Dynamic response optimization of structures with viscoelastic material using the equivalent static loads method

Abstract

Viscoelastic material is widely used in automotive structures due to its outstanding vibration-damping characteristics with appropriate stiffness. Viscoelastic material, which has viscosity and elasticity, shows energy absorption and dissipation. The material properties of viscoelastic material are dependent upon time, temperature, and loading path. Hence, these characteristics have to be considered when performing structural optimization. Studies on the constitutive equations of viscoelastic material are widely carried out, and structural optimization using harmonic excitation in the frequency-domain is often reported. However, structural optimization in the time-domain is rarely performed. One of the reasons is that the cost of sensitivity analysis is quite expensive. The Equivalent Static Loads Method (ESLM) is a linear/nonlinear dynamic response structural optimization method. In this research, a practical structural optimization method to consider the characteristics of viscoelastic material is proposed using ESLM. Equivalent static loads (ESLs) are defined as the static loads that generate the same displacement field as that from dynamic analysis. In ESLM, dynamic analysis and linear static response optimization are alternatively repeated until convergence is achieved. Viscoelastic material reduces the vibration amplitude and the stored energy in a structural system. Thus, excellent damping performance is required for a part with viscoelastic material, while the proper stiffness is maintained. An appropriate design formulation is made for the design of viscoelastic material. In this research, the sum of damping ratios, the sum of weighted damping ratios, and the sum of squared displacements are considered as the objective functions. These three objective functions deal with the peak displacements of damped vibration. Three case studies are defined by optimizations of some typical automotive parts with viscoelastic material. They are a sandwich panel, a rubber bushing, and a seat cushion. The damping performances of the objective functions are compared and discussed.