The determination of elastic constants of isotropic tube-shaped samples from ultrasonic vibrations

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Abstract
A method of simultaneous measurement of both elastic constants of tube-shaped isotropic ferromagnetic metals is presented. It can be extended to nonmagnetic material. The experimental device operates at ultrasonic frequencies and provides a fast and easy change between torsional and extensional modes. Inexpensive equipment is used to measure the ultrasound velocities to good accuracy by a high-order standing-wave method. The mechanism of magnetostrictive generation of torsional and extensional vibrations and the procedure of evaluating the elastic constants are described. In the case of extensional vibrations the coupling between axial, circumferential and thickness modes are considered. Approximate relations between velocity and elastic constants are given which are independent of dispersion on geometrical grounds.