Chaotic motion of shape memory alloy beam model with asymmetric structure. (Chinese. English summary) Zbl 1474.74061
Summary: The influence of asymmetry and non-smooth factors of the shape memory alloy beam model with unilateral constraint on the chaotic motion of the system is discussed. By studying the smooth Melnikov function and the non-smooth Melnikov function coexisting with the nonlinear vibro-impact system, the necessary conditions for Smale horseshoe chaos generated by the smooth homoclinic and non-smooth homoclinic bifurcations are obtained. The numerical simulation results of phase diagram, Poincaré cross-sectional diagram, bifurcation diagram and maximum Lyapunov exponent are used to verify the chaotic threshold conditions. The results show that the larger harmonic force is beneficial to the bifurcation of homoclinic orbits and chaos under certain parameters, and the interaction of smooth homoclinic bifurcation and non-smooth homoclinic bifurcation can induce the occurrence of chaotic mergers.
MSC:
| 74H65 | Chaotic behavior of solutions to dynamical problems in solid mechanics |
| 74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |
| 74D99 | Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials) |
| 37J46 | Periodic, homoclinic and heteroclinic orbits of finite-dimensional Hamiltonian systems |
| 37N15 | Dynamical systems in solid mechanics |
| 37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |
