Plane Waves and Uniqueness Theorems in the Coupled Linear Theory of Elasticity for Solids with Double Porosity

Abstract

This paper concerns with the coupled linear dynamical theory of elasticity for solids with double porosity. Basic properties of plane harmonic waves are established. Radiation conditions of regular vectors are given. Basic internal and external boundary value problems (BVPs) of steady vibrations are formulated, and finally, uniqueness theorems for regular (classical) solutions of these BVPs are proved

The solution of the Dirichlet BVP in the fully coupled theory of elasticity for spherical layer with double porosity

“…So, the solution of Problem B has the form (17), where w j ðxÞ are given by formulae (24). For absolutely and uniformly convergence of series in (11), (16), (23) and (24), together with their first derivatives, it is sufficient to assume that x AE ; h AE and h AE 1 satisfy the following conditions h AE 2 C 5 ðS i Þ; h AE 1 2 C 5 ðS i Þ; x AE 2 C 5 ðS i Þ; i ¼ 1; 2:…”

“…Many authors have investigated the BVPs of the theory of elasticity for materials with double porosity, that are published in a large number of papers (some of these results can be see in [15][16][17][18][19][20][21][22][23][24][25] and references therein).…”

Fundamental solutions in the theory of elasticity for triple porosity materials

“…The fundamental solutions in the theories of elasticity and thermoelasticity for materials with double porosity are constructed by Scarpetta et al [30], Svanadze [35], Svanadze and De Cicco [37]. The basic properties of plane harmonic waves in the coupled linear theory of elasticity for solid with double porosity are established by Ciarletta et al [10]. The convection with local thermal non-equilibrium and microfluidic effects in the double-and multi-porosity media are investigated in the new book of Straughan [33].…”

Explicit solution of one boundary value problem in the full coupled theory of elasticity for solids with double porosity

“…In the last years, many authors have investigated the BVPs of the 2-dimensional and 3-dimensional theories of elasticity for materials with double porosity, publishing a large number of papers(for details, see [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24] and references therein). There the explicit solutions on some BVPs in the form of series and in quadratures are given in a form useful for engineering practice.…”