Details

Autor(en) / Beteiligte

• da Costa Alves, Marco Alexandre

Titel

Vibration of Nanobeams Under Electrostatic Actuation

Ort / Verlag

ProQuest Dissertations & Theses

Erscheinungsjahr

2016

Link zum Volltext

• ProQuest

Quelle

ProQuest Dissertations & Theses A&I

Beschreibungen/Notizen

• Micro and nanobeam based devices (MEMS and NEMS) are employed in sensors, displays, portable power generation, localized drug delivery, and in all applications it is essential to understand their dynamic behaviour. The dynamics of these devices are inherently non-linear, due to the large displacements in comparison to the thickness and also to the non-linearity of the electrostatic force that is used to actuate them. The knowledge of the modes of vibration and the natural frequencies of nanobeams are essential to describe the dynamics of these systems, and to successfully implement them in the aforementioned applications.In this dissertation, the non-linear modes of vibration of electrostatically actuated nanobeams are investigated. A p-version finite element derived by Galerkin’s method is used to reduce the partial differential equations of motion into a finite dimensional system of non-linear ordinary differential equations in the time domain. The Timoshenko beam theory is applied, as well as the beam analogue of the von Karm´ an’s plate theory ´ in order to take into account the geometrical non-linearity. The formulation considers nonlocal effects which affects the inertia of the system as well as the non-linear stiffness terms and the electrostatic force. The harmonic balance method (HBM) 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. Several harmonics are used in the periodic solution considered in the HBM.The different terms related to the effects considered in the proposed model are validated with different numerical and experimental results published in the literature. The static deflection of electrostatically actuated nanobeams is determined using the Newton method. The influence of geometric properties and nonlocal effects in the static deformation is investigated. The influence in the dynamic response of the electrostatic force, fringing fields and nonlocal effects, combined with the geometrical non-linearity is investigated. One found that different combination of these effects lead to different outcomes in the system dynamics changing the natural frequencies, mode shapes, and leading to hardening, softening or even the combination of both effects. Non-linear phenomena such as internal resonances and bifurcation points, which may lead to secondary branches, are studied.An introduction to the Molecular Dynamic algorithm is presented, and this algorithm is used to calculate the natural frequencies of a carbon nanotube. The results are then compared to the ones derived with the developed continuum model in an attempt to establish a correct value for the nonlocal parameter of the nanotube analysed.