Third-harmonic studies of nonlinear anelasticity and determination of higher-order elastic constants in Mn[sbnd]7 at.% Cu

Abstract

A nonlinear equation of motion relevant to a vibrating reed with one end clamped and the other free has been derived in order to analyse nonlinear anelasticity due to motion of twin boundaries. Application of the iteration method of Duffing to solve the equation has yielded an expression describing the shape of a resonance curve and an approximate solution that contains the third harmonic, the amplitude of which is a function of strain and higher-order elastic constants. Nonlinear resonance curves and third harmonics were measured for the martensite of a Mn-7 at.% Cu shape-memory alloy in an effort to test the theory. The experimental results have been found to be consistent with the theory, and the even-order elastic constants have been determined as high as the eighth order.