Analytic detection of chaos zones in response of a shape memory alloy beam under simultaneous external and parametric excitations

Abstract

ABTRACT In this article, the dynamic stability and chaotic behavior of a shape memory alloy (SMA) beam with large deformation under simultaneous lateral and axial excitations is investigated through a fully analytic approach. First, the nonlinear governing equation of motion is derived. Second, Melnikov’s method, as an analytic approach, is employed to obtain the chaos zones. After that, by introducing non-dimensional parameters, border curves of chaotic areas were evaluated and plotted for some case studies which give a reader a precise and clear look at how the material and load properties can affect the chaos zones. Finally, the sufficient condition is approved via corresponding poincaré maps.