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

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Journal of Vibration and Shock ›› 2019, Vol. 38 ›› Issue (6) : 62-66.

MA Jianjun, QIN Ziguo, LIU Fengjun, GAO Xiaojuan

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Abstract

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. 

Key words

Beam on elastic foundation / Winkler model / soil motion / natural frequency / free vibration

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MA Jianjun, QIN Ziguo, LIU Fengjun, GAO Xiaojuan. Free vibration of beams on winkler foundation with the consideration of finite-depth soil motion[J]. Journal of Vibration and Shock, 2019, 38(6): 62-66

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