摘要
本文利用边界条件Fourier展开法计算任意形状薄板的微振动振型。结合Berger方程的动力学推广形式,得到了关于未知的时间特性函数的非线性常微分方程,以及用第一类完全椭圆积分表示的任意形状薄板的非线性振动频率比,给出了有关圆板、椭圆板单振型大幅振动的数值结果。
The use of the method of Fourier expansion of boundary condition to determinethe linear free-vibration modes of plates with arbitrary shape, together with the useof the dynamic analog of Berger's equation, yields the nonlinear ordinary differen-tial equation of the unknown time function, from which the expression of nonlinearfrequencies in terms of the complete elliptic integral of the first kind is obtained.Numerical examples are given for the nonlinear frequencies of single-mode forcircular and elliptic plates with edges clamped, and the comparison is made withthose previously known, which clarify the advantages of the present method.
出处
《复旦学报（自然科学版）》
CAS
CSCD
北大核心
1989年第2期164-169,共6页
Journal of Fudan University：Natural Science
关键词
薄板
非线性振动
弹性振动
nonlinear vibration
plates
elastic vibration
analytic-numerical technique.
