热环境下混凝土矩形薄板在弹性地基上的振动

VIBRATION OF CONCRETE RECTANGULAR THIN PLATE SUBJECTED TO THERMAL ENVIRONMENT WITH SIMPLY SUPPORTED EDGES ON ELASTIC FOUNDATION

基于刚性板的小挠度理论,考虑混凝土的材料非线性,推导了双参数弹性地基上混凝土矩形薄板热弹性问题的动力方程。采用级数法,导出了热环境下双参数弹性地基上四边简支混凝土矩形薄板的固有频率计算公式和强迫振动下的挠度函数。为便于工程应用,给出了双参数弹性地基上四边简支混凝土矩形薄板在恒向变温和温度均匀变化时的固有频率和均布荷载作用下的挠度函数。针对W inkler弹性地基的情况,讨论了板的材料弹性常数、几何尺寸(长宽比)、相对厚度、刚度系数k和温度对薄板固有频率和挠度函数的影响,从而为工程结构中热环境下弹性地基上混凝土矩形薄板的振动计算提供了理论依据。

Based on the small deflection theory of plate and in consideration of the physical nonlinearity of concrete,the dynamic equation of concrete rectangular plate subjected to thermal environment on two-parameters elastic foundation is derived.Using Galerkin principle,the nonlinear dynamic equation and its closed-form solution for a simply supported concrete rectangular plate on elastic foundation under uniform heat change are presented,and the influences of material constant,length-width ratio,relative thickness,rigidity coefficient and temperature on natural frequencies of plate are discussed.The theoratical base about its dynamic calculation is provided.