Stress equations of motion of Ignaczak type for the second axisymmetric problem of micropolar elastodynamics

Janusz Dyszlewicz

Applicationes Mathematicae (1997)

  • Volume: 24, Issue: 3, page 251-265
  • ISSN: 1233-7234

Abstract

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A second axially-symmetric initial-boundary value problem of linear homogeneous isotropic micropolar elastodynamics in which the displacement and rotation take the forms u ̲ = ( 0 , u θ , 0 ) , φ ̲ = ( φ r , 0 , φ z ) ((r,θ,z) are cylindrical coordinates; cf. [17]) is formulated in a pure stress language similar to that of [12]. In particular, it is shown how u ̲ and φ ̲ can be recovered from a solution of the associated pure stress initial-boundary value problem, and how a singular solution corresponding to harmonic vibrations of a concentrated body couple in an infinite space can be obtained from the solution of a pure stress problem.

How to cite

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Dyszlewicz, Janusz. "Stress equations of motion of Ignaczak type for the second axisymmetric problem of micropolar elastodynamics." Applicationes Mathematicae 24.3 (1997): 251-265. <http://eudml.org/doc/219167>.

@article{Dyszlewicz1997,
abstract = {A second axially-symmetric initial-boundary value problem of linear homogeneous isotropic micropolar elastodynamics in which the displacement and rotation take the forms $\underline\{u\}=(0,u_θ,0)$, $\underline\{φ\}=(φ_r,0,φ_z)$ ((r,θ,z) are cylindrical coordinates; cf. [17]) is formulated in a pure stress language similar to that of [12]. In particular, it is shown how $\underline\{u\}$ and $\underline\{φ\}$ can be recovered from a solution of the associated pure stress initial-boundary value problem, and how a singular solution corresponding to harmonic vibrations of a concentrated body couple in an infinite space can be obtained from the solution of a pure stress problem.},
author = {Dyszlewicz, Janusz},
journal = {Applicationes Mathematicae},
keywords = {stress equations of motion problem (SEMP); micropolar elasticity theory; initial-boundary value problem; displacement; rotation; cylindrical coordinates; associated pure stress initial-boundary value problem; singular solution; harmonic vibrations},
language = {eng},
number = {3},
pages = {251-265},
title = {Stress equations of motion of Ignaczak type for the second axisymmetric problem of micropolar elastodynamics},
url = {http://eudml.org/doc/219167},
volume = {24},
year = {1997},
}

TY - JOUR
AU - Dyszlewicz, Janusz
TI - Stress equations of motion of Ignaczak type for the second axisymmetric problem of micropolar elastodynamics
JO - Applicationes Mathematicae
PY - 1997
VL - 24
IS - 3
SP - 251
EP - 265
AB - A second axially-symmetric initial-boundary value problem of linear homogeneous isotropic micropolar elastodynamics in which the displacement and rotation take the forms $\underline{u}=(0,u_θ,0)$, $\underline{φ}=(φ_r,0,φ_z)$ ((r,θ,z) are cylindrical coordinates; cf. [17]) is formulated in a pure stress language similar to that of [12]. In particular, it is shown how $\underline{u}$ and $\underline{φ}$ can be recovered from a solution of the associated pure stress initial-boundary value problem, and how a singular solution corresponding to harmonic vibrations of a concentrated body couple in an infinite space can be obtained from the solution of a pure stress problem.
LA - eng
KW - stress equations of motion problem (SEMP); micropolar elasticity theory; initial-boundary value problem; displacement; rotation; cylindrical coordinates; associated pure stress initial-boundary value problem; singular solution; harmonic vibrations
UR - http://eudml.org/doc/219167
ER -

References

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  3. [3] J. Dyszlewicz, The stress and displacement functions for the second axisymmetric problem of micropolar elastostatics, Arch. Mech. 27 (1975), 393-404. Zbl0375.73003
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  15. [15] J. Mikusiński, Operational Calculus, Pergamon, New York, 1959. 
  16. [16] W. Nowacki, Theory of Elasticity, PWN, Warszawa, 1970 (in Polish). Zbl0211.28701
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