具有正交各向异性涂层的矩形板动力学问题解析解  

An Analytical Solution for the Dynamics of Rectangular Plates with Orthotropic Coating Layers

作　　者：李映辉[1] 邓一三[1] 赵华[1] 

机构地区：[1]西南交通大学应用力学与工程系,四川成都610031

出　　处：《四川大学学报（工程科学版）》2007年第4期63-67,共5页Journal of Sichuan University (Engineering Science Edition)

基　　金：国家自然科学基金资助项目(10472097);四川省应用基础项目(05JY029-006-3)

摘　　要：针对涂层结构数值模拟计算中关心的问题,研究了上下表面覆盖正交各向异性涂层的简支矩形板的自由振动及其在横向载荷作用下的强迫振动的三维解析解。基于正交各向异性涂层及各向同性板的本构方程,在不计体力的情况下给出了涂层板的弹性动力学方程。然后基于满足上下表面边界条件及涂层界面协调条件的位移函数,将涂层板的弹性动力学方程简化为一组常微分方程组,并给出了幂级数方法求解该微分方程组的方法。最后以涂层方板为例,分别用本方法和有限元法计算了该涂层板的固有频率、涂层表面压力作用下的静态响应、涂层表面简谐压力作用下的动态位移响应。算例表明解析解具有较高的计算精度。In order to overcome the problems on numerical simulation of structures with thin coating layers on its surfaces, a three-dimensional analytical solution was tangular thick plates with thick orthotropic coating forces, the elastic dynamic equations of the coated presented for free and forced vibrations of simply supported reclayers on the top and bottom surfaces. In the absence of body plate the constitutive description of the anisotropic coating lay- ers, and the isotropic plate were given first. Then the suitable displacement functions that identically satisfy boundary conditions on the top and the bottom surface and the interface conditions between the plate and the coating layers were used to reduce equations to a set of coupled ordinary differential equations, which were then solved by the power series method. Finally by the comparison of the analytical natural frequencies, displacements and stresses of a rectangular coated plate apphed a sinusoidal spatial pressure on its top surface with those given by the finite element method （FEM）, the validity of the analytical solution given in this paper is testified .

关 键 词：正交各向异性涂层 矩形板 振动 

分 类 号：TF12[冶金工程—粉末冶金] TB44[冶金工程—冶金物理化学]