Coupled Bending-Bending Vibrations of Pretwisted Non-uniform Beams

• Main Authors: Hsian-Lee Chiou, 邱顯澧
• Other Authors: Sen-Yung Lee
• Format: Others
• Language: zh-TW
• Published: 1996
• Online Access: http://ndltd.ncl.edu.tw/handle/86032222915496628193

碩士 === 國立成功大學 === 機械工程研究所 === 84 === Based on the Bernoulli-Euler beam theory, the governing equations and associated boundary conditions for the coupled bending-bending vibration of nonuniform pretwisted cantilever beams of rectangular cross-section are derived. The explicit relations between the two flexural displacements are established. The two coupled differential equations are decoupled into two complete integral-differential equations expressed in two flexural displacements, respectively. While taking the limiting studies for the beam without pretwisting, the integral-differential equation is reduced to a fourth-order differential equation. Finally, we can get the closed-form solutions of the governing equations through the decoupled differential equations and boundary conditions. The frequency equation is expressed in terms of the eight fundamental solutions of the system. Finally, a semi-exact solution method is used to find natural frequencies of the system.