黏弹性介质中平、柱面波动传播的应力场及应用探讨

Stress field in viscoelastic medium with propagation of plane and cylindrical waves and the discussion of its application

采用黏弹性介质的三维本构模型,基于工程波动理论推导了入射简谐波情况下平面波和柱面波在黏弹性介质中传播的应力场,扩展了波动理论在黏弹性介质中的应用。结合有限元人工黏弹性边界参数取值的弹性经典解,得到了在平面波和柱面波假设情况下的黏弹性边界参数取值。通过编制频域分析有限元计算程序讨论了基于理论解的黏弹性边界在有限元计算中的应用效果。结果表明:与基于弹性介质推导的传统黏弹性边界和黏性边界相比,采用黏弹性边界得到的模拟精度更高。同时指出,由于理论分析与时域分析有限元法在本构模型、参数设置等关键问题上存在根本差别,结果并不完全适用于常规的时域分析有限元法。最后,结合时域分析有限元法的特点为研究的进一步发展提供了建议。

In order to study stress field of plane and cylindrical waves in viscoelastic medium, the wave motion theories were selected and the stress at the wave front was established. A 3 D constitutive model of viscoelastic medium was adopted to describe the dynamic behavior of the medium. The analysis presented herein extended application of wave motion theory in viscoelastic medium. Additionally, the parameter values of viscoelastic boundary were obtained referring to the classical solution in which the behavior of the medium was assumed as linear elastic. The application of the visco-elastic artificial boundary defined by the derivation of this paper was investigated using the finite element program calculated in frequency domain. The results show that high accuracy could be achieved using the artificial boundary established herein, compared with the classical visco-elastic boundary and the viscous boundary which are deduced in elastic medium. As a result of the constitutive model and parameter setting differences between the theoretical analysis in the present paper and the time domain finite element method, a conclusion could be reached that the present results could not be used in the time domain finite element method. Last but not least, a suggestion on further development of the present study has been given, combining the characteristics of time domain finite element method.