Modelling of a discrete-continuous system with a shape memory alloy support

This paper presents the hysteretic damping effect caused by a shape memory alloy spring which is used as a support of a cantilever beam. Free vibration diagrams of the discrete-continuous system are compared with amplitude envelopes obtained for two equivalent one-degree-of-freedom systems with the nonlinear pseudoelastic spring. Also the logarithmic decrement to amplitude relations have been calculated. The problems of modelling of the considered discrete-continuous structure by means of the proposed simplified one-degree-of-freedom systems, and some remarks concerning inaccuracy of the applied asymptotic method have been presented and discussed.