波传播模拟中的分布阶分数本构应力应变关系
Distributed order fractional constitutive stress-strain relation in wave propagation modeling
摘要：
采用分布阶分数阶粘弹性体模型来描述波在无限介质中的传播。研究了分数阶波动方程的广义Cauchy问题基本解的存在唯一性。计算了基本解的显式形式，发现由于解的支撑引起的波传播速度与初始时刻的材料性质有关。建立了四类物理上可接受的线性分数阶本构模型和幂型分布阶模型所对应的分数阶波动方程的基本解的存在唯一性，并得到了相应基本解的显式形式.
英文摘要：
Distributed order fractional model of viscoelastic body is used in order to describe wave propagation in infinite media. Existence and uniqueness of fundamental solution to the generalized Cauchy problem, corresponding to fractional wave equation, is studied. The explicit form of fundamental solution is calculated, and wave propagation speed, arising from solution's support, is found to be connected with the material properties at initial time instant. Existence and uniqueness of the fundamental solutions to the fractional wave equations corresponding to four thermodynamically acceptable classes of linear fractional constitutive models, as well as to power type distributed order model, are established and explicit forms of the corresponding fundamental solutions are obtained.
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