Application of Spectral Element Method for the Vibration Analysis of Passive Constrained Layer Damping Beams

This paper introduces a spectrally formulated element method (SEM) for the beams treated with passive constrained layer damping (PCLD), The viscoelastic core of the beams has a complex modulus that varies with frequency. The SEM is formulated in the frequency domain using dynamic shape functions based on the exact displacement solutions from progressive wave methods, which implicitly account for the frequency-dependent complex modulus of the viscoelastic core. The frequency response function and dynamic responses obtained by the SEM and the conventional finite element method (CHM) are compared to evaluate the validity and accuracy of the present spectral PCLD beam element model. The spectral PCLD beam element model is found to provide very reliable results when compared with the conventional finite element model.