Normal modes of a continuous system with quadratic and cubic non-linearities
- 作者：Qaisi ; M.I.
- 刊名：Journal of Sound and Vibration
- 出版年：2003
- 期刊代码：91_0022460x
- 类别：ph
- 出版时间：August 7, 2003
- 卷：265
- 期：2
- 页码：329-335
- 文件大小：115 K
摘要
A power series solution is presented for the free vibrations of simply supported beams resting on elastic foundation having quadratic and cubic non-linearities. The time-dependence is assumed harmonic and the problem is posed as a non-linear eigenvalue problem. The spatial variable is transformed into an independent variable that satisfies the boundary conditions. This permits a power series expansion of the beam motion in terms of the new variable. A recurrence relation is obtained from the governing equation and used in conjunction with the Rayleigh energy principle to compute the natural frequencies. The results show that, for a first order approximation, only the lower frequencies and first mode shape are significantly affected by the cubic non-linearity.