Optimal constrained layer damping placement on a planar structure for minimization of radiated sound power and vibratory energy

An optimization study of a constrained layer damping (CLD) treatment for noise control is presented. The energy-based approach and assumed-mode method are used to derive the equations governing the displacement responses of a simply-supported beam with a partial CLD patch to formulate the objective function of the optimization problem. The vibration responses of the damped structure is calculated in a frequency range of interest by employing the direct frequency response method and the results are used to obtain the baffled structure's radiated sound power by Rayleigh's integral formulae. A genetic algorithm-based penalty function method is employed to search for the optimal placement of the partial CLD patch and shear modulus of the viscoelastic layer for minimizing the radiated sound power from the damped beam under a broadband transverse force. The results are compared with those for the minimization of vibratory energy. It is revealed that certain differences exist between the optimal CLD placements for the two different objectives. More reduction in the sound power radiated from the damped structure can be achieved by optimizing the CLD patch with the objective to minimize the radiated sound power than that to minimize the vibratory energy under the constraint in additive weight duo to CLD treatment.