Closed-Form Solutions for Dynamic Finite Deformation of Vulcanised Rubber Cylinders
Nwagwu Isaac Ogazie *
Department of Mathematics, Federal University of Technology, Owerri, Nigeria.
Noah Moses Friday
Department of Mathematics, Federal University of Technology, Owerri, Nigeria.
Erumaka Ephiram Ngozi
Department of Mathematics, Federal University of Technology, Owerri, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
Cylindrical tubes are subjected to internal pressures and, as a result, they undergo finite deformations. Therefore, a good understanding and knowledge of deformation mechanisms of many structures and materials under different loading conditions are to be known because of great importance to materials testing and product development. In this work, the dynamic case of the deformation of an internally pressurised hollow cylinder made of natural vulcanised rubber material is considered. The analysis of the deformation led to a non-linear second-order partial differential equation for the determination of stresses and displacement. Knowing that most of the wave equations are weakly non-linear and as such their solution are time independent. The Monge method was employed, which reduces the equation into a linear second-order ordinary differential equation where the D operator Method of solution was sought, and appropriate boundary conditions were applied for the determination of a closed-form solution of the displacement and stresses at various parts of the cylindrical tubes.
Keywords: Vulcanised rubber, displacement, undeformed radius, stresses and Hollow cylinder