scholarly journals Bifurcation and Chaos in Integer and Fractional Order Two-Degree-of-Freedom Shape Memory Alloy Oscillators

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Karthikeyan Rajagopal ◽  
Anitha Karthikeyan ◽  
Prakash Duraisamy ◽  
Riessom Weldegiorgis
Keyword(s):  
Shape Memory Alloy ◽  
Shape Memory ◽  
Fractional Order ◽  
Dynamical Behavior ◽  
Degree Of Freedom ◽  
Order Model ◽  
Bifurcation And Chaos ◽  
Fractional Order Model ◽  
Two Degree Of Freedom ◽  
Fractional Orders

A two-degree-of-freedom shape memory oscillator derived using polynomial constitutive model is investigated. Periodic, quasiperiodic, chaotic, and hyperchaotic oscillations are shown by the shape memory alloy based oscillator for selected values of the operating temperatures and excitation parameters. Bifurcation plots are derived to investigate the system behavior with change in parameters. A fractional order model of the shape memory oscillator is presented and dynamical behavior of the system with fractional orders and parameters are investigated.

Design of a 2 DOF Shape Memory Alloy Actuator Using SMA Springs

2021 ◽  
Author(s):  
Hussein F. M. Ali ◽  
Youngshik Kim
Keyword(s):  
Shape Memory Alloy ◽  
Shape Memory ◽  
Open Loop ◽  
Degree Of Freedom ◽  
Biologically Inspired ◽  
Loop Control ◽  
Actuator System ◽  
Sma Actuator ◽  
Sma Spring ◽  
Two Degree Of Freedom

Abstract In this paper, we developed two degree of freedom shape memory alloy (SMA) actuator using SMA springs. This module can be applied easily to various applications: device holder, artificial finger, grippes, fish robot, and many other biologically inspired applications, where small size and small wight of the actuator are very critical. This actuator is composed of two sets of SMA springs: one set is for the rotation around the X axis (roll angle) and the other set is for the rotation around the Y axis (pitch angle). Each set contains two elements: one SMA spring and one antagonistic SMA spring. We used an inertia sensor (IMU) and two potentiometers for angles feedback. The SMA actuator system is modeled mathematically and then tested experimentally in open-loop and closed-loop control. We designed and experimentally tuned a proportional integrator derivative (PID) controller to follow the set points and to track the desired trajectories. The main goal of the presented controller is to control roll and pitch angles simultaneously in order to satisfy set points and trajectories within the work space. The experimental results show that the two degree of freedom SMA actuator system follows the desired setpoints with acceptable rise time and overshoot.

Angular control of differential shape-memory alloy spring actuator for underactuated dynamic system

2021 ◽  
pp. 107754632110216
Author(s):  
M Banu Sundareswari ◽  
G Then Mozhi ◽  
K Dhanalakshmi
Keyword(s):  
Shape Memory Alloy ◽  
Shape Memory ◽  
Fractional Order ◽  
Position Control ◽  
Sliding Mode ◽  
Control Effort ◽  
Control Laws ◽  
Integer Order ◽  
Two Degree Of Freedom ◽  
Outer Primary

This article dwells on two technical aspects, the design and implementation of an upgraded version of the differential shape-memory alloy–based revolute actuator/rotary actuating mechanism for stabilization and position control of a two-degree-of-freedom centrally hinged ball on beam system. The actuator is configured with differential and inclined placement of shape-memory alloy springs to provide bidirectional angular shift. The shape-memory alloy spring actuator occupies a smaller space and provides more extensive reformation with justifiable actuation force than an equally able shape-memory alloy wire. The cross or diagonal architecture of shape-memory alloy springs provides force amplification and reduces the actuator’s control effort. The shape-memory alloy spring–embodied actuator’s function is exemplified by the highly dynamic underactuated custom-designed ball balancing system. The ball position control is experimentally demonstrated by cascade control using the control laws that have been unattempted for shape-memory alloy actuated systems; the ball is positioned with linear (integer-order and fractional-order) proportional–integral–derivative controllers optimized with genetic algorithm and particle swarm optimization at the outer/primary loop. Angular control of the shape-memory alloy actuated beam is obtained with nonlinear (integer-order and fractional-order sliding mode control) control algorithms in the inner/secondary loop.

