Dynamic Response Analysis of Structures Using Legendre–Galerkin Matrix Method

The solution of the motion equation for a structural system under prescribed loading and prediction induced accelerations, velocities, displacements is special importance in engineering applications. In most cases, however, it impossible to propose an exact analytical solution, as case systems subjected stochastic input motions or forces. This also non-linear systems, where numerical approaches shall be taken into account handle governing differential equations. Legendre–Galerkin matrix (LGM) method, this regard, one basic solving As spectral estimates response set polynomials. Using Legendre’s orthogonal basis considering Galerkin’s approach transforms algebraic polynomials then solves acquired equations which eventually yield problem solution. paper, LGM method used solve single-degree (SDOF) multi-degree-of-freedom (MDOF) systems. obtained outputs are compared with methods (when available), step-by-step linear Newmark-β method. presented results show that offers outstanding accuracy.