Dynamic Behavior of a Nonlinear Viscoelastic Cylindrical Shell Subjected to Internal Pressure

The problem considered here is a dynamic problem for pressure applied uniformly to the interior surface of the viscoelastic hollow circular cylinder encased by and bonded to an elastic cylindrical casing. The solution is obtained from a second order nonlinear integro-differential equation of Volterra type of the second kind. The integro-differential equation is shown to have a unique solution. A numerical procedure is derived and shown to produce approximations that converge to the solution. Some numerical results are presented and discussed. Applications arise in the manufacture of solid rocket propellants, polymers, casting of various materials, etc. One interesting application would be the short time combustion of a solid rocket where the dynamics of the interior boundary did not come into play yet possible pressure variations could excite higher modes of the resonance frequency. The question of resonance is discussed in the discussion of the numerical results.