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Analysis of wave motion in micropolar plate possessing cubic symmetry

Kumar R., Partap G.

International Journal of Applied Mechanics and Engineering

2009

Vol. 14, no 2

403-414

The present paper concentrates at studying the analysis of wave motion in a homogenous isotropic micropolar plate possessing cubic symmetry. The upper and lower surfaces of the plate are subjected to stress free conditions. The frequency equations for symmetric and skewsymmetric wave modes of propagation are derived. The amplitudes of displacement components and microrotation are also computed and presented graphically during the symmetric and skewsymmetric motion of the plate. Finally, in order to illustrate and verify the analytical developments, numerical solution of frequency equation corresponding to stress free micropolar cubic crystal plate is carried out for magnesium crystal material and represented graphically. The results of phase velocity, displacements and microrotation have been compared for micropolar cubic crystal plate and micropolar elastic plate and illustrated graphically.

Flexural and extensional waves propagation in transversely isotropic plates in generalized thermoelasticity

Verma K. L., Verma S. C., Hasebe N.

International Journal of Applied Mechanics and Engineering

2004

Vol. 9, no 3

587-606

In this paper, the boundary value problem concerning the propagation of plane harmonic thermoelastic waves in flat infinite homogeneous transversely isotropic plate of finite thickness in the generalized theory of thermoelasticity with two thermal relaxation times is studied. The frequency equations for a heat conducting thermoelastic plate corresponding to the extensional (symmetric) and flexural (antisymmetric) thermoelastic modes of vibration are obtained and discussed. Special cases of the frequency equations are also discussed. The horizontally polarized SH wave gets decoupled from the rest of motion and propagates without dispersion or damping, and is not affected by thermal variations on the same plate. A numerical solution to the frequency equations for an aluminum plate (isotropic) and zinc plate (transversely isotropic) is given, and the dispersion curves are presented. The three motions namely, longitudinal, transverse and thermal of the medium are found dispersive and coupled with each other due to the thermal and anisotropic effects. The phase velocity of the waves is modified due to the thermal and anisotropic effects and is also influenced by the thermal relaxation time. Relevant results of previous investigations are deduced as special cases.