In-place Free Vibration Analysis for Laminated Composite Arch Structures of Variable Curvature

• Main Authors: Kao, Ming-Sun, 高銘遜
• Other Authors: Tseng, Yi-Ping
• Format: Others
• Language: zh-TW
• Published: 1998
• Online Access: http://ndltd.ncl.edu.tw/handle/84825457612817982999

碩士 === 淡江大學 === 土木工程學系 === 86 === 　　The laminated composite materials show the benefits of high strength-weight rate and corrosion-resistance through careful design. Curved beams have the characteristics of high compression capacity. Consequently, the composte laminated curved beam is expected to be an efficient member used in many ways. Generally, there are closed-form solutions for vibration of circular beam, but not for curved beam of variable curvature. Based on the Mindlin curved beam theory, this paper incorporates the dynamic stiffness method with a series solution to solve the in-plane free vibration analysis of composite arch structures of variable curvature, wherein the shear deformation and rotation inertia are included. 　　In this thesis, the free vibraton of cross-ply and angle-ply composite laminated arch are studied.The structure is divided into several elements in the dynamic stiffness method. The partial differential equation of curved beam are solved theoretically, and then the dynamic stiffness is formulated. Therefor, the dynamic stiffness is considered to be an analytical soluton. However, there do not exist analytical solution for the curved beam of variable curvature. It is then necessary to use the series solution method. First of all, the displacement is assumed in series form. The geometric curve of variable curvature is also expressed in Taylor series. Both series are substituted into the goerning equaton of composite laminated arch structures.The element dynamic stiffness is then obtained. The global dynamic stiffness in term of frequency can be assembled. At last, the bisection method is used to solve for the natural frequency. 　　The present method combines the benefidts of the series solution method and the finite element method, and then can be used to analyze complicated structures. In addition, very high accurate results can be obtained by a few terms of series, since the structure system is subdivided into elements. The obtained natural frequencies can be a reference of practical engineering design.