性模量、地基刚度、阻尼、密度等参数对其亚谐共振幅频响应的影响,并通过与非共振硬激励情况对比分析1/3次亚谐共振对系统实际动力反应的影响。研究结果表明:1/3次亚谐共振区域对外激励幅值敏感;阻尼或地基刚度大于一定值后,系统将不出现1/3次亚谐共振响应;1/3次亚谐共振显著增大系统稳态动力响应位移。更多还原

【Abstract】 The nonlinear vibration of finite-length beams on the Winkler foundation subjected to harmonic lateral loads is investigated in the present paper.Based on the Winkler foundation model and the Euler-Bernoulli beam theory,the nonlinear motion equation of the finite-length beam on elastic foundation is derived.The approximate solution of the finite-length beam for the case of the 1/3 sub-harmonic resonance is obtained by using the Galerkin method and the multi-scale method.To illustrate the characteristics of the 1/3 sub-harmonic resonance,the effects of the slenderness ratio,modulus of elasticity,stiffness coefficient of foundation,damping coefficient and beam density on the frequency-response curves of the finite-length beam on the Winkler foundation are studied.The effect of the 1/3 sub-harmonic resonance on the actual dynamic response of this system is analyzed with the contrast to the non-resonant situation.The numerical results show that the excitation amplitude has significant impact on the 1/3 sub-harmonic resonance region;the resonance of the finite-length beam on elastic foundation will not appear when the damping coefficient or the stiffness coefficient of foundation is greater than a certain value;the 1/3 sub-harmonic resonance significantly increases the displacement of the stationary response.更多还原