Wave equation for generalized Zener model containing complex order fractional derivatives. (English) Zbl 1365.74043
Summary: We study waves in a viscoelastic rod whose constitutive equation is of generalized Zener type that contains fractional derivatives of complex order. The restrictions following from the Second Law of Thermodynamics are derived. The initial boundary value problem for such materials is formulated and solution is presented in the form of convolution. Two specific examples are analyzed.
MSC:
| 74D05 | Linear constitutive equations for materials with memory |
| 35Q74 | PDEs in connection with mechanics of deformable solids |
| 35R11 | Fractional partial differential equations |
| 74F05 | Thermal effects in solid mechanics |
| 74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |
| 80A10 | Classical and relativistic thermodynamics |
Keywords:
fractional derivative of complex order; constitutive equation; thermodynamical restriction; wave propagationReferences:
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