Spectral element methods for nonlinear spatio-temporal dynamics of an Euler-Bernoulli beam (Q1368127)

The space-time spectral element method is employed to solve a simply supported modified Euler-Bernoulli nonlinear beam undergoing forced lateral vibrations. This system was chosen for analysis due to the availability of a reference solution of the form of a forced Duffing's equation. Two formulations were examined: i) a generalized Galerkin method with Hermitian polynomials as interpolants both in spatial and temporal discretization, ii) a mixed discontinuous Galerkin formulation with Hermitian cubic polynomials as interpolants for spatial discretization and Lagrangian spectral polynomials as interpolants for temporal discretization.