NONLINEAR RADIAL OSCILLATIONS OF A THIN-WALLED DOUBLE-LAYER HYPERELASTIC CYLINDRICAL TUBE

Non-linear radial oscillations of an infinitely long, double-layer, hy perelastic thin-walled cylindrical tube of incompressible material are considered. Conditions are derived on the strain-energy functions of each layer for the radial equation of motion to reduce to the Ermakov- Pinney equation. The conditions are satisfied by the Mooney-Rivlin str ain-energy function. Non-linear superposition theory for the solution of the Ermakov-Pinney equation in terms of two linearly independent so lutions of the time dependent linear harmonic oscillator equation is r eviewed and applied. Exact solutions for the inner radius of the doubl e-layer, thin-walled cylinder are derived for free oscillations and fo r the Heaviside step loading boundary condition. The radial oscillatio ns of single-layer and double-layer cylindrical tubes of the same thic kness and subjected to the same boundary conditions are analysed and c ompared. The conclusions deduced for the composite cylindrical tube ma y have application to the dynamics of composite bodies. (C) 1997 Elsev ier Science Ltd.