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Bifurcation structure and scaling properties of a subsonic periodically driven panel with geometric nonlinearity
Author(s) -
Li Peng,
Yang Yiren,
Dong Yu
Publication year - 2015
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201200275
Subject(s) - galerkin method , bifurcation , nonlinear system , mathematics , scaling , mathematical analysis , bifurcation diagram , bifurcation theory , saddle node bifurcation , ordinary differential equation , physics , differential equation , geometry , quantum mechanics
Bifurcation structure and scaling properties of a nonlinear subsonic panel with a harmonic excitation are investigated numerically and theoretically in this paper. The panel under study is two‐dimensional and simply supported considering Kelvin's model of structural damping and geometric nonlinearity generating by large deflection based on the von Kármán's theory. Galerkin method is used to derive the subsonic aerodynamic pressure and transform the governing partial equations to a series of ordinary differential equations. Numerical calculations were conducted to the analysis on the bifurcation structure of the nonlinear panel system and the distributions of complex responses regions are shown in a two‐parameter space. The interesting scaling properties of the bifurcation structure are discussed in terms of a discrete mapping theoretically based on linear approximation. The proposed approximate analytical method shows a good agreement with the numerically found scaling properties.