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On the solutions in the linear theory of micropolar viscoelasticity |
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| Affiliation: | 1. Sapienza Università di Roma, Rome, Italy and Department of Structural Engineering, University of California, San Diego, USA;2. Department of Structural Engineering, University of California, San Diego, La Jolla, CA 92093-0085, USA;1. Grupo de Investigación en Multifísica Aplicada (GIMAP), Universidad Tecnológica Nacional, Facultad Regional Bahía Blanca, Consejo Nacional de Investigaciones Científicas y Técnicas, Argentina;2. Grupo de Investigación en Multifísica Aplicada (GIMAP), Universidad Tecnológica Nacional, Facultad Regional Bahía Blanca, Consejo Nacional de Investigaciones Científicas y Técnicas, Departamento de Ingeniería, Universidad Nacional del Sur, Argentina |
| Abstract: | In the present paper the linear theory of micropolar viscoelasticity is considered. The explicit expression of fundamental solution of the system of equations of steady vibrations is constructed by means of elementary functions and its basic properties are established. The Green's formulas in the considered theory are obtained. The formulas of integral representations of Somigliana-type of regular vector and regular (classical) solution are presented. The representation formulas of Galerkin-type solution of the system of nonhomogeneous equations and of the general solution of the system of homogeneous equations by means of eight metaharmonic functions are presented. The completeness of these solutions is proved. |
| Keywords: | Micropolar viscoelasticity Steady vibrations Fundamental solution Representation of solution |
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