Non-linear modes of vibration of Timoshenko nanobeams under electrostatic actuation

• Type: Article in International Scientific Journal
• Date: 2017

Authors

Alves, M (Author) Other; Pedro Leal Ribeiro (Author) FEUP

Journal

Title: International Journal of Mechanical Sciences

Vol. 130

Pages: 188-202

ISSN: 0020-7403

Publisher: Elsevier

Indexing

ISI Web of Knowledge - 4 Citations

Other information

Authenticus ID: P-00N-289

DOI: 10.1016/j.ijmecsci.2017.06.003

Abstract (EN): The non-linear dynamical behaviour of electrostatically actuated nanobeams of rectangular cross section is investigated using a p-version finite element derived by Galerkin's method, where the partial differential equations of motion are reduced into a finite dimensional system of non-linear ordinary differential equations in the time domain. Timoshenko's beam theory is applied, as well as the beam analogue of von Karman's plate theory in order to take into account the geometrical non-linearity. The formulation considers non-local effects which affect the inertia of the system, the non-linear stiffness terms and the electrostatic force. Considering several harmonics for the periodic solution, the harmonic balance method is used to transform the ordinary differential equations into algebraic equations of motion in the frequency domain, which are then solved by an arc-length continuation method. Convergence studies show that accurate results are achieved with a reasonably low number of degrees of freedom, and the different terms related to the effects considered in the proposed model are validated with results published in the literature. The importance of the shear deformation and the rotary inertia in this problem is investigated, as well as the influence on the dynamic response of the electrostatic force, fringing fields and non-local effects, combined with the geometrical non-linearity. It is found that different combinations of these effects lead to different outcomes in the system dynamics, changing the natural frequencies and, to a smaller extent, the mode shapes, and leading to hardening, softening or even the combination of both. Furthermore, non-linear phenomena such as internal resonances and bifurcations are studied.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 15