圆形刚性承载板载荷作用下双参数地基上多层矩形板的动力响应

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振动与冲击 ›› 2015, Vol. 34 ›› Issue (17) : 199-206.

论文

张震东，马大为，何强，朱忠领

作者信息 +

Dynamic response of multi-layer rectangle plate on two-parameter foundation model under circular rigid bearing plate load

Zhang Zhen-dong Ma Da-wei He Qiang Zhu Zhong-ling

Author information +

文章历史 +

摘要

提出了一种考虑水平阻尼的双参数地基模型，推导了此地基模型上多层矩形板的中性面位置表达式，建立了水平动载荷与垂向动载荷联合作用下多层地基板内力平衡方程，并在此基础上给出了板的运动微分方程。采用级数分解和Laplace积分变换相结合的方法，求解了圆形刚性承载板载荷作用下多层地基板的挠度解析表达式。在MATLAB软件中编写计算程序，以三层地基板为例深入分析了水平阻尼系数、摩擦系数、运动方向对板动力响应的影响。研究表明，随着水平阻尼系数的增大，板的挠度逐步减小，摩擦系数和运动方向对载荷作用面圆心处的动力响应几乎没有影响，而对远离圆心处点的挠度影响较大。

Abstract

A two-parameter foundation model is proposed considering horizontal damping. Then the express of neutral layer location of multi-layer rectangle plate on the foundation model is deduced. In order to get the motion differential equation of plate, internal force equilibrium equation of multi-layer plate is built under horizontal dynamic load and vertical dynamic load. Then the expression of multi-layer rectangle plate deflection under circular rigid bearing plate load is deduced by combing Laplace integral transformation and triangular series methods. To evaluate of the influence of horizontal damping coefficient, friction coefficient and motion direction on dynamic response of plate, arithmetic program applies to three-layer plate is complied by using MATLAB software. Results indicate that the deflection of plate reduces gradually as the value of horizontal damping coefficient increases, friction coefficient and motion direction have greater influence on deflection of the point situated away from the center. While for the dynamic response of load action region center, this influence can be ignored.

导出引用

张震东，马大为，何强，朱忠领. 圆形刚性承载板载荷作用下双参数地基上多层矩形板的动力响应[J]. 振动与冲击, 2015, 34(17): 199-206

Zhang Zhen-dong Ma Da-wei He Qiang Zhu Zhong-ling. Dynamic response of multi-layer rectangle plate on two-parameter foundation model under circular rigid bearing plate load[J]. Journal of Vibration and Shock, 2015, 34(17): 199-206

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