Wave propagation in a circular membrane subjected to an impulsively applied pressure load

Abstract

The elastic deformation of a circular membrane subjected to an impulsively applied pressure of constant magnitude is investigated. The membrane is assumed to be clamped at the periphery after being subjected to a small radial extension. The differential equations of motion are derived and classified as completely hyperbolic. Results are obtained using the method of characteristics and the technique of numerical integration along the characteristic lines. Both strain waves and inertia waves propagate through the membrane as the deformation takes place. The numerical results show that while the membrane material is in the elastic range, the two types of waves propagate with constant, but unequal, velocities. It is pointed out that the phenomenon of constant wave velocities could possibly be used to simplify the equations of motion and obtain an approximate, closed form solution applicable to the elastic range. Although only the elastic case is considered, the analysis presented is applicable to material behavior obeying any finite constitutive relation. In particular, extension of the procedure to the study of plastic deformation is discussed.