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- W1997437532 abstract "We determine the response of bowed structural elements to a two-frequency, transverse load. The effects of both initial curvature (i.e., quadratic nonlinearities) and mid-surface stretching (i.e., cubic nonlinearities) are included. We investigate possible large-amplitude-low-frequency responses to excitations of such structural elements (drumming) and determine the conditions under which the one-half subharmonics of the transverse load can be excited individually in the presence of three-to-one internal resonance. The method of multiple time scales is used to determine four first-order nonlinear ordinary differential equations that govern the time variation of the amplitudes and phases of the interacting modes. The fixed points of these equations are obtained and their stability is determined. Numerical solutions are carried out and graphical representations of the results are presented. The region of multivalued disappear for increasing the parameters µ22, d6, Γ2 and decreasing the parameters d2, d4, d5 and ω1. The nontrivial solution has unstable solution for increasing the damping factors. The trivial solution has unstable and stable solutions for decreasing the parameters Γ1 and Γ2 respectively." @default.
- W1997437532 created "2016-06-24" @default.
- W1997437532 creator A5054473926 @default.
- W1997437532 date "2005-01-01" @default.
- W1997437532 modified "2023-10-17" @default.
- W1997437532 title "Three-to-one Internal Resonance in The Non Linear Oscillation of Shallow Arch" @default.
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- W1997437532 doi "https://doi.org/10.1088/0031-8949/72/6/003" @default.
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