A new heuristic topology optimization method for constrained layer damping design in plates: Numerical and experimental analysis

Metal plates can be the main source of noise and vibration in structures. A mitigation strategy is the use of constrained layers damping (CLD) with viscoelastic materials. However, defining the optimal CLD layout remains computationally challenging. In this sense, this work presents a heuristic topology optimization method to determine the best CLD distribution on plates for vibration reduction in a large range of frequencies. The structure is discretized into finite elements (FE) and grouped into equal-sized sets. CLD is, then, applied individually to each set, followed by harmonic analysis to compute an objective function: the Euclidean norm of Inertance Frequency Response Function, evaluated in a frequency range of interest. At the end of each harmonic analysis, an improvement index is calculated for each set of FE with CLD treatment. Thereafter, the FE sets are classified and those with the highest improvement index are selected for CLD treatment. It is an iterative process and continues until the maximum coverage area is reached. The novelty of this technique lies in the formulation of the improvement index, the addition strategy based on sets of elements, and the ability to control large frequency bands with a relatively low computational cost and a minimal checkerboard pattern. The method is applied to a rectangular plate to reduce vibrations of frequency bands covering the first and second mode, individually, as well as to a frequency range that covers the first to the fourth vibration mode simultaneously. Results are compared to the Modal Strain Energy (MSE) method under similar coverage and experimental validation shows vibration reductions between 20 and 38 dB.