Multistability and Coexisting Attractors in a New Circulant Chaotic System

2019 ◽  
Vol 29 (13) ◽  
pp. 1950174 ◽  
Author(s):  
Karthikeyan Rajagopal ◽  
Akif Akgul ◽  
Viet-Thanh Pham ◽  
Fawaz E. Alsaadi ◽  
Fahimeh Nazarimehr ◽  
...  
Keyword(s):  
Fractional Order ◽  
Order System ◽  
Cyclic Symmetry ◽  
Order Model ◽  
Coexisting Attractors ◽  
Circuit Realization ◽  
Chaotic Flow ◽  
Fractional Order Model ◽  
Dynamical Properties ◽  
Fractional Orders

In this paper, a new four-dimensional chaotic flow is proposed. The system has a cyclic symmetry in its structure and shows a complicated, chaotic attractor. The dynamical properties of the system are investigated. The system shows multistability in an interval of its parameter. Fractional order model of the proposed system is discussed in various fractional orders. Bifurcation analysis of the fractional order system shows that it has a kind of multistability like the integer order system, which is a very rare phenomenon. Circuit realization of the proposed system is also carried out to show that it is usable for engineering applications.

scholarly journals Numerical solution of a fractal-fractional order chaotic circuit system

2021 ◽  
Vol 67 (5 Sep-Oct) ◽  
Author(s):  
Muhammad Altaf Khan ◽  
Abdon Atangana ◽  
Taseer Muhammad ◽  
Ebraheem Alzahrani
Keyword(s):  
Numerical Solution ◽  
Fractional Order ◽  
Research Area ◽  
Fractional Operators ◽  
Chaotic Circuit ◽  
Order Model ◽  
Fractional Order Model ◽  
Chaotic Model ◽  
Important Research Area ◽  
Fractional Orders

The dynamical system has an important research area and due to its wide applications many researchers and scientists working to develop new model and techniques for their solution. We present in this work the dynamics of a chaotic model in the presence of newly introduced fractal-fractional operators. The model is formulated initially in ordinary differential equations and then we utilize the fractal-fractional (FF) in power law, exponential and Mittag-Leffler to generalize the model. For each fractal-fractional order model, we briefly study its numerical solution via the numerical algorithm. We present some graphical results with arbitrary order of fractal and fractional orders, and present that these operators provide different chaotic attractors for different fractal and fractional order values. The graphical results demonstrate the effectiveness of the fractal-fractional operators.

scholarly journals Dynamical Analysis of Approximate Solutions of HIV-1 Model with an Arbitrary Order

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-7 ◽  
Author(s):  
Asma ◽  
Nigar Ali ◽  
Gul Zaman ◽  
Anwar Zeb ◽  
Vedat Suat Erturk ◽  
...  
Keyword(s):  
Fractional Order ◽  
Dynamical Behavior ◽  
Adomian Decomposition Method ◽  
Approximate Solutions ◽  
Dynamical Analysis ◽  
Order Model ◽  
Hiv Model ◽  
Fractional Order Model ◽  
Adomian Decomposition ◽  
Hiv 1

This article studies the dynamical behavior of the analytical solutions of the system of fraction order model of HIV-1 infection. For this purpose, first, the proposed integer order model is converted into fractional order model. Then, Laplace-Adomian decomposition method (L-ADM) is applied to solve this fractional order HIV model. Moreover, the convergence of this method is also discussed. It can be observed from the numerical solution that (L-ADM) is very simple and accurate to solve fraction order HIV model.

Effect of constitutive model parameters on the aeroelastic behavior of an airfoil with shape memory alloy springs

2016 ◽  
Vol 24 (6) ◽  
pp. 1065-1085 ◽  
Author(s):  
Vagner Candido de Sousa ◽  
Carlos De Marqui Junior ◽  
Mohammad H Elahinia
Keyword(s):  
Shape Memory Alloy ◽  
Shape Memory ◽  
Pure Shear ◽  
Degree Of Freedom ◽  
Model Parameters ◽  
Cross Sectional ◽  
Helical Springs ◽  
Flutter Boundary ◽  
Tension Compression Asymmetry ◽  
Two Degree Of Freedom

The effects of the pseudoelastic hysteresis of shape memory alloy springs on the aeroelastic behavior of a typical airfoil section are numerically investigated for six different sets of alloy constitutive properties. A two-degree-of-freedom (namely, plunge and pitch) typical section is modeled. Shape memory alloy helical springs are considered in the pitch degree-of-freedom based on classical phenomenological models modified by the pure shear assumption. Tension–compression asymmetry and nonhomogeneous distributions of shear strain, shear stress and martensitic fraction in the cross-sectional area of the coiled shape memory alloy wire are considered. A linear model is used to determine the unsteady aerodynamic loads. Attractive alloy characteristics, which can enhance the aeroelastic behavior of the typical section at the flutter boundary and at the post-flutter regime, are identified and discussed in detail.

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