Response of a Finite Tube to Moving Pressure

Determination of the transient axisymmetric vibration of a thin-walled elastic tube of finite length based on the Herrmann-Mirsky equation is examined. The orthogonality of the natural modes of vibration which are generated from the shell equation and the general homogeneous boundary conditions is shown. An analytic solution for a tube with simply supported boundary conditions and general initial conditions contains an infinite trigonometric series that can be obtained by superposition of natural modes. The analysis is applied to a solution of the deflection response at the midspan of a tube to a step pressure moving with various velocities. The solution is compared to those from more approximate theories. The range of validity of the more approximate theories to a finite tube under a moving step pressure is established.