SMA in SNA exploration of SNA in a SMA three leg parallel manipulator

1. Exploration of Strange Nonchaotic Attractor in a
Shape Memory Alloy three leg parallel manipulator
Authors
Prakash Duraisamy
Premraj Durairaj
Prasanth Durairaj
Anitha Karthikeyan
Karthikeyan Rajagopal
ICNCS 2024

2. Content
➢ Introduction - SMA - SNA
➢ SMA based Parallel manipulator
➢ Mathematical Modeling
➢ Dynamic Analysis- Bifurcation plot - Lyapunov Spectrum
➢ Confirmation analysis for SNA
➢ Significance of SNA in Mechanical systems

3. Introduction - Shape Memory Alloys

7. Introduction - Strange Nonchaotic attractor
Where
Strange nonchaotic attractors (SNAs) typically
appear in quasiperiodically forced dynamical
systems
Who
Thanks to Dr. Grebogi et al.,
What
SNAs exhibit some properties of regular as well as chaotic
attractors. Like regular attractors, their dynamics is
nonchaotic in the sense that they do not have a positive
Lyapunov exponent; like usual chaotic attractors, they have a
geometrically strange (fractal) structure.

9. Challenges in mechanical systems or Need of SNA in mechanical systems
➢ Major challenge is to identify and characterize SNAs, since they are
often hidden or mixed with other types of attractors.
➢ Another challenge is to design and implement quasiperiodic forcing
in a practical way, since it requires precise tuning of the frequency
and amplitude of the driving signals.
➢ A third challenge is to understand the mechanisms and routes of
transitions between SNAs and other attractors, such as tori, chaos, or
periodic orbits.

10. SMA based Three leg support

11. Different Cases

12. Lyapunov Spectrum
(Case 1) Recurrence Plots

13. Lyapunov Spectrum for case 2 & 3

14. Confirmation Analysis for SNA
1. Poincare surface section
2. Separation of Nearby trajectories
3. Singular continuous spectrum analysis

18. Strange nonchaotic attractors (SNAs) are complex dynamical patterns that arise in
certain nonlinear systems that are driven by quasiperiodic forces. They have fractal
geometry, but unlike chaotic attractors, they do not show exponential sensitivity to initial
conditions. This means that the motion on SNAs is stable and predictable, yet aperiodic
.
Mechanical systems, such as pendulums, oscillators, or rotors, can exhibit SNAs under
quasiperiodic forcing. The significance of SNAs in mechanical systems is that they can
provide a way to control or optimize the system’s behavior, such as enhancing
synchronization, reducing vibrations, or increasing efficiency.
Summary