Modeling of Q for Generalized Linear Solid |
| Liu Xuefenga, Fan Youhuab, Chang Dongmeic
aSchool of Aeronautical Engineering, Civil Aviation University of China, Tianjin 300300, China bSchool of Science, Harbin Institute of Technology, Shenzhen 518055, China cTianjin Key Laboratory of High Speed Cutting and Precision Machining, Tianjin University of Technology and Education, Tianjin 300222, China |
| Received: May 9, 2018; revised version May 14, 2019; in final form January 16, 2020 |
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| Modeling a given quality factor Q with a relaxation spectrum is important to time-domain simulations of wave propagation in a viscoelastic medium. In this paper, we present an optimal scheme of modeling the quality factor with a relaxation spectrum based on a generalized linear solid, which is available for both constant and frequency-dependent Q. A detailed study is conducted on the distribution of stress relaxation times and the error in the modeling scheme. From the study, we find that the error will be larger if the distribution range is too small or too wide, especially, the error is always larger if the distribution range equals the frequency range of interest. Since seeking the distribution range that yields the highest accuracy needs a series of calculation, for convenience, we suggest distributing the reciprocals of stress relaxation times logarithmically over the range from half the minimal frequency of interest to twice the maximal frequency of interest, which always yields a high accuracy. The value of the frequency-independent Q has little effect on the error. Moreover, effect of the number of SLSs (short for standard linear solid, a spring and a dashpot in parallel in series with a spring) on the accuracy is studied. We find that employing at least 5 SLSs leads to a higher accuracy. With this scheme, we model the frequency-dependent Q functions. The modeling result shows the validity of the scheme, and the error is larger when modeling some Q functions that decrease with frequency. |
DOI:10.12693/APhysPolA.137.276 topics: viscoelastic, Q factor, generalized linear solid, relaxation time |