Fractional Burgers wave equation

Abstract

Thermodynamically consistent fractional Burgers constitutive models for viscoelastic media, divided into two classes according to model behavior in stress relaxation and creep tests near the initial time instant, are coupled with the equation of motion and strain forming the fractional Burgers wave equations. Cauchy problem is solved for both classes of Burgers models using integral transform method and analytical solution is obtained as a convolution of the solution kernels and initial data. The form of solution kernel is found to be dependent on model parameters, while its support properties implied infinite wave propagation speed for the first class and finite for the second class. Spatial profiles corresponding to the initial Dirac delta displacement with zero initial velocity display features which are not expected in wave propagation behavior.

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Cited by in corpus (5)

• 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
• Wave propagation in three-dimensional fractional viscoelastic infinite solid body
• 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