Distributed order fractional constitutive stress-strain relation in wave propagation modeling
arXiv:1709.01339 · doi:10.1007/s00033-019-1097-z
Abstract
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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Cited by in corpus (8)
- Energy balance for fractional anti-Zener and Zener models in terms of relaxation modulus and creep compliance
- Energy dissipation for hereditary and energy conservation for non-local fractional wave equations
- Fractional Burgers wave equation
- Micro-local and qualitative analysis of the fractional Zener wave equation
- Wave propagation in three-dimensional fractional viscoelastic infinite solid body
- Distributed-order time-fractional wave equations
- Stress and power as a response to harmonic excitation of a fractional anti-Zener and Zener type viscoelastic body
- Fractional Burgers wave equation on a finite domain