On the solutions of quasi-static and steady vibrations equations in the theory of viscoelasticity for materials with double porosity
In the present paper the linear theory of viscoelasticity for Kelvin–Voigt materials with double porosity is considered. Some basic results on the solutions of the quasi-static and steady vibrations equations are obtained. Indeed, the fundamental solutions of the systems of equations of quasi-static...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2018-08-01
|
| Series: | Transactions of A. Razmadze Mathematical Institute |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2346809217301460 |
| id |
doaj-efaf28afc11e4e7ea874a8391f75f105 |
|---|---|
| record_format |
Article |
| spelling |
doaj-efaf28afc11e4e7ea874a8391f75f1052020-11-25T01:48:41ZengElsevierTransactions of A. Razmadze Mathematical Institute2346-80922018-08-011722276292On the solutions of quasi-static and steady vibrations equations in the theory of viscoelasticity for materials with double porosityMaia M. Svanadze0Faculty of Exact and Natural Sciences, I. Javakhishvili Tbilisi State University, I. Chavchavadze Ave., 3, 0179 Tbilisi, GeorgiaIn the present paper the linear theory of viscoelasticity for Kelvin–Voigt materials with double porosity is considered. Some basic results on the solutions of the quasi-static and steady vibrations equations are obtained. Indeed, the fundamental solutions of the systems of equations of quasi-static and steady vibrations are constructed by elementary functions and their basic properties are established. Green’s formulae and the integral representation of regular solution in the considered theory are obtained. Finally, a wide class of the internal boundary value problems of quasi-static and steady vibrations is formulated and on the basis of Green’s formulae the uniqueness theorems for classical solutions of these problems are proved. Keywords: Viscoelasticity, Double porosity, Fundamental solution, Uniqueness theorems, Quasi-static, Steady vibrationshttp://www.sciencedirect.com/science/article/pii/S2346809217301460 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Maia M. Svanadze |
| spellingShingle |
Maia M. Svanadze On the solutions of quasi-static and steady vibrations equations in the theory of viscoelasticity for materials with double porosity Transactions of A. Razmadze Mathematical Institute |
| author_facet |
Maia M. Svanadze |
| author_sort |
Maia M. Svanadze |
| title |
On the solutions of quasi-static and steady vibrations equations in the theory of viscoelasticity for materials with double porosity |
| title_short |
On the solutions of quasi-static and steady vibrations equations in the theory of viscoelasticity for materials with double porosity |
| title_full |
On the solutions of quasi-static and steady vibrations equations in the theory of viscoelasticity for materials with double porosity |
| title_fullStr |
On the solutions of quasi-static and steady vibrations equations in the theory of viscoelasticity for materials with double porosity |
| title_full_unstemmed |
On the solutions of quasi-static and steady vibrations equations in the theory of viscoelasticity for materials with double porosity |
| title_sort |
on the solutions of quasi-static and steady vibrations equations in the theory of viscoelasticity for materials with double porosity |
| publisher |
Elsevier |
| series |
Transactions of A. Razmadze Mathematical Institute |
| issn |
2346-8092 |
| publishDate |
2018-08-01 |
| description |
In the present paper the linear theory of viscoelasticity for Kelvin–Voigt materials with double porosity is considered. Some basic results on the solutions of the quasi-static and steady vibrations equations are obtained. Indeed, the fundamental solutions of the systems of equations of quasi-static and steady vibrations are constructed by elementary functions and their basic properties are established. Green’s formulae and the integral representation of regular solution in the considered theory are obtained. Finally, a wide class of the internal boundary value problems of quasi-static and steady vibrations is formulated and on the basis of Green’s formulae the uniqueness theorems for classical solutions of these problems are proved. Keywords: Viscoelasticity, Double porosity, Fundamental solution, Uniqueness theorems, Quasi-static, Steady vibrations |
| url |
http://www.sciencedirect.com/science/article/pii/S2346809217301460 |
| work_keys_str_mv |
AT maiamsvanadze onthesolutionsofquasistaticandsteadyvibrationsequationsinthetheoryofviscoelasticityformaterialswithdoubleporosity |
| _version_ |
1725010721954070528 |