Electromagnetic effects in the theory of rods. (English) Zbl 0568.73108

Green, A. E.; Naghdi, P. M.

Philos. Trans. R. Soc. Lond., A 314, 311-352 (1985).

(Authors’ summary.) This paper is concerned with the nonlinear and linear thermomechanical theories of deformable rod-like bodies in which account is taken of electromagnetic effects. The development is made by a direct approach with the use of one-dimensional formulation of a theory of directed media called a Cosserat curve. The first part of the paper deals with the formulation of appropriate nonlinear equations governing the motion of a rod in the presence of electromagnetic and thermal effects. In the second part of the paper, emphasis is placed on the linearized version of the theory, a general discussion of the linear constitutive equations and determination of the constitutive coefficients, along with applications in a number of special cases including a magnetic thermoelastic rod and a non-conducting rod in free space.

Reviewer: A.Ghaleb

MSC:

74F15	Electromagnetic effects in solid mechanics
74K10	Rods (beams, columns, shafts, arches, rings, etc.)
74A15	Thermodynamics in solid mechanics
74F05	Thermal effects in solid mechanics

Keywords:

straight rods; piezoelectric crystal rods; rectangular cross-section; nonlinear equations of motion; nonlinear and linear thermomechanical theories; deformable rod-like bodies; electromagnetic effects; one- dimensional formulation; directed media; Cosserat curve; thermal effects; linearized version; linear constitutive equations; constitutive coefficients; magnetic thermoelastic rod; non-conducting rod in free space