Dynamic response of beam on Winkler foundation with finite depth under moving load

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Journal of Vibration and Shock ›› 2023, Vol. 42 ›› Issue (13) : 193-198.

WANG Ju1, MA Jianjun1, 2, HAN Shujuan1, LI Da1, GUO Ying2

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Abstract

Based on the theory of beam on Winkler foundation considering finite depth soil mass motions, the lateral motion equation of the finite-length beam on elastic foundation subjected to moving load is derived. The modal superposition method is used to obtain the analytical solution of the dynamic response of the finite-length beam subjected to the moving load. The separation variable method is used to get the first-order approximate answer of the finite-length beam vibration after the moving load. Using the numerical calculation and parameter analysis, the dynamic characteristics of beams with simply supported boundary conditions on the Winkler foundation with finite depth subjected to moving load are revealed. The effects of the mass of the foundation, the viscous damping coefficient of the foundation, and the moving speed of load on the dynamic response of the finite length beam in the forced vibration stage and the free vibration stage are analyzed, and it fully reveals the effect of the soil movement on the critical velocity. The results show that the depth of the foundation significantly reduces the critical speed; Moreover, the viscous damping of the elastic foundation significantly prolongs the decay time of the free vibration; the moving speed of the load intensifies the interaction effect between the finite depth elastic foundation and its supporting beam, the amplitude and response period of the system vibration are significantly changed.

Key words

Winkler foundation beam / soil motion / moving load / Modal superposition / dynamic response.

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WANG Ju1, MA Jianjun1, 2, HAN Shujuan1, LI Da1, GUO Ying2. Dynamic response of beam on Winkler foundation with finite depth under moving load[J]. Journal of Vibration and Shock, 2023, 42(13): 193-198

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