ISSN:
1573-269X
Keywords:
Nonlinear vibration of a beam
;
three mode interaction
;
mid-plane stretching
;
method of multiple scales
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract 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,ωn . Three mode interaction (ω2 ≈ 3ω1 and ω3 ≈ ω1 + 2ω2) is considered and its influence on the response is studied. The case of two mode interaction (ω2 ≈ 3ω1) 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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00045432
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