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A finite element–equivalent energy linearization technique for the analysis of nonlinear plate vibration
Author(s) -
Ghabrial M. A. E.,
Miller R. K.,
Wellford L. C.
Publication year - 1985
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620210811
Subject(s) - linearization , finite element method , nonlinear system , discretization , vibration , mathematics , equivalence (formal languages) , boundary value problem , mathematical analysis , control theory (sociology) , computer science , structural engineering , engineering , physics , control (management) , discrete mathematics , quantum mechanics , artificial intelligence
A simplified technique for the dynamic analysis of geometrically nonlinear plate structures is developed. The essence of this technique is the construction of a linear substitute of the nonlinear problem. The linear substitute problem is derived from an equivalence criterion which involves balancing the energies of the linear substitute model and the nonlinear model over one period of oscillation. The linearized equations are discretized by a finite element method, and solutions at different amplitudes are obtained numerically by an incremental‐iterative scheme. To verify the equivalent energy linearization approach, example problems consisting of the free and forced vibration of nonlinear circular plates with various boundary conditions are studied. All results are compared to theoretical and numerical solutions in the literature. In addition, the forced vibration results are compared to available experimental results. These comparisons tend to validate the assumptions made in the equivalent energy linearization procedure. The proposed method is found to be computationally more efficient than other available procedures.