Academic Journal
Potential Method in the Linear Theory of Viscoelastic Materials with Voids: Potential method in the linear theory of viscoelastic materials with voids
| Title: | Potential Method in the Linear Theory of Viscoelastic Materials with Voids: Potential method in the linear theory of viscoelastic materials with voids |
|---|---|
| Authors: | Maia M. Svanadze |
| Contributors: | Svanadze, Maia M. |
| Source: | Journal of Elasticity. 114:101-126 |
| Publisher Information: | Springer Science and Business Media LLC, 2013. |
| Publication Year: | 2013 |
| Subject Terms: | Kelvin-Voigt material with voids, uniqueness and existence theorems, Mechanical Engineering, potential method, 0206 medical engineering, Uniqueness of solutions of dynamical problems in solid mechanics, steady vibrations, 02 engineering and technology, Materials Science(all), Vibrations in dynamical problems in solid mechanics, 0203 mechanical engineering, Mechanics of Materials, Existence of solutions of dynamical problems in solid mechanics, Linear constitutive equations for materials with memory, Linear waves in solid mechanics, viscoelasticity |
| Description: | In the present paper the linear theory of viscoelasticity for Kelvin–Voigt materials with voids is considered and some basic results of the classical theory of elasticity are generalized. Indeed, the basic properties of plane harmonic waves are established. The explicit expression of fundamental solution of the system of equations of steady vibrations is constructed by means of elementary functions. The Green’s formulas in the considered theory are obtained. The uniqueness theorems of the internal and external basic boundary value problems (BVPs) are proved. The representation of Galerkin type solution is obtained and the completeness of this solution is established. The formulas of integral representations of Somigliana type of regular vector and regular (classical) solution are obtained. The Sommerfeld-Kupradze type radiation conditions are established. The basic properties of elastopotentials and singular integral operators are given. Finally, the existence theorems for classical solutions of the internal and external basic BVPs of steady vibrations are proved by using of the potential method (boundary integral method) and the theory of singular integral equations. |
| Document Type: | Article |
| File Description: | application/xml |
| Language: | English |
| ISSN: | 1573-2681 0374-3535 |
| DOI: | 10.1007/s10659-013-9429-2 |
| Access URL: | https://link.springer.com/content/pdf/10.1007%2Fs10659-013-9429-2.pdf https://zbmath.org/6257878 https://doi.org/10.1007/s10659-013-9429-2 https://link.springer.com/content/pdf/10.1007%2Fs10659-013-9429-2.pdf https://link.springer.com/article/10.1007/s10659-013-9429-2 https://core.ac.uk/display/81835364 https://paperity.org/p/18554239/potential-method-in-the-linear-theory-of-viscoelastic-materials-with-voids https://link.springer.com/article/10.1007/s10659-013-9429-2/fulltext.html https://resolver.sub.uni-goettingen.de/purl?gro-2/34987 https://resolver.sub.uni-goettingen.de/purl?gs-1/10246 |
| Rights: | CC BY |
| Accession Number: | edsair.doi.dedup.....5032ed4424f2eb8a08f42ba619e71ff4 |
| Database: | OpenAIRE |
Be the first to leave a comment!