Bounds on phase velocity changes of plane waves in elastic media due to changes in elastic moduli

By using the normality of the acoustic tensor for homogeneous, linearly elastic media, bounds are obtained for the changes in plane wave phase velocities due to changes in the elastic moduli of the medium. The bounds, which hold for arbitrary propagation directions and arbitrary changes in elastic moduli are then speck&d to the cases where a single modulus is varied holding all the rest constant. Three dimensional bounding surfaces are derived and graphically presented for the possible changes in phase velocity (actually, square of phase velocity times mass density) of any given mode while propagating in any direction due to the changes in a specik elastic modulus. The results of this paper can be used in analytical developments wherever a need exists to place bounds on possible changes in a solution due to changes in elastic moduli, such as in the reconstruction of elastic moduli from phase or group velocity information. 0 1997 Elsevier Science Ltd.