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本文对受均载的四边简支及四边固支均质正交各向异性弹性矩形薄板在支座受正弦激扰下的大挠度瞬态响应进行了理论研究,首先将控制方程和边界条件无量纲化,同时分别将挠度和力函数的解假设为在空间域上满足边界条件的双重梁函数级数形式,由于是动态,所以这些试函数每项的待定幅值都设为时间t的函数,然后用Galerkin法消去空间自变量函从而得到一组在时域上关于待定幅值的表为单自变量t的非线性常微分方程组。由于是非线性,所以它们是互相耦合的。最后,用变步长的Runge-Kutta法在IBM-5550计算机上求得瞬态响应的数值解。同时,作为正交各向异性弹性薄板的一个特例,本文对各向同性均质弹性矩形薄板在均布载荷下支座受到正弦激扰的大挠度瞬态响应进行了实验,测出了板的前四阶固有频率以及板振动的中心点最大挠度值。最后,将实验值与理论值进行了比较与分析。
In this paper, the theoretical analysis of the large deflection transient response of the bearing subjected to sinusoidal perturbation is carried out on four kinds of simply-supported and four-legged fixed orthotropic elastic rectangular plates under load. Firstly, the governing equations and boundary conditions are immeasurable At the same time, the solution of deflection and force function is assumed to be the form of dual-beam function that satisfies the boundary conditions in the space domain. Since they are dynamic, the undetermined amplitude of each of these trial functions is set as a function of time t Then, the Galerkin method is used to eliminate the spatial argument and obtain a set of nonlinear ordinary differential equations in the time domain about the unknown amplitude as a single independent variable t. Because they are non-linear, they are coupled to each other. Finally, the numerical solution of the transient response is obtained on the IBM-5550 computer using a variable-step Runge-Kutta method. In the meantime, as a special case of an orthotropic elastic sheet, a large-deflection transient response of the isotropic homogeneous elastic rectangular sheet subjected to sinusoidal perturbation under uniform load is experimentally investigated. The first four natural frequencies and the plate center of the maximum deflection value. Finally, the experimental values and theoretical values were compared and analyzed.