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Size effects on stability and bifurcation of nonlinear viscoelastic microcantilevers based on strain gradient

Taheran, F ; Sharif University of Technology | 2022

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  1. Type of Document: Article
  2. DOI: 10.1007/s40430-021-03316-7
  3. Publisher: Springer Science and Business Media Deutschland GmbH , 2022
  4. Abstract:
  5. Analytical frequency analysis of a nonlinear viscoelastic microcantilever is performed based on strain gradient theory. The Kelvin–Voigt scheme is utilized to model the viscoelasticity effect. Due to the microcantilever shortening effect via Euler–Bernoulli inextensibility condition, geometric, inertia, stiffness, and inherent damping nonlinearities are considered. The equation of motion is derived from Hamilton’s principle, and discretized using Galerkin method. The multiple timescale perturbation method is performed to solve the time response equation. Implying steady-state condition, the nonlinear relation between detuning parameter and amplitude of the vibration of a nonlinear viscoelastic microcantilever in the framework of the strain gradient theory is developed, and stability and bifurcation criteria near primary resonance is analytically evaluated. Results show that the damping nonlinearities cause the microcantilever to be softer while size effects via geometric and inertia nonlinearities have the opposite effect. It is also found that utilizing strain gradient theory has a considerable effect on natural frequency, stability criteria, the amplitude of oscillation, force, and frequency bandwidth, in comparison with classical and modified coupled stress theory, especially when the ratio of beam thickness to length scale parameter reduces. © 2021, The Author(s), under exclusive licence to The Brazilian Society of Mechanical Sciences and Engineering
  6. Keywords:
  7. Microcantilever ; Nonlinear vibration ; Stability and bifurcation ; Strain gradient theory ; Bifurcation (mathematics) ; Control nonlinearities ; Damping ; Equations of motion ; Galerkin methods ; Stability criteria ; Vibration analysis ; Viscoelasticity ; Analytical frequencies ; Frequency Analysis ; Micro-cantilevers ; Non-linear vibrations ; Nonlinear visco-elastic ; Sizes effect ; Strain gradients ; Viscoelastic damping ; Perturbation techniques
  8. Source: Journal of the Brazilian Society of Mechanical Sciences and Engineering ; Volume 44, Issue 1 , 2022 ; 16785878 (ISSN)
  9. URL: https://link.springer.com/article/10.1007/s40430-021-03316-7