热载下钢筋混凝土矩形简支薄板的自由振动

Vibration of reinforced concrete rectangular plate subjected to thermal loading condition with simply supported boundary conditions

为了得到工程结构中热载作用下钢筋混凝土矩形薄板的自由振动规律,基于刚性板和小挠度理论,按照iliushin小弹塑性理论和Hognestad等建议的混凝土本构模型,建立了混凝土薄板下应力-应变的非线性弹性本构方程,推导了热载作用下钢筋混凝土矩形薄板的动力方程.利用Galerkin原理,得到了四边简支钢筋混凝土矩形薄板在温度均匀变化时的非线性动力方程及其解析解.结果表明:板的材料弹性常数、几何尺寸(长宽比)、相对厚度和温度对薄板的固有频率具有一定的影响.

In order to obtain the laws of free vibration about the reinforced concrete rectangular plate subjected to thermal loading in engineering structures, based on the rigidity plate and the small deflection plate theory, the nonlinear - elastic constitutive equations of stress - strain for concrete plate were established according to the Ilyushin＇ s small elastic - plastic theory and the constitutive equations of concrete proposed by Hognestad, et al. And the dynamic equation of reinforced concrete rectangular plate subjected to thermal loading was derived. Using Galerkin principle, the nonlinear dynamic equation and its analytic solution were obtained for a simply supported rectangular plate made of reinforced concrete under uniform heat change. The results show that material constant, length -breadth ratio, relative thickness and temperature have an effect on the natural frequency of plate.