Mathematical modeling of wave propagation in viscoelastic media with the fractional Zener model
نویسندگان
چکیده
The question of interest for the presented study is mathematical modeling wave propagation in dissipative media. generalized fractional Zener model case dimension d (d=1,2,3) considered. This work devoted to analysis such model: existence and uniqueness strong weak solution energy decay result which guarantees dissipation. shown using a priori estimates solutions are also presented.
منابع مشابه
Modeling Diffusion to Thermal Wave Heat Propagation by Using Fractional Heat Conduction Constitutive Model
Based on the recently introduced fractional Taylor’s formula, a fractional heat conduction constitutive equation is formulated by expanding the single-phase lag model using the fractional Taylor’s formula. Combining with the energy balance equation, the derived fractional heat conduction equation has been shown to be capable of modeling diffusion-to-Thermal wave behavior of heat propagation by ...
متن کاملRheological Response and Validity of Viscoelastic Model Through Propagation of Harmonic Wave in Non-Homogeneous Viscoelastic Rods
This study is concerned to check the validity and applicability of a five parameter viscoelastic model for harmonic wave propagating in the non-homogeneous viscoelastic rods of varying density. The constitutive relation for five parameter model is first developed and validity of these relations is checked. The non-homogeneous viscoelastic rods are assumed to be initially unstressed and at rest....
متن کاملModeling of wave propagation in inhomogeneous media.
We present a methodology providing a new perspective on modeling and inversion of wave propagation satisfying time-reversal invariance and reciprocity in generally inhomogeneous media. The approach relies on a representation theorem of the wave equation to express the Green function between points in the interior as an integral over the response in those points due to sources on a surface surro...
متن کاملSpace-time fractional Zener wave equation.
The space-time fractional Zener wave equation, describing viscoelastic materials obeying the time-fractional Zener model and the space-fractional strain measure, is derived and analysed. This model includes waves with finite speed, as well as non-propagating disturbances. The existence and the uniqueness of the solution to the generalized Cauchy problem are proved. Special cases are investigate...
متن کاملWave Propagation in Fibre-Reinforced Transversely Isotropic Thermoelastic Media with Initial Stress at the Boundary Surface
The reflection and transmission of thermoelastic plane waves at an imperfect boundary of two dissimilar fibre-reinforced transversely isotropic thermoelastic solid half-spaces under hydrostatic initial stress has been investigated. The appropriate boundary conditions are applied at the interface to obtain the reflection and transmission coefficients of various reflected and transmitted waves wi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematical modeling and computing
سال: 2021
ISSN: ['2312-9794', '2415-3788']
DOI: https://doi.org/10.23939/mmc2021.04.601