Nonlinear analysis of the forced response of a beam with three mode interaction

✍ Scribed by W. K. Lee; K. Y. Soh

• Publisher: Springer Netherlands
• Year: 1994
• Tongue: English
• Weight: 703 KB
• Volume: 6
• Category: Article
• ISSN: 0924-090X
• DOI: 10.1007/bf00045432

✦ Synopsis

An analysis is presented for the primary resonance of a clamped-hinged beam, which occurs when the frequency of excitation is near one of the natural frequencies, cv~. Three mode interaction (co: ,~ 3cot and cv3 ,,~ cv~ + 2cv2) is considered and its influence on the response is studied. The case of two mode interaction (aJ2 ~ 3COl) is also considered to compare it with the case of three mode interaction. The straight beam experiencing mid-plane stretching is governed by a nonlinear partial differential equation. By using Galerkin's method the governing equation is reduced to a system of nonautonomous ordinary differential equations. The method of multiple scales is applied to solve the system. Steady-state responses and their stability are examined. Results of numerical investigations show that there exists no significant difference between both modal interactions' influences on the responses.