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Abstract

The symmetries for the wave equation governing the radial deformations of circular cylinders composed of Blatz-Ko materials are studied. It is found that the wave equation possesses a special symmetry --- the inverse time translational symmetry (ITTS) named by us. We find that this special symmetry is not possessed by the wave equations for cylinders composed of other two compressible elastic materials. However, it appears again when we study the invariant properties of the wave equation governing radially deformed BlatzKo spheres and the one governing Blatz-Ko blocks in uniaxial tensile motion. We therefore infer that ITTS is a special property inherited by many dynamical problems associated with Blatz-Ko materials. It is also found that this special symmetry can help us to construct correspondence between different initial-boundary value problems of the wave equation for Blatz-Ko cylinders. Making use of this correspondence we can obtain non-trivial solutions from known solutions. Also, if we need to perform an experiment for a Blatz-Ko cylinder for a long time period, we may use this correspondence to design a substitute experiment that only runs in a short time period.

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