On amplification of stress waves in cylindrical tubes under internal dynamic pressures

This paper presents a set of closed form solutions for the elastodynamic structural response of thin cylindrical tubes to internal moving pressures with specific profiles. The solution set includes newly derived expressions for transverse shear and axial strains plus modified expressions for the reflected structural waves. These expressions are used to study the amplification of flexural and shear stress waves caused by internal gaseous detonation and shock loading. It is shown how the three different critical speeds at which the resonance of the structural waves occur can be computed. The development of stress waves in a thin aluminum tube is studied over a wide range of speeds and the magnitudes of dynamic amplification factors are determined. In particular, the occurrence of transverse shear resonance at the second critical speed is studied. The peak value of the shear stress at this speed is found to be significantly higher than the finite element results reported by other researchers. Finally, an adjusted form of the general solution is used to investigate the response of a thin tube to internal shock loading. The predicted vibrational spectrums were in very good agreement with the experimental results reported in the literature.