Likely oscillatory motions of stochastic hyperelastic spherical shells and tubes

Abstract

We examine theoretically the dynamic inflation and finite amplitude oscillatory motion of inhomogeneous spherical shells and cylindrical tubes of stochastic hyperelastic material. These bodies are deformed by radially symmetric uniform inflation, and are subjected to either a surface dead load or an impulse traction, uniformly applied in the radial direction. We consider composite shells and tubes with two concentric stochastic homogeneous neo-Hookean phases, and inhomogeneous bodies of stochastic neo-Hookean material with constitutive parameters varying continuously in the radial direction. For the homogeneous materials, we define the elastic parameters as spatially-independent random variables, while for the radially inhomogeneous bodies, we take the parameters as spatially-dependent random fields, described by non-Gaussian probability density functions. Under radially symmetric dynamic deformation treated as quasi-equilibrated motion, we show that the bodies oscillate, i.e., the radius increases up to a point, then decreases, then increases again, and so on, and the amplitude and period of the oscillations are characterised by probability distributions, depending on the initial conditions, the geometry, and the probabilistic material properties.