Homogenization and Topology Optimization of Constrained Layer Damping Treatments

Abstract

Constrained Layer Damping (CLD) has been extensively used in structural designs as a powerful mean to damp out resonant structural vibrations. The main goal of this work is to investigate the use of homogenization and structural topology optimization as a tool to optimize the CLD treatments in order to enhance the energy dissipation characteristics of the vibrating structures. Homogenization theory is introduced in the first part along with structural topology optimization techniques. In the second part, finite element models are presented for sandwiched beams and plates with viscoelastic cores. An optimal shear modulus methodology, featuring the Inverse Homogenization Approach (IHA), is developed to determine the optimal shear strain energy of the viscoelastic material that leads to the highest energy dissipation. The method is applied to sandwiched beam with viscoelastic cores to reduce the peak displacements of the first mode and the results are verified experimentally. Experiments are conducted to validate the theoretical results. Moreover, the optimal shear modulus approach is employed with a multiobjective topology optimization methodology to optimize the damping of multi-modes of vibration of sandwiched plates with viscoelastic cores and the results are validated experimentally. The theoretical and experimental results are found to be in good agreement and thereby demonstrating the efficiency of the proposed technique in generating CLD treatments with high damping characteristics per unit volume as compared to conventional viscoelastic damping treatments. Moreover, the method is extended to design Active Constrained Layer Damping (ACLD) treatments for beams and plates. The proposed method has been shown to generate damping treatment topologies that are capable of attenuating low frequency structural vibrations without the need for using active control techniques. Finally, CLD treatments generated with topology optimization by the optimal shear modulus approach are compared with their counterparts that are designed by the Modal Strain Energy (MSE) method.