Chaotic Contact Dynamics of Two Microbeams under Various Kinematic Hypotheses

V. A. Krysko, J. Awrejcewicz, I. V. Papkova, O. A. Saltykova, A. V. Krysko

Research output: Contribution to journalArticle

Abstract

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 x0.2 x \approx 0.2 and x0.8 x \approx 0.8 instead of the beams central points.

Original languageEnglish
JournalInternational Journal of Nonlinear Sciences and Numerical Simulation
DOIs
Publication statusPublished - 1 Jan 2019

Fingerprint

Dynamic Contact
microbeams
Kinematics
kinematics
Contact
Wavelets
electric contacts
Interaction
Euler Function
Finite difference method
Ordinary differential equations
Fourier Spectrum
Geometric Nonlinearity
Second-order Approximation
Partial differential equations
Kinematic Model
Approximation Order
Phase Portrait
Time series
Synchronization

Keywords

  • beam
  • chaos
  • contact interaction
  • dynamics
  • finite difference method

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Computational Mechanics
  • Modelling and Simulation
  • Engineering (miscellaneous)
  • Mechanics of Materials
  • Physics and Astronomy(all)
  • Applied Mathematics

Cite this

Chaotic Contact Dynamics of Two Microbeams under Various Kinematic Hypotheses. / Krysko, V. A.; Awrejcewicz, J.; Papkova, I. V.; Saltykova, O. A.; Krysko, A. V.

In: International Journal of Nonlinear Sciences and Numerical Simulation, 01.01.2019.

Research output: Contribution to journalArticle

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