Cross-sectional flattening-induced nonlinear damped vibration of elastic tubes subjected to transverse loads

Abstract

This paper presents an analytical solution of the cross-sectional flattening-induced nonlinear vibration of elastic tubes when subjected to transverse harmonic excitation. It is shown that the equation of motion describing the beam-type transverse vibration of elastic tubes can be characterized by the Duffing equation with cubic nonlinearity, in which the nonlinear term reflects the influence of the cross-sectional flattening on the beam-type transverse vibration of the tubes. The degree of nonlinearity of the transverse vibration is found to be governed directly by the dimensionless amplitude of the harmonic force. The nonlinear feature and corresponding stability of the beam-type response of the tubes under the action of harmonic excitation are discussed. Numerical examples are provided to demonstrate the rationality of the present analytical model.