移动荷载下有限深度Winkler地基上梁的动力响应研究

王举1,马建军1, 2,韩书娟1,李达1,郭颖2

振动与冲击 ›› 2023, Vol. 42 ›› Issue (13) : 193-198.

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振动与冲击 ›› 2023, Vol. 42 ›› Issue (13) : 193-198.
论文

移动荷载下有限深度Winkler地基上梁的动力响应研究

  • 王举1,马建军1, 2,韩书娟1,李达1,郭颖2
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Dynamic response of beam on Winkler foundation with finite depth under moving load

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

基于考虑有限深度土体运动的Winkler地基梁理论,建立移动荷载作用下弹性地基上有限长梁的横向运动方程。利用模态叠加法求得移动荷载作用下有限长梁动力响应的解析解,进而以移动荷载离开时梁的响应为初值,采用分离变量法求得有限长梁自由振动的一阶近似解。通过数值计算和参数分析,揭示了移动荷载作用下有限深度Winkler地基上简支边界梁的动力学特性,分析了地基深度、地基黏滞阻尼系数和荷载移动速度等对有限长梁受迫振动阶段和自由振动阶段动力响应的影响,全面揭示了有限深度土体运动对临界速度的作用效应。结果表明:地基深度显著降低了临界速度,而且弹性地基黏滞阻尼明显延长了自由振动衰减时间;荷载移动速度加剧了有限深度弹性地基与其支承梁的相互作用效应,系统振动的幅值和响应周期均发生显著变化。

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.

关键词

Winkler地基梁 / 土体运动 / 移动荷载 / 模态叠加法 / 动力响应

Key words

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

引用本文

导出引用
王举1,马建军1, 2,韩书娟1,李达1,郭颖2. 移动荷载下有限深度Winkler地基上梁的动力响应研究[J]. 振动与冲击, 2023, 42(13): 193-198
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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