Third harmonic generation of transverse acoustic waves in crystals and ceramics

When transverse acoustic waves propagate in isotropic solids and in some specially orientated crystals the quadratic or the second order nonlinearity does not exist. The third harmonic generation (THG) of transverse waves in such materials is investigated in this paper. Since the quadratic nonlinearity does not exist, the third harmonic wave is generated solely by the cubic nonlinear interactions of the fundamental waves. A nonlinearity parameter for the THG is defined analog to the second harmonic generation of longitudinal waves. This parameter involves the linear combination of the second-, third- and fourth-order elastic constants. If the relevant second- and third-order constants are known, the fourth-order constants can be isolated from the measured nonlinearity parameters. Experiments of third harmonic generation in shear waves are carried out for poled and unpoled PZT4 ceramics. The appropriate nonlinearity parameters are determined, which give some combinations of the second, third- and fourth-order elastic constants. This THG provides a new way to determine the fourth-order elastic constants of materials in addition to the static pressure measurements.