Energy-consistent, Galerkin approach for the nonlinear dynamics of beams using intrinsic equations

The paper presents a Galerkin approach for the solution of nonlinear beam equations. The approach is energy consistent, that is, it is shown that the weighted residual integral describes energy flow. The Galerkin approach gives accurate results with fewer degrees of freedom as compared to low-order finite-element formulation. The Galerkin approach also leads to a nonlinear order-reduction technique that can be used to further decrease the order of the system. The reduced-order model is shown to capture the dominant nonlinearities in the system and is ideal for preliminary design and control synthesis.