边界弹性支撑地基板在移动荷载作用下的振动分析

Dynamic Analysis of the Elastic Boundary Support Plates Traversed by Moving Load on Elastic Foundation

刚性道面的接缝都具有一定的传荷能力,充分考虑此点可使设计更为经济合理,因此把刚性道面板建立为运动荷载作用下,弹性半空间地基上四边具有弹性支撑有限矩形板,此模型为一种新的力学模型。然后以单位力作用下的四边简支矩形板为基本系统,通过简化约束,考虑板挠曲面微分方程与振型函数在数学及力学上的相似性并利用互等功定理及变分法原理,求解出在匀速移动荷载作用下该矩形板的动力响应解析解。最后根据机场工程中实测的道面板弯沉值,利用此解析解反算出了板四边弹性支撑的刚度系数。通过该方法可以寻找接缝板动力挠度响应问题的一般规律,进而为从理论上找出动态接缝传荷(传剪)能力问题的一般规律提供参考,最终使有限矩形道面板的设计更加有效合理。

The joints of rigid pavement have certain load transfer capacity, and taking full consideration of this can make design more efficiently. So a new mechanical model about rigid pavement plates is presented. This model depicts that the four joints of the rectangular plates＇ edges in the airport＇ s rigid pavement are considered as elastic boundary supports. By choosing a basic system that has four simple supported edges and that is loaded with a unit force and by simplifying the edges of the real system and considering differential equation of plate＇ s flexure plane similar to mode shape function, the author concludes the analytical solution of the rectangular plate with four elastic boundary supports on elastic foundations subjected to the uniform velocity moving point - load by Betti＇ s reciprocal theorem of work. According to the flexible data of engineering, deduces the rigid modulus of elastic boundary supports. By this means general rule of the rectangular plates＇ joints dynamic response can be found, which can provide reference when solving question of the dynamic load transfer capacity of the joints.