Nonlinear behaviour of different flexible size-dependent beams models based on the modified couple stress theory. Part 2. Chaotic dynamics of flexible beams |
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| Institution: | 1. Department of Applied Mathematics and Systems Analysis, Saratov State Technical University, 410054 Saratov, Russian Federation;2. Cybernetic Institute, National Research Tomsk Polytechnic University, 30 Lenin Avenue, 634050 Tomsk, Russian Federation;3. Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, 1/15 Stefanowskiego St., 90-924 Lodz, Poland;4. Department of Vehicles, Warsaw University of Technology, 84 Narbutta St., 02-524 Warszawa, Poland;5. Saratov State Technical University, Department of Mathematics and Modelling, 77 Politechnicheskaya Str., 410054 Saratov, Russian Federation;1. Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, 1/15 Stefanowski St., 90-924 Lodz, Poland;2. Department of Vehicles, Warsaw University of Technology, 84 Narbutta Str., 02-524 Warsaw, Poland;3. Cybernetic Institute, National Research Tomsk Polytechnic University, 30 Lenin Avenue, 634050 Tomsk, Russian Federation;4. Department of Applied Mathematics and Systems Analysis, Saratov State Technical University, 77 Politehnicheskaya Str., 410054 Saratov, Russian Federation;5. Department of Mathematics and Modeling, Saratov State Technical University, 77 Politehnicheskaya Str., 410054 Saratov, Russian Federation;1. Department of Solid Mechanic, Faculty of Mechanical Engineering, University of Kashan, Kashan 87317-51167, Iran;2. Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia;3. Department of Mathematics, Faculty of Science, Kafrelsheikh University, Kafrelsheikh 33516, Egypt;1. Lodz University of Technology, Department of Automation, Biomechanics and Mechatronics, 1/15 Stefanowskiego Str., 90-924 ?ód? and Warsaw University of Technology, Department of Vehicles, 84 Narbutta Str., 02-524 Warsaw, Poland;2. Saratov State Technical University, Department of Mathematics and Modelling, Politehnicheskaya 77, 410054 Saratov, Russian Federation |
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| Abstract: | In the present part of the paper various problems of non-linear dynamics of nano-beams within the modified couple stress theory as well as the Bernoulli-Euler, Timoshenko, and Sheremetev-Pelekh-Reddy-Levinson models are studied taking into account the geometric non-linearity. Different characteristics of the vibrational process, including Fourier spectra, wavelet spectra, phase portraits, Poincaré maps as well as the largest Lyapunov exponents, are studied for the same physical-geometric parameter with and without consideration of the size-dependent behaviour. Vibration graphs are constructed and analysed, and scenarios of transition from regular to chaotic vibrations are illustrated and discussed. |
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| Keywords: | Beam models Vibrations Chaos Nano-mechanics |
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