考虑有限深度土体运动的Winkler地基梁自由振动分析

利用Winkler地基梁理论,考虑有限深度土体运动的影响,建立了弹性地基梁的线性运动方程。采用分离变量法,求得弹性地基梁的模态构型、固有频率和有阻尼自由振动。通过数值计算和参数分析,揭示了有限深度Winkler地基上固支-自由梁的线性动力学特性,分析了土体质量、地基深度和阻尼等对系统固有频率和线性自由振动响应的影响。研究结果表明:若将有限深度土体运动引入到弹性地基梁的动力学模型,系统的固有频率将显著降低;土体质量和地基深度均抑制阻尼对弹性地基梁动力响应影响的发挥,在一定程度上减慢其动能耗散的速度。

Free vibration of beams on winkler foundation with the consideration of finite-depth soil motion

Based on the Winkler foundation model, considering the effect of finite depth soil motions, the linear vibration equation of a beam on elastic foundation was derived. Using the separation of variables, the mode configuration, natural frequency and damped free vibration of the beam on elastic foundation were obtained. By means of numerical calculation and parameter analysis, the linear dynamic characteristics of the clamped-free beam on Winkler foundation of finite depth were revealed. Meanwhile, the effects of the soil mass, foundation depth and damping on the natural frequency and dynamic response of the system were analyzed. The numerical results show that the natural frequency of the beam on elastic foundation decreases significantly, when the motion of finite depth foundation is considered integratedly in the dynamic model of the system. Moreover, the mass and depth of foundation inhibit the effect of damping on the dynamic response of the beam on elastic foundation, and slow down the kinetic energy dissipation rate to some extent.