Spectral element method in structural dynamics

The authors present a brief review of the spectral element method (SEM) in structural dynamics. A background discussion is included that provides a reference to previous works. The dynamic shape function approach of spectral element formulation is reviewed, and the state-vector approach is introduced for one-dimensional structures. The SEM for the forced vibrations of one-dimensional structures is briefly introduced in a general form for both the point and the distributed dynamic loads and is applied to Levy-type plates and smart beam structures. The accuracy of the spectral element is verified by comparing the SEM solutions with the solutions obtained by other methods including the conventional finite element method.