A finite element–equivalent energy linearization technique for the analysis of nonlinear plate vibration

✍ Scribed by M. A. E. Ghabrial; R. K. Miller; L. C. Wellford Jr.

• Publisher: John Wiley and Sons
• Year: 1985
• Tongue: English
• Weight: 1010 KB
• Volume: 21
• Category: Article
• ISSN: 0029-5981
• DOI: 10.1002/nme.1620210811

✦ Synopsis

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.