郝际平
    （西安建筑科技大学 710055）

[提要]  用Ritz法研究了薄圆板的非线性振动问题，考虑了圆柱正交异性材料参数及边界转动弹性约束刚度对非线性固有频率的影响。为提高精度，在应用Ritz法时，不同时设定反映本文研究问题的泛函中所含有的两个未知函数，而是建立两未知函数之间精确关系的微分方程，在设定一个未知函数的基础上，寻找最好的另一未知函数，然后再实施Ritz法。在设定一个未知函数时，用Legendre多项式构造而成，即试图通过这样两方面的努力来提高Ritz法的精度。结果表明；所述方法切实可行，以Legendre多项式构成的域函数收敛快、精度高。
[关键词]  薄圆板 非线性振动 Ritz法 Legendre多项式  固有频率

Nonlinear vibration of circular thin plates has been investagted in this paper. The Ritz method was used with Legendre's multionmial expansion as a trial function of deflection that is one of the un-known funotion of energy funf:tional. Another unknown function-Airy stress function was obtained through differential relation between deflection and Airy stress function. Some examples are compared with the reference and they are in good agreement.
Keywords: thin slab; nonlinear vibration; Ritz method; Legendre's multionmial expansion