Vibration analysis of one-dimensional structures using the spectral transfer matrix method

The spectral element matrix, often named the dynamic stiffness matrix, is known to provide the accurate dynamic characteristics of a structure because it is formed by exact shape functions. However, it is not always easy to derive the exact shape functions for any structure. Thus this paper first introduces a general approach to spectral element formulation for one-dimensional structures, in which the spectral element matrix is computed numerically directly from the transfer (or transition) matrix formulated from the state vector equation of motion of a structure. Next, by combining the promising features of the spectral element method (i.e., high accuracy) and the well-known transfer matrix method (i.e., high analysis efficiency for one-dimensional structures), a new solution approach named the spectral transfer matrix method (STMM) is introduced herein. Lastly a beam with periodic supports and a plane lattice structure with several beam-like periodic lattice substructures are considered as illustrative examples.