•Experimental and mathematical models of a pendulum driven by DC motors are developed.•Good agreement between numerical simulations and experimental data is obtained.•Bifurcation dynamics is ...investigated by experimental and numerical methods.•Passive control of chaos with magnetic rheological rotational damper is proposed.
In the present work, we deal with a dynamical analysis and passive control of chaos with magnetic rheological (MR) rotational damper in a pendulum driven by a DC motor via slider mechanism. A mathematical model for electromechanical system composed of a pendulum driven horizontally by through a DC motor and a slider-crank mechanism is presented and the parameters are estimated based on experimental data. Numerical and experimental results demonstrate that for certain values of the motor input voltage they can lead the system to chaotic behavior. For dynamic analysis, bifurcation diagrams, Poincaré sections, phase diagrams and 0–1 test are considered. In order to suppress the chaotic behavior, it is proposed to include MR rotational damper, as a passive control. In the case of the passive rotational MR damper, the influence of the introduction of the MR damper in a pendulum is performed considering the bifurcation diagrams. The numerical results show that the introduction of a passive rotational MR damper suppresses the chaotic behavior of the system. Additionally it is shown that it is possible to keep the pendulum oscillating with periodic behavior using the rotational MR damper with energizing discontinuity.
In this work, we explore the nonlinear dynamics for capturing energy from a device, which is considered support with cantilever beam ferromagnetic containing piezoceramic patches connected to an ...electrical circuit that collects energy for capture. The free end of the ferromagnetic cantilever beam is under the effect of two magnetic poles, and we consider an asymmetric potential for the magnetic poles. However, the influence of asymmetry in bi-stable energy collectors can change the potential well and adjust the distribution of its potential energy. Charging in the potential well also modifies the unstable equilibrium positions thus altering the dynamic characteristics of the device and thus benefiting the use of energy under various excitation conditions. Furthermore, asymmetric potentials combine with the movement of human lower limbs for applications in energy harvesting devices in such displacement. As numerical results, we explored the nonlinear dynamics and established the sets of parameters for the convergence of the trajectories and the regions of maximum average output power.
In this paper, we investigate a nonlinear dynamic model of the trolling mode in atomic force microscopy (AFM-TR) considering the fractional viscoelasticity. The term fractional viscoelasticity is an ...approximate representation of the medium in which the system is used for the analysis of biological samples. The fractional nonlinear dynamic model of the AFM-TR considers a nanoneedle coupled to a nanobeam that, when subjected to vibrations during the interaction with the sample surface, generates a three-dimensional image of its topology. These interactions between the nanoneedle and sample are Van Der Waals force type, and other interactions are considered biological environment. With these considerations, the fractional dynamics were analyzed considering the Riemann–Liouville fractional derivative operator. The results obtained the intervals in which the system has a chaotic or periodic behavior, such analyses corroborate to determine a set of parameters in which the term of fractional viscoelasticity may influence the dynamics of the AFM-TR.
We investigated the nonlinear dynamic behavior of the system for energy harvesting using ocean wave motion. The system consists of a linear electromagnetic system coupled to a float to move with ...ocean waves. We define the mathematical modeling of a structure together with the parameters for energy harvesting. In this way, we analyzed average power for the parameters linked to the wave profile, the resistance load of the electromechanical motor, and the nonlinear parameters of spring cubic. Therefore, we also analyze the nonlinear dynamic behavior with Maximum Lyapunov exponent, bifurcation diagrams, phase portraits, and Poincaré maps.
We investigate the nonlinear dynamic model of the Atomic Force Microscopy model (AFM) with the influence of a viscoelastic term. The mathematical model is based on non-resonant and almost linear ...responses, together with the deflection of the microcantilever, and also considers the interaction forces between the atoms of the analysis tip and the sample surface. Our results show the influence on the nonlinear dynamics of this model considering the term viscoelastic. We also analyzed the generalized model with the fractional calculus with the Riemann–Liouville operator derivative applied to the viscoelastic term and thus having the fractional nonlinear dynamics of the AFM system. For the analysis of the system, we used the classic tooling of nonlinear dynamics (Bifurcation diagram, 0–1 Test, and Poincaré maps, and the Maximum Lyapunov Exponent), however, the results showed the chaotic and periodic regions of the fractional system.
We investigated the nonlinear behavior of an atomic force microscopy system with the contribution of the medium viscoelasticity term. Atomic force microscopy is one of the most used techniques for ...analyzing the surface topology of samples of interest. We propose a mathematical model for the nonlinear dynamics of the probe and we also assign a term that describes the viscoelasticity of the medium in which the probe is inserted. For our numerical analysis of nonlinear dynamics, we used the Lyapunov Exponent, Bifurcation Diagram, phase maps and Poincaré maps. We also determine a solution for a set of parameters using perturbation theory. In this paper, it is also shown that using higher approximations of averaging method, which allows to solve systems of differential equations with slowly changing variables instead systems with fast change of variables, is very effective to study dynamics of an atomic force microscopy.
This paper presents the results of investigating the dynamics of an economic system with chaotic behavior and a suboptimal control proposal to suppress the chaotic behavior. Numerical results using ...phase portraits, bifurcation diagrams, Lyapunov exponents, and 0-1 testing confirmed chaotic and hyperchaotic behavior. The results also proved the effectiveness of the control, showing errors below 1%, even in cases where the control design is subject to parametric errors. Additionally, an investigation of the system in fractional order is included, demonstrating that the system has periodic, constant, or chaotic behavior for specific values of the order of the derivative.
In this paper, we investigate the mechanism of atomic force microscopy in tapping mode (AFM-TM) under the Casimir and van der Waals (VdW) forces. The dynamic behavior of the system is analyzed ...through a nonlinear dimensionless mathematical model. Numerical tools as Poincaré maps, Lyapunov exponents, and bifurcation diagrams are accounted for the analysis of the system. With that, the regions in which the system presents chaotic and periodic behaviors are obtained and investigated. Moreover, the fractional calculus is introduced into the mathematical model, employing the Riemann-Liouville kernel discretization in the viscoelastic term of the system. The 0-1 test is implemented to analyze the new dynamics of the system, allowing the identification of the chaotic and periodic regimes of the AFM system. The dynamic results of the conventional (integer derivative) and fractional models reveal the need for the application of control techniques such as Optimum Linear Feedback Control (OLFC), State-Dependent Riccati Equations (SDRE) by using feedback control, and the Time-Delayed Feedback Control. The results of the control techniques are efficient with and without the fractional-order derivative.
The atomic force microscope (AFM) on the nanoscale measurements comes from nanotechnology and is currently a multidisciplinary field of research. The present research proposal aims to contribute to ...scientific research on AFM considering that the system is operating in the intermittent mode and the contact of the tip with sample generates a damping represented by squeeze-film damping, and that the damping dynamics of the squeeze-film damping can be represented by fractional calculus through numerical simulation and dynamic analysis to prove chaotic regimes. To suppress chaotic behavior, we will use and analyze two control strategies, the SDRE (Riccati Equation Dependent States) and OLFC (Linear Control for Optimum Feedback) controls.
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