Linear and nonlinear characterization of limestone rock using noncollinear ultrasonic wave mixing

Characterization of dolomitic limestone rock is presented using linear and nonlinear ultrasonic approaches. The linear approach is based upon the concept of complex moduli, which is estimated using ultrasonic dilatational and shear phase velocity measurements and the corresponding attenuations. The nonlinear approach is based upon non-collinear wave mixing, involving mixing of two dilatational waves. Criteria were used to assure that the detected scattered wave originated via wave interaction in the limestone and not from nonlinearities in the testing equipment. These criteria included frequency and propagating direction of the resultant scattered wave, and the time-of-flight separation between the two primary waves and the resulting scattered wave. Three cases of non-collinear interaction of two longitudinal waves are presented and discussed including one that requires only access to a plane surface of the stone test sample.