Large amplitude vibration of a beam based on a higher-order deformation theory

✍ Scribed by Ji-Liang Doong; Chun-Sheng Chen

• Publisher: Elsevier Science
• Year: 1988
• Tongue: English
• Weight: 552 KB
• Volume: 25
• Category: Article
• ISSN: 0003-682X
• DOI: 10.1016/0003-682x(88)90062-x

✦ Synopsis

A BSTRA CT A higher-order formulation of large amplitude vibrations of simply supported beams subjected to initial stress is presented. The initial stress is taken to be a combination of a pure bending stress plus an extensional stress of the neutral axis of the beam. By neglecting the higher-order terms and introducing the shear correction factor into governing equations, these equations can be reduced to Timoshenko beam theory ( present first-order beam theory). The Galerkin method is used to reduce the governing nonlinear partial differential equations to ordinary nonlinear differential equations in terms o fan unknown function of time. The Runge-Kutta method is. used to obtain the period. Numerical results show that if the amplitude ratio increases, significant errors in the first-order beam theory can be observed, and that higher-order shear deformation terms are necessary to solve this problem.