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Analytical solutions for bending, vibration and stability of multilayer orthotropic rectangular thin plates

DOI：10.7511/jslx20200715002

 作者 单位 E-mail 曹彩芹 西安建筑科技大学 理学院, 西安 710055 宋永超 西安建筑科技大学 理学院, 西安 710055 1148856190@qq.com

构造了带有补充项的双重正弦傅里叶级数通解来求解各种边界条件的多层正交各向异性矩形薄板的弯曲、振动和稳定问题。将坐标轴取在中性面上，求出用挠度表示的应力表达式，然后由横截面上每单位宽度的应力合成板的内力；再将层合板的内力代入板的平衡方程中得到板的控制方程，将多层板的物理参数折算为等价的单层板物理参数；最后联立控制方程与边界条件，求得未知量的系数并代入本文的通解中。本文的通解不需要叠加即可求解各种边界条件的板的弯曲、振动和稳定问题；现有的对于单层板的研究都可以用本文的方法拓展到多层板领域；对于复杂边界条件的板，也可以使用该通解分析。

A general solution of double sine Fourier series with supplementary terms is constructed to solve the bending, vibration and buckling problems of multi-layer orthotropic rectangular thin plates with various boundary conditions.First, the stress expressed in tems of deflection at the coordinate axis on the neutral plane is found, then the internal force of the plate on cross section is obtained;then the physical parameters of the multi-layer plate are coverted into the equivalent physical parameters of the single-layer plate;finally, the control equations and boundary conditions are combined to obtain the coefficients of the unknown quantity and bring them into the general solution.The general solution in this paper can solve the bending, vibration and buckling problems of various boundary conditions without superposition;the existing research on single-layer plates can be extended to the field of multi-layer plates by this method;plates with complex boundary conditions can also be analyzed using this general solution.