Nonlinear periodic oscillation of a cylindrical microvoid centered at an isotropic incompressible ogden cylinder

We study the dynamic mathematical model for an infinitely long cylinder composed of an isotropic incompressible ogden material with a microvoid at its center,where the outer surface of the cylinder is subjected to a uniform radial tensile load. using the incompressibility condition and the boundary conditions,we obtain a second-order nonlinear ordinary differential equation that describes the motion of the microvoid with time. qualitatively,we find that this equation has two types of solutions. one is a classical nonlinear periodic solution which describes that the motion of the microvoid is a nonlinear periodic oscillation; the other is a blow-up solution. significantly,for the isotropic incompressible ogden material,there exist some special values of material parameters,the phase diagrams of the motion equation have homoclinic orbits,which means that the amplitude of a nonlinear periodic oscillation increases discontinuously with the increasing load. © 2012 wenzheng zhang et al.