Optimal position and shape of applied damping material

The frequency averaged transverse vibration levels of a plate with a harmonic excitation is minimized by optimizing the position and shape of attached passive constrained layer damping. A modified gradient method is used in the finite-element context to successively add pieces of constrained damping layers at the elemental positions showing the steepest gradient of the goal function as a result of the treatment. The coding is done in MATLAB and different stop conditions can be included so as to set limits for the cost or weight that can be spent on the treatment of the structure. It is demonstrated that for a square plate, only a few iterations are needed to reduce the average vibration level with up to 18 dB by covering less than 30 percent of the surface with a sandwich type applied damping material. For an industrial example, measurements show that the solution proposed by the optimization procedure will decrease the vibration levels for the two dominant modes of vibrations with 3–4 dB, by covering 3.4 percent of the surface with a single-sided constraining layer type applied damping material.