Analysis of non-linear vibrations of a microresonator under piezoelectric and electrostatic actuations

Abstract

In this article, the non-linear vibrations of a piezoelectrically actuated microresonator is studied. The microresonator is assumed as a clamped—clamped Bernouli—Euler microbeam. In contrast to previous researches in which the piezoelectric layer has been deposited on the integral length of the microbeam, here it is assumed that the piezoelectric layer is deposited on a part of microbeam length with equal distance from two ends. The microbeam is actuated by an AC voltage between upper and lower sides of the piezoelectric layer. Also, an electrostatic actuation is applied between the microbeam and an electrode plate, for the first time. The non-linear equation of motion has been derived by using the Hamilton principle by stretching the neutral axis assumption. The obtained equations are solved using the Galerkin, Rayleigh—Ritz, and multiple scale perturbation methods. It is shown that the sensitivity and natural frequency of the piezoelectrically actuated microresonator may be altered and controlled conveniently by applying an electrostatic actuation to the microresonator. Also, it has been shown that the system shows softening or hardening behaviour depending on the value of piezoelectric actuation, electrostatic actuation, axial load, thickness, length, and elasticity module of piezoelectric layer; thickness of microbeam; and its distance from the electrode plate. It is shown that non-linear behaviour of the piezoelectrically actuated microbeam may be changed to a linear behaviour by applying a suitable electrostatic actuation to the microbeam.

Vibration Analysis and Stability Analysis of Double-Walled Carbon Nanotubes Subