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  

Dynamic response of a multi-layer rectangular plate on a two-parameter foundation under a circular rigid bearing plate's load

作　　者：张震东[1] 马大为[1] 何强[1] 朱忠领[1] 

机构地区：[1]南京理工大学机械工程学院,南京210094

出　　处：《振动与冲击》2015年第17期199-206,共8页Journal of Vibration and Shock

基　　金：国防基础科研(B2620110005)

摘　　要：提出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。A two-parameter foundation model was proposed considering horizontal damping.Then the displacement expressions of neutral layer plane of a multi-layer rectangular plate on the foundation model were deduced.In order to get the motion differential equation of the plate,its internal force equilibrium equations were built under the combined action of horizontal dynamic load and vertical dynamic one.Then the analytical expression of the plate deflection under a circular rigid bearing plate＇s load was solved with the combination of Laplace integral transformation and the triangular series methods.The influences of horizontal damping coefficient,friction coefficient and motion direction on the dynamic response of the plate were analyzed by using MATLAB software and taking a three-layer plate as an example.Results indicated that the deflection of the plate decreases gradually with increase in horizontal damping coefficient;the friction coefficient and motion direction have a greater influence on the deflection of the point far from the circuar plate center,but their effects on the dynamic response of the circular plate center can be ignored.

关 键 词：圆形刚性承载板 水平阻尼系数 双参数地基模型 多层板 水平动载荷 垂向动载荷 

分 类 号：TJ768.1[兵器科学与技术—武器系统与运用工程]