Free Vibration Analysis of Micropolar Thermoelastic Cylindrical Curved Plate in Circumferential Direction

Subject Areas : Engineering

G Partap ¹ , R Kumar ²

1 - Department of Mathematics, Dr. B.R. Ambedkar National Institute of Technology, Jalandhar, Punjab
2 - Department of Mathematics, Kurukshetra University

Received: 2010-08-07 Accepted : 2010-11-02 Published : 2010-09-30

Keywords: Phase velocity, Micropolar, Circumferential wave number, Thermoelasticity type III, Thermoelasticity without energy dissipation,

Abstract :

The free vibration analysis ofhomogeneous isotropic micropolar thermoelastic cylindrical curved plate in circumferential direction has been investigated in the context of generalized themoelasticity III, recently developed by Green and Naghdi. The model has been simplified using Helmholtz decomposition technique and the resulting equations have been solved using separation of variable method. Mathematical modeling of the problem to obtain dispersion curves for curved isotropic plate leads to coupled differential equations and solutions are obtained by using Bessel functions. The frequency equations connecting the frequency with circumferential wave number and other physical parameters are derived for stress free cylindrical plate. In order to illustrate theoretical development, numerical solutions are obtained and presented graphically for a magnesium crystal.

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