广义线性固体Q值的建模研究

Study on modeling Q value of generalized linear solid

基于广义线性固体给出一种Q值松弛时间建模的优化方法,该方法对恒定和随时间变化的Q值均适用.深入研究了建模初始应力松弛时间选取方法及建模的误差问题.通过研究发现将应力松弛时间的倒数的对数均匀分布在从最低频率的一半到最高频率的二倍的区间内可以得到较高的建模精度,同等条件下分布区间选取过大或过小均会造成建模精度的降低.对实际数据进行建模发现该方法在恒定Q值建模中有较高的精度.通过这种建模方法,对近似于有机玻璃(PMMA)和改铸高岭土的随时间变化的Q值进行建模,建模结果验证了该方法的有效性.对于随时间减小的Q值函数的建模误差相对更大,可以采用增加SLS(一个阻尼器和一个弹簧串联再与一个弹簧并联)个数的方法提高建模精度.

The quality factor Q is an important parameter in describing the dissipation behavior of viscoelastic media,such as stone,soil and metal. It is significant to model quality factor Q exactly with strain and stress relaxation times for wave field modeling of viscoelastic medium. In this paper, an optimal scheme of modeling quality factor Q with a relaxation spectrum based on generalized linear solid was presented. By comparing the errors,we found that it is available for both constant and frequency-dependent Q. The error of modeling can be influenced by the distribution of stress relaxation time spectrum. A detailed study was conducted on the distribution of stress relaxation time spectrum and the error in the modeling scheme. We found that 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 yields a very high accuracy. By modeling real field data,the method is efficient for the modeling of constant Q value. With this scheme,the frequency-dependent Q functions that similar to the experimental data of polymethyl methacrylate（ PMMA） and remolded kaolin were modeled. The results show the validity of the scheme. The accuracy can be greatly improved by employing more LSLs（ a spring and a dashpot in series in parallel with a spring）.