Dynamic topology optimization of two-phase viscoelastic composite structures considering frequency- and temperature-dependent properties under random excitation

This article proposes an efficient optimum design method of constrained layer damping (CLD) plates characterized by non-proportional damping subjected to random excitation. Considering frequency and temperature dependence, a two-phase viscoelastic composite material composed of stiffness-phase and damping-phase materials is used as the damping layer. The pseudo excitation and hybrid expansion methods are adopted to compute the random responses at the specified frequency intervals as the objective functions. The sensitivity analysis is performed through the adjoint vector method. The similarity index is defined to distinguish the various optimal layouts quantitatively. Several numerical examples clearly demonstrate the robustness and effectiveness of the proposed method, highlighting a remarkable improvement of over 60% in computational efficiency. Furthermore, it is proved that, when subjected to broadband random excitation, the damping materials' temperature- and frequency-dependent properties are critical factors in obtaining accurate vibration responses and desirable optimal layouts. The effects of the layer thicknesses and volume fractions of composite structures on topology optimization are also discussed. The results indicate that both layer thickness and volume fraction can change the mechanical properties of the composite structure and further affect the distribution characteristics of the damping material.