Damping analysis of beams covered with multiple PCLD patches

An analytical approach for vibration damping analysis of beams with partial passive constrained layer damping (PCLD) treatments is extended to the case where the structure is covered by multiple patches. The energy-based approach and assumed-mode method are used to derive the equations governing the vibration displacement responses of the system, which is characterized in terms of the identical transverse displacement of all layers, and the longitudinal displacements of the base beam and the constraining layers. Furthermore, the longitudinal displacements of the base beam and constraining layer are independent of each other, which is in contrast to Kerwin's weak core assumption. The direct frequency response method is employed to determine the modal loss factors of the damped beam in a frequency range of interest. A convergence study is made on the damped beam to determine appropriate numbers of the mode functions for frequency response function (FRF) calculations. Parametric studies are performed with the established analytical approach and the determined numbers of mode functions to study the effects of dividing a PCLD patch into two pieces in different length ratios and also the spacing between the patches on the damping performance of a simply supported beam.