Analysis of Nonlinear Elastic Membrane Oscillations by Eigenfunction Expansion
نویسنده
چکیده
In this paper we examine a spatially two–dimensional forced, damped Boussinesq equation with quadratic nonlinearity. This equation describes small, nonlinear oscillations of a circular, elastic membrane in the presence of viscosity. The eigenfunction expansion method is used for the purpose of constructing solutions for small initial data analytically. The constructive method enables us to perform numerical simulations as well. The conservative theoretical results are extended through numerical simulations: we examine the convergence properties, the smallness requirement on the perturbation parameter, and the long–time behavior of the system. Key-Words: Numerical simulation, Boussinesq equation, Eigenvalue expansion, Quadratic nonlinearity.
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