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

Xing-Huai Huang,Ye-Shou Xu,Ze-Feng He

doi:10.3389/fmats.2019.00109

Xing-Huai Huang, Ye-Shou Xu + Show 1 more

Open Access

https://doi.org/10.3389/fmats.2019.00109

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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.

Highlights

Viscoelastic material has strong energy dissipation capacity based on massive fillers within high molecular polymers, which exhibits physical properties of both viscous and elastic
The maximum output of the system calculated by the two-step transformation approach is 56.2315 kN, and the maximum output of the damper calculated by the equivalent linearization method is 124.6607 kN, and the proposed method improve the system accuracy by 121.69%
The maximum output of the viscoelastic system calculated by the two-step transformation approach is 55.7772 kN, and the maximum output of the damper calculated by the equivalent linearization method is 108.7909 kN, and the proposed method improve the system accuracy reaches 95.05%

Summary

INTRODUCTION

Viscoelastic material has strong energy dissipation capacity based on massive fillers within high molecular polymers, which exhibits physical properties of both viscous and elastic. The dynamic response of the viscoelastic damper of 9050A viscoelastic material under harmonic displacement excitation is calculated by equivalent linearization method and time domain extension method, respectively. The comparison of the calculation results between the proposed approach and the equivalent linearization method, the maximum error of the energy storage modulus G1 is 0.0054%, the maximum error of the loss Factor η is 0.2797%, and the error analysis indicates that the time domain extension method has sufficient precision for solving the solution. The equivalent linearization method is adopted in the following comparisons because it is based on ESS model and is usually adopted to calculate the response of viscoelastic material.

Mpa η η

Findings

CONCLUSION AND PROSPECT