Abstract
The present study concerns the coupled vector differential equations of the linear theory of micropolar elasticity formulated in terms of displacements and micro-rotations in the case of a harmonic dependence of the physical fields on time. The system is known from many previous discussions on the micropolar elasticity. A new analysis aimed at uncoupling the coupled vector differential equation of the linear theory of micropolar elasticity is carried out. A notion of proportionality of the vortex parts of the displacements and microrotations to a single vector, which satisfies the screw equation, is employed. Finally the problem of finding the vortex parts of the displacements and micro-rotations fields is reduced to solution of four uncoupled screw differential equations. Corresponding representation formulae are given. Obtained results can be applied to problems of the linear micropolar elasticity concerning harmonic waves propagation along cylindrical waveguides.
Highlights
The aim of the present work is to study the coupled system of vector differential equations of the linear micropolar theory of an isotropic elastic body in the case of the harmonic dependence of displacement and micro-rotation fields on time
Related problems and problem formulations arise in applied problems of the coupled thermoelasticity [7], especially in the case of propagation of harmonic waves in hyperbolic thermoelastic media
In this paper an alternative scheme for splitting the main coupled system of vector differential equations of the harmonic micropolar elasticity into uncoupled equations is developed. The latter will take the form of screw equations
Summary
The aim of the present work is to study the coupled system of vector differential equations of the linear micropolar theory of an isotropic elastic body in the case of the harmonic dependence of displacement and micro-rotation fields on time. Their study and transformation by the aid of dynamic potentials (vortex-free and vortex) lead to various interesting systems of vector differential equations (both coupled and uncoupled). In this paper an alternative scheme for splitting the main coupled system of vector differential equations of the harmonic micropolar elasticity into uncoupled equations is developed. The latter will take the form of screw equations. Are screw fields with the same abnormality A; 2) screw vector field Υ satisfies the vector Helmholtz differential equation
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