Dynamic analysis of smart composite beams by using the frequency-domain spectral element method

Abstract

To excite or measure the dynamic responses of a laminated composite structure for the active controls of vibrations or noises, wafer-type piezoelectric transducers are often bonded on the surface of the composite structure to form a multi-layer smart composite structure. Thus, for such smart composite structures, it is very important to develop and use a very reliable mathematical and/or computational model for predicting accurate dynamic characteristics. In this paper, the axial-bending coupled equations of motion and boundary conditions are derived for two-layer smart composite beams by using the Hamilton’s principle with Lagrange multipliers. The spectral element model is then formulated in the frequency domain by using the variation approach. Through some numerical examples, the extremely high accuracy of the present spectral element model is verified by comparing with the solutions by the conventional finite element model provided in this paper. The effects of the lay-up of composite laminates and surface-bonded wafer-type piezoelectric (PZT) layer on the dynamics and wave characteristics of smart composite beams are investigated. The effective constraint forces at the interface between the base beam and PZT layer are also investigated via Lagrange multipliers.