Izv. Saratov Univ. Math. Mech. Inform., 2020, Volume 20, Issue 4, Pages 468–477
Representation of waves of displacements and micro-rotations by systems of the screw vector fields
Yu. N. Radayev
Institute for Problems in Mechanics of RAS (IPMech RAS), 101 Vernadskogo Ave., Moscow 119526, Russia
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 micro-rotations 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.
micropolar elasticity, displacement vector, micro-rotation vector, coupled, vector potential, vortex part, screw equation, screw field, Helmholtz equation, waveguide.
PDF file (239 kB)
Yu. N. Radayev, “Representation of waves of displacements and micro-rotations by systems of the screw vector fields”, Izv. Saratov Univ. Math. Mech. Inform., 20:4 (2020), 468–477
Citation in format AMSBIB
\paper Representation of waves of displacements and micro-rotations by systems of the screw vector fields
\jour Izv. Saratov Univ. Math. Mech. Inform.
Citing articles on Google Scholar:
Related articles on Google Scholar:
|Number of views:|