A Two-Step Transformation Approach for ESS Model of Viscoelastic Material to Time Domain

Abstract

ESS (Equivalent Standard solid) model is proofed to be accurate for describing the physical properties of viscoelastic material under different temperatures and excitation frequencies. However, the ESS model faces difficulties for calculating time history responses. Therefore, a two-step transformation approach for ESS model to time domain is proposed, which can obtain precise time history response of structural finite element models of with dampers made of viscoelastic materials. In the first step of the approach, ESS model is extended from frequency domain to complex frequency domain. In the second step, a high-precision numerical inverse Laplace transform method is chosen to transform the model from complex frequency domain to time domain. Experimental and numerical tests are conducted to verify the effectiveness of the two-step transformation approach under simple harmonic external excitation. The comparisons indicate that the approach is accurate under different temperatures and excitation frequencies. Finally, the time domain dynamic responses of the viscoelastic dampers are obtained under earthquake excitations. Comparing to the equivalent linearization method for ESS model, the proposed two-step transformation approach has absolute advantage to obtain accurate results under random excitation, such as earthquake excitations.