Cloud Publications International Journal of Advanced Mathematics and Statistics 2012, Volume 1, Issue 1, pp. 7-16, Article ID Sci-51 ____________________________________________________________________________________________________ Finitesimale Deformation in a Rotating Disc Having Variable Density Parameter Pankaj Thakur Department of Mathematics, Indus International University, Bathu, Una, Himachal Pradesh, India Correspondence should be addressed to Pankaj Thakur, pankaj_thakur15@yahoo.co.in Publication Date: 19 December 2012 Article Link: http://scientific.cloud-journals.com/index.php/IJAMS/article/view/Sci-51 Copyright © 2012 Pankaj Thakur. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract Finitesimale deformation in a rotating disc having variable density parameter has been studied by using Seth’s transition theory. With the effect of density variation parameter, rotating disc requires lesser angular speed for compressible as well as incompressible materials. Circumferential stresses are maximum at the internal surface for incompressible materials as compared to compressible material. Rotating disc is likely to fracture by cleavage close to the bore. Keywords Disc, Stresses, Deformation, Yielding, Angular Speed, Density 1. Introduction Disc plays an important role in machine design. Stress analysis of rotating discs has an important role in engineering design. Rotating discs are the most critical part of rotors, turbines motor, compressors, high speed gears, flywheel, sink fits, turbo jet engines and computer’s disc drive etc. Solutions for thin isotropic discs can be found in most of the standard elasticity and plasticity textbooks [1, 2, 3, 4, 5]. Chakrabarty [4] and Heyman [6] solved the problem for the plastic state by utilizing the solution in the elastic state and consider the plastic range with the help of Tresca’s yield condition. Further, to obtain the elastic-plastic stresses, these authors matched the elastic and plastic stresses at the same radius r = c of the disc. Perfectly elasticity and ideal plasticity are two extreme properties of the material and the use of ad-hoc rule like yield condition amounts to divide the two extreme properties by a sharp line, which is not physically possible. Seth’s transition theory [7] does not required any assumptions like an yield criterion, incompressibility condition, associated flow rule and thus poses and solves a more general problem from which cases pertaining to the above assumptions can be worked out. This theory [7] utilizes the concept of generalized strain measure and asymptotic solution at critical points or turning points of the differential equations defining the deformed field and has been successfully applied to a large number of problems [7-29]. Seth [8] has defined the generalized principal strain measures as: Open Access Research Article