Optimization of partial constrained layer damping treatment for vibrational energy minimization of vibrating beams

An optimization study is presented in this paper with aim to minimize the vibrational energy (VE) of vibrating beams with passive constrained layer damping (PCLD) treatment. First, the governing equation of motion of a partially PCLD covered beam is derived on the basis of energy approach, and assumed-modes method is used to solve it. Parametric studies are then performed to identify those dominant parameters on the vibration response of the damped beam. With objective to minimize the integrated global VE of the base beam over a frequency range of interest, a genetic algorithm (GA) based penalty function method is further employed to search for the optimum of the location/length of the PCLD patch and VL’s shear modulus for a simply-supported beam with a transverse force applied at its central location. Optimal solutions are given and discussed for different cases where the VE of the beam over a frequency range covering the first four resonant modes and that at a specific resonant mode is to be minimized, without and with inclusion of the restriction of minimum damping material used.