Chaotic Contact Dynamics of Two Microbeams under Various Kinematic Hypotheses
| Autor: | O. A. Saltykova, Irina V Papkova, Jan Awrejcewicz, V.A. Krysko, Anton V. Krysko |
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| Rok vydání: | 2019 |
| Předmět: |
Physics
Applied Mathematics Computational Mechanics Chaotic General Physics and Astronomy Statistical and Nonlinear Physics 02 engineering and technology Kinematics 021001 nanoscience & nanotechnology 020303 mechanical engineering & transports Classical mechanics 0203 mechanical engineering Mechanics of Materials Modeling and Simulation Contact dynamics 0210 nano-technology Engineering (miscellaneous) |
| Zdroj: | International Journal of Nonlinear Sciences and Numerical Simulation. 20:373-386 |
| ISSN: | 2191-0294 1565-1339 |
| Popis: | Different kinematic mathematical models of nonlinear dynamics of a contact interaction of two microbeams are derived and studied. Dynamics of one of the microbeams is governed by kinematic hypotheses of the first, second, and third approximation orders. The second beam is excited through a contact interaction with the first beam and is described by the kinematic hypothesis of the second-order approximation in both geometric linear and nonlinear frameworks. The derived nonlinear partial differential equations (PDEs) are transformed to the counterpart system of nonlinear ordinary differential equations (ODEs) by the finite difference method. Nonlinear contact interaction dynamics of the microbeam structure is analyzed with the help of time series (signals), Fourier spectra, and wavelet spectra based on various mother wavelets, Morlet wavelet spectra employed to study synchronization phenomena, Poincaré maps, phase portraits, and the Lyapunov exponents estimated with the Wolf, Kantz, and Rosenstein algorithms. We have illustrated that neglecting the shear function (Euler–Bernoulli model) yields erroneous numerical results. We have shown that the geometric nonlinearity cannot be neglected in the analysis even for small two-layer microbeam deflection. In addition, we have detected that the contact between two microbeams takes place in the vicinity of x ≈ 0.2 x \approx 0.2 and x ≈ 0.8 x \approx 0.8 instead of the beams central points. |
| Databáze: | OpenAIRE |
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