Phase portraits of spatial moments of a collimated wave beam in controlled and free modes.

AbstractIn this paper vibrations of the isotropic micro/nanoplates subjected to transverse and in-plane excitation are investigated. The governing equations of the problem are based on the von Kármán plate theory and Kirchhoff–Love hypothesis. The small-size effect is taken into account due to the nonlocal elasticity theory. The formulation of the problem is mixed and employs the Airy stress function. The two-mode approximation of the deflection and application of the Bubnov–Galerkin method reduces the governing system of equations to the system of ordinary differential equations. Varying the load parameters and the nonlocal parameter, the bifurcation analysis is performed. The bifurcations diagrams, the maximum Lyapunov exponents, phase portraits as well as Poincare maps are constructed based on the numerical simulations. It is shown that for some excitation conditions the chaotic motion may occur in the system. Also, the small-scale effects on the character of vibrating regimes are illustrated and discussed.

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Chaotic Path Planning for 3D Area Coverage Using a Pseudo-Random Bit Generator from a 1D Chaotic Map

Mathematics ◽

10.3390/math9151821 ◽

2021 ◽

Vol 9 (15) ◽

pp. 1821

Author(s):

Lazaros Moysis ◽

Karthikeyan Rajagopal ◽

Aleksandra V. Tutueva ◽

Christos Volos ◽

Beteley Teka ◽

...

Keyword(s):

Path Planning ◽

Chaotic Map ◽

Dynamical Behavior ◽

Area Coverage ◽

Phase Portraits ◽

Planning Strategy ◽

Spline Curves ◽

Key Space ◽

Aerial Vehicle ◽

Discrete Motion

This work proposes a one-dimensional chaotic map with a simple structure and three parameters. The phase portraits, bifurcation diagrams, and Lyapunov exponent diagrams are first plotted to study the dynamical behavior of the map. It is seen that the map exhibits areas of constant chaos with respect to all parameters. This map is then applied to the problem of pseudo-random bit generation using a simple technique to generate four bits per iteration. It is shown that the algorithm passes all statistical NIST and ENT tests, as well as shows low correlation and an acceptable key space. The generated bitstream is applied to the problem of chaotic path planning, for an autonomous robot or generally an unmanned aerial vehicle (UAV) exploring a given 3D area. The aim is to ensure efficient area coverage, while also maintaining an unpredictable motion. Numerical simulations were performed to evaluate the performance of the path planning strategy, and it is shown that the coverage percentage converges exponentially to 100% as the number of iterations increases. The discrete motion is also adapted to a smooth one through the use of B-Spline curves.

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Coupled effects of surface interaction and damping on electromechanical stability of functionally graded nanotubes reinforced torsional micromirror actuator

The Journal of Strain Analysis for Engineering Design ◽

10.1177/03093247211036826 ◽

2021 ◽

pp. 030932472110368

Author(s):

Weidong Yang ◽

Menglong Liu ◽

Linwei Ying ◽

Xi Wang

Keyword(s):

Casimir Force ◽

Volume Fraction ◽

Nonlocal Parameter ◽

Saddle Points ◽

Functionally Graded ◽

Heteroclinic Orbits ◽

Phase Portraits ◽

Squeeze Film ◽

Squeeze Film Damping ◽

Tilting Angle

This paper demonstrated the coupled surface effects of thermal Casimir force and squeeze film damping (SFD) on size-dependent electromechanical stability and bifurcation of torsion micromirror actuator. The governing equations of micromirror system are derived, and the pull-in voltage and critical tilting angle are obtained. Also, the twisting deformation of torsion nanobeam can be tuned by functionally graded carbon nanotubes reinforced composites (FG-CNTRC). A finite element analysis (FEA) model is established on the COMSOL Multiphysics platform, and the simulation of the effect of thermal Casimir force on pull-in instability is utilized to verify the present analytical model. The results indicate that the numerical results well agree with the theoretical results in this work and experimental data in the literature. Further, the influences of volume fraction and geometrical distribution of CNTs, thermal Casimir force, nonlocal parameter, and squeeze film damping on electrically actuated instability and free-standing behavior are detailedly discussed. Besides, the evolution of equilibrium states of micromirror system is investigated, and bifurcation diagrams and phase portraits including the periodic, homoclinic, and heteroclinic orbits are described as well. The results demonstrated that the amplitude of the tilting angle for FGX-CNTRC type micromirror attenuates slower than for FGO-CNTRC type, and the increment of CNTs volume ratio slows down the attenuation due to the stiffening effect. When considering squeeze film damping, the stable center point evolves into one focus point with homoclinic orbits, and the dynamic system maintains two unstable saddle points with the heteroclinic orbits due to the effect of thermal Casimir force.

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Circularly‐polarised end‐fire antenna and arrays for 5G millimetre‐wave beam‐steering systems

IET Microwaves Antennas & Propagation ◽

10.1049/iet-map.2019.1119 ◽

2020 ◽

Vol 14 (9) ◽

pp. 980-987 ◽

Cited By ~ 1

Author(s):

Khaled Al‐Amoodi ◽

Mohammad Mahdi Honari ◽

Rashid Mirzavand ◽

Jordan Melzer ◽

Duncan G. Elliott ◽

...

Keyword(s):

Wave Beam ◽

Beam Steering ◽

Millimetre Wave

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Phase portraits of dystrophic and nondystrophic mouse muscle-fiber action potentials

American Journal of Physiology-Legacy Content ◽

10.1152/ajplegacy.1965.208.4.724 ◽

1965 ◽

Vol 208 (4) ◽

pp. 724-731 ◽

Cited By ~ 5

Author(s):

Titus C. Evans ◽

Byron A. Schottelius

Keyword(s):

Muscle Fiber ◽

Action Potentials ◽

Sodium Ion ◽

Phase Portraits ◽

Dystrophic Muscle ◽

General Increase ◽

Ion Conductance ◽

Mouse Muscle ◽

Intracellular Action ◽

Fiber Action

Intracellular action potentials from normal, control nondystrophic and dystrophic mouse soleus muscle fibers were recorded in both voltage-time and phase-portrait plots. Flattening of a normally curved portion in certain dystrophic muscle-fiber phase portraits suggested a greater than usual secondary entry of sodium ions after the peak of the action potential. Low-chloride studies excluded an abnormal chloride current as the cause of the flattening. It appears that inactivation of sodium ion conductance may be delayed or reduced, or both, in certain fibers of mice with hereditary muscular dystrophy. This is consistent with a general increase in membrane permeability. No definite negative afterpotential was noted in most mouse muscle-fiber action potentials.

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