Spectral finite element analysis of elastically connected double-beam systems

A spectral finite element method for two parallel beams connected to each other by the vertical springs uniformly distributed along the beam length is introduced in this paper. The effects of the shear deformation and rotary inertia of the beams are accounted for. The coupled equations of motion are derived by using Hamilton's principle and the spectral element matrix is established based on the exact solutions of the governing equations. The use of the proposed spectral element formulation to investigate the free vibration characteristics of the particular double-beam systems is demonstrated by applying the Muller root search algorithm. Once the natural frequencies and mode shapes are obtained, a spectral element based normal mode method is introduced to compute the dynamic response of the double-beam systems subjected to various kinds of concentrated and distributed loads. Numerical results of the present method are verified by comparing with those available in the literature.