Analysis of nonlinear vibrations and stability of rotating asymmetrical nano-shafts incorporating surface energy effects
| Autor: | Maryam Ghodousi, Gholamhassan Payganeh, Majid Shahgholi |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Surface (mathematics)
Physics Van der Pol oscillator Steady state Surface stress General Physics and Astronomy Equations of motion 02 engineering and technology Mechanics 01 natural sciences Surface energy Nonlinear system 020303 mechanical engineering & transports 0203 mechanical engineering Mechanics of Materials 0103 physical sciences General Materials Science Homoclinic orbit 010301 acoustics |
| Zdroj: | Continuum Mechanics and Thermodynamics. 30:783-803 |
| ISSN: | 1432-0959 0935-1175 |
| DOI: | 10.1007/s00161-018-0640-z |
| Popis: | The objective of the present work is to investigate the nonlinear vibrations of the rotating asymmetrical nano-shafts by considering surface effect. In order to compute the surface stress tensor, the surface elasticity theory is used. The governing nonlinear equations of motion are obtained with the aid of variational approach. Bubnov–Galerkin is a very effective method for exploiting the reduced-order model of the equations of motion. The averaging method is employed to analyze the reduced-order model of the system. For this purpose, the well-known Van der Pol transformation in the complex form and angle-action transformation are utilized. The effect of surface stress on the forward and backward speeds, steady state responses of the system, fixed points, close orbits and stability of the solutions is examined. The preliminary results of the research show that the absolute values of forward and backward whirling speeds in the presence of surface effect with positive residual surface stress are higher than those of regarding the system without surface effect and in the presence of surface effect with negative residual surface stress. In addition, it is seen that the undamped rotating asymmetrical nano-shaft, for specified value of detuning parameter, in the absence or presence of surface effect has various number of stable and unstable periodic solutions. Besides, there is different number of separatrix (homoclinic orbit type). Furthermore, bifurcations, number of solutions and their stability for damped rotating asymmetrical nano-shaft are investigated. Also, the above results have been obtained for rotating symmetrical nano-shaft. |
| Databáze: | OpenAIRE |
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