Analytic detection of chaos zones in response of a shape memory alloy beam under simultaneous external and parametric excitations
- 22 October 2022
- journal article
- research article
- Published by Taylor & Francis in Mechanics Based Design of Structures and Machines
- Vol. 52 (2) , 1060-1073
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.Keywords
This publication has 36 references indexed in Scilit:
- Analysis of nonlinear free vibration and damping of a clamped–clamped beam with embedded prestrained shape memory alloy wiresJournal of Intelligent Material Systems and Structures, 2012
- Seismic Response Control Using Shape Memory Alloys: A ReviewJournal of Intelligent Material Systems and Structures, 2011
- Overview of Potential and Existing Applications of Shape Memory Alloys in BridgesJournal of Bridge Engineering, 2011
- A 3-D phenomenological constitutive model for shape memory alloys under multiaxial loadingsInternational Journal of Plasticity, 2010
- Post-critical behavior of damped beam columns with variable cross section subjected to distributed follower forcesNonlinear Dynamics, 2008
- A three-dimensional phenomenological model for martensite reorientation in shape memory alloysJournal of the Mechanics and Physics of Solids, 2007
- Non-linear dynamic stability of damped Beck's column with variable cross-sectionInternational Journal of Non-Linear Mechanics, 2007
- Fatigue analysis of shape memory alloys: energy approachSmart Materials and Structures, 2005
- Analysis of the pseudoelastic behavior of a SMA beam by the element-free Galerkin methodEngineering Analysis with Boundary Elements, 2004
- Analysis of the behavior of a Shape Memory Alloy beam under dynamical loadingEuropean Journal of Mechanics - A/Solids, 2001