An approach for topology optimization of damping layer under harmonic excitations based on piecewise constant level set method

The topology optimization of a thin plate structure with bounded damping layer patches under external harmonic excitations to suppress the vibrations of specified points in the plate is investigated. The piecewise constant level set (PCLS) method is applied to represent the region with damping material and the region only with base material. Applying Melosh-Zienkiewicz-Cheung (MZC) element, the stiffness matrix, the mass matrix and the damping matrix are expressed in detail, where the global non-proportional damping matrix is considered. The functional derivative of the objective function (the squared vibration amplitudes of specified points in a plate) with respect to the PCLS function is deduced, by introducing the adjoint problems and applying matrix sensitivity analysis. The quadratic penalty method and the total variation regularization are utilized to fulfill the volume constraint and to avoid checkerboard patterns, respectively. A penalty gradient algorithm is proposed. In numerical experiments, three rectangular plates with different boundary conditions and locations of the external excitations are investigated. Effects of the excitation frequency as well as the damping coefficients on topology optimization results are also discussed.