Propagation of elastic waves in a micropolar sphere

The problem of harmonic wave propagation in a solid micropolar sphere is solved by considering the two scalar and two vector equations governing the motion. Stress free boundary conditions are applied and a characteristic equation is obtained. The characteristic determinant can be resolved into the product of two independent determinants. Two classes of motion are observed which have been analysed in detail.     

Propagation of acceleration waves in micropolar elastic solids

The propagation and growth of acceleration waves of arbitrary form propagating into a deformed micropolar elastic solid are investigated. The speeds of propagation are obtained for isotropic micropolar elastic materials and the growth equation is established. The growth equation of acceleration wave is integrated in the case of principle waves for isotropic materials and the decay conditions are examined for both macro- and micro-amplitudes.     

Thermo elastic waves with thermal relaxation in isotropic micropolar plate

In the present investigation, we have discussed about the features of waves in different modes of wave propagation in an infinitely long thermoelastic, isotropic micropolar plate, when the generalized theory of Lord–Shulman (L–S) is considered. A more general dispersion equation is obtained. The different analytic expressions in symmetric and anti-symmetric vibration for short as well as long waves are obtained in different regions of phase velocities. It is found that results agree with that of the existing results predicted by Sharma and Eringen in the context of various theories of classical as well as micropolar thermoelasticity.     

A note on infinitesimal shear waves in a finitely deformed elastic solid

In the present note we discuss a class of small dynamic deformations imposed on a large static deformation. A semi-inverse method is used to obtain the equations of motion for the small deformations in a simple manner. The results are used to extend known results for a tube of hyperelastic material subject to inflation and extension, when additional telescopic and rotational shears are applied.     

A note on the low frequency diffraction of elastic waves by a Griffith crack

The two dimensional problem of the diffraction of normally incident compressional and antiplane shear waves by a Griffith crack in an infinite isotropic elastic medium is considered. For wavelengths long compared to the crack length, the stress intensity factors as well as the maximum crack openings are expressed in series of ascending powers of the normalized wave number. The approximate solutions are compared with exact solutions obtained in a previous paper[1], for a Poisson's solid. The results indicate that a five term expansion of each of the series solutions is sufficiently accurate for most problems of practical interest.     

On the surface waves in an elastic micropolar and microstretch medium with nonlocal cohesion

Summary A brief review of the main points of Eringen's theory of micromorphic bodies is first given, and balance equations for the linear isotropic micropolar and microstretch body are established. By appeal to the Fourier exponential transformation, nonlocal constitutive equations are derived, and assumptions with regard to the nonlocal moduli are made. The general field equations governing the propagation of a nonlocal surface wave are particularized so as to coincide with the results obtained directly in references [12], [17], [22], and [23], respectively. As an illustrative example, propagation of a microrotation and microstretch wave in a nonlocal medium in the entire Brillouin zone is examined.     

Influence of couple stresses on the propagation of elastic waves in a micropolar cubically anisotropic medium

Expressions for the phase and radial velocities of propagation of three-dimensional fronts of quasilongitudinal and quasitransverse elastic waves in a micropolar cubically anisotropic medium have been obtained. An analysis of the influence of the micropolar elastic constant on the dependence of the wave velocities on the angle of inclination of the normal to the wave surface has been made. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 79, No. 2, pp. 178–182, March–April, 2006.     

Thermal stresses in micropolar elastic cylinders

Summary The present paper is concerned with the static problem in the linear theory of micropolar thermoelasticity for homogeneous and isotropic cylinders. The problem is solved using some results established in [1]–[5].

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Wärmespannungen in mikropolaren elastischen Zylindern

Zusammenfassung Die vorliegende Arbeit beschäftigt sich mit dem statischen Problem der linearen Theorie der mikropolaren Thermoelastizität für homogene und isotrope Zylinder. Das Problem wird mit Hilfe einiger in [1]–[5] enthaltenen Ergebnisse gelöst.

     

A note on surface waves in anisotropic media

Summary An examination of possible forms of traction free surface wave in anisotropic elastic materials is undertaken. The results yield some interesting features of a certain arbitrariness which exists in displacement waves on a traction free surface in anisotropic media.     

Stability of linear micropolar elastic media

The theory of elastic stability of linear micropolar elastic media is examined. A functional is constructed which is suitable for the study of the stability of motion of linear micropolar elastic media. An example of stability of undeformed state is solved to show the applicability of the method. The uniqueness criteria are also discussed.     

Deformation of loaded micropolar elastic cylinders

In this paper we solve the general problem of deformation of a composite elastic cylinder. We consider the case when the cross-section of the cylinder is occupied by different inhomogeneous and anisotropic micropolar elastic materials. The elastic coefficients are assumed to be independent of the axial coordinate and are discontinuous, in general, over the surface of separation of the materials. The cylinder is subjected to body loads and to tractions on the lateral surface, and to appropriate stress and couple-stress resultants over its ends.     

Thermo-poroacoustic acceleration waves in elastic materials with voids without energy dissipation

We present a model for acoustic wave propagation in a porous material which also allows for propagation of a thermal displacement wave. The thermodynamics is based on an approach of A.E. Green, F.R.S. and P.M. Naghdi and is presented for a modification of the theory of elastic materials with voids.     

On wave propagation in a micropolar elastic cylinder

An asymptotic analysis of the free vibrations of a micropolar elastic cylinder is earned out postulating the displacements, the micro-rotations and the frequency as power series in the nondimensional $\text{? = 2π}\text{radius/(wave length)}$.     

On the crack propagation in micropolar elastic solids

This paper is concerned with the dynamic energy release rate for a sharp, straight crack in a micropolar elastic body.     

Axi-symmetric problem in micropolar elastic half-space with stretch

The present investigation is concerned with axisymmetric problem in micropolar elastic half-space with stretch. The displacement, force stress, couple stress and vector first moment are obtained for a half-space subjected to an arbitrary normal load and a particular case of impulsive force is studied in detail. The graphs for various quantities have been drawn to illustrate the effect of stretch in each particular case.     

On flexural vibrations of micropolar elastic cylinders

An exact derivation of the frequency equation for the flexural modes of free vibrations of an infinite solid circular cylinder made of an isotropic homogeneous centrosymmetric micropolar material is presented and some particular cases are noted.