Critical Velocities of Single-layer and Two-layer Composite Tubes of Transversely Isotropic Materials Based on a Potential Function Method in 3-D Elasticity

Critical velocities of a single-layer tube of a transversely isotropic material and a two-layer composite tube consisting of two perfectly-bonded cylindrical layers of dissimilar transversely isotropic materials are analytically determined using the potential function method of Elliott in three-dimensional (3-D) elasticity. The displacement and stress components in each transversely isotropic layer of the tube subjected to a uniform internal pressure moving at a constant velocity are derived in integral forms by applying the Fourier transform method. The solution includes those for a tube composed of two dissimilar cubic or isotropic materials as special cases. In addition, it is shown that the model for the two-layer composite tube can be reduced to that for the single-layer tube. Closed-form expressions for four critical velocities are derived for the single-layer tube. The lowest critical velocity is obtained from plotting the velocity curve and finding the inflection point for both the single-layer and two-layer composite tubes. To illustrate the newly developed models, two cases are studied as examples – one for a single-layer isotropic steel tube and the other for a two-layer composite tube consisting of an isotropic steel inner layer and a transversely isotropic glass-epoxy outer layer. The numerical values of the lowest critical velocity predicted by the new 3-D elasticity-based models are obtained and compared with those given by existing models based on thin- and thick-shell theories.