Dispersion of thermo elastic waves in a homogeneous isotropic rotating cylindrical panel

Abstract

The three dimensional dispersion of thermo elastic waves in a homogeneous isotropic rotating cylindrical panel is investigated in the context of the linear theory of thermo elasticity. Three displacement potential functions are introduced to uncouple the equations of motion. The frequency equations are obtained for traction free boundary conditions using Bessel function solutions.In order to illustrate theoretical development, numerical solutions are obtained and presented graphically for a zinc material. In this study we found that the wave characteristics are more stable and realistic in the presence of thermal and the rotation parameters. Keyword:Bessel Corresponding Author:R .Selvamani, Departement of Mathematics, Karunya University, Coimbatore, Tamil Nadu, India, 64114. Email: selvam1729@gmail.com INTRODUCTIONThe dispersion of displacement, temperature change in a rotating cylindrical panel is plays a vital role in smart material applications and rotating gyroscope. This type of model analysis is very important in bio sensing applications in nuclear magnetic resonance (NMR), magnetic resonance imaging (MRI) and echo planar imaging (EPI). The analysis of thermally induced vibration of rotating cylindrical panel is common place in the design of structures, atomic reactors, steam turbines, supersonic aircraft, and other devices operating at elevated temperature. At the present time applied mathematicians are exhibiting considerable interest in dynamical methods of elasticity, since the usual quasi static approach ignores certain very important features of the problems under consideration. That approach is based on the assumption that the inertia terms may be omitted from the equations of motion. This assumption holds good only when the variations in stresses and displacements, but there arise number of problems in engineering and technology, when this assumption may not hold good and the inertia terms in the equations of motion may have lead to cases of considerable mathematical complications. In the field of nondestructive evaluation, laser-generated waves have attracted great attention owing to their potential application to noncontact and nondestructive evaluation of sheet materials. The high velocities of modern aircraft give rise to aerodynamic heating, which produces intense thermal stresses, reducing the strength of the aircraft structure. In the nuclear field, the extremely high temperatures and temperature gradients originating inside nuclear reactors influence their design and operations. Moreover, it is well recognized that the investigation of the thermal effects on rototing elastic wave propagation has bearing on many structural applications.The static analysis cannot predict the behavior of the material due to the thermal stresses changes very rapidly. Therefore in case of suddenly applied load, thermal deformation and the role of inertia are getting more important. This thermo elastic stress response being significant leads to the propagation of

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“…is used in Refs. [16,17,20]. Other more significant variations of the above forms that one might better refer to as "Buchwald-type" representations are ubiquitous in the literature (see, for example, Ref.…”

“…The Buchwald representation is also applicable to problems involving isotropic media [13,14]. Application of the Buchwald representation to such problems is however rare [15][16][17].…”

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“…[5][6][7] and references therein). The Buchwald representation is also applicable to problems involving isotropic media [8,9], but its application to such problems is relatively rare [10][11][12].…”