Critical velocities of a three-layer composite tube under a moving internal pressure are derived in the closed-form expressions. The formulation is based on a first-order shear deformation shell theory that accounts for the transverse shear, rotary inertia and material anisotropy. The composite tube consists of three perfectly bonded cylindrical layers of dissimilar materials, each of which can be orthotropic, transversely isotropic, cubic or isotropic. Closed-form formulas for four critical velocities are first obtained for the general case by considering the effects of transverse shear, rotary inertia, material orthotropy and radial stress. These general formulas are then reduced to specific ones for composite tubes without the transverse shear, rotary inertia or radial stress effect and for tubes with simpler anisotropy. In addition, it is shown that the current model for three-layer tubes can recover those for single- and two-layer tubes as special cases. To demonstrate the newly derived closed-form formulas, an example is given for a three-layer composite tube made of an isotropic inner layer, an orthotropic core and an isotropic outer layer. All four critical velocities of this three-layer composite tube are determined by directly applying the new model. Numerical results reveal that three values of the lowest critical velocity predicted by the current analytical model agree well with those computationally obtained in an existing study.
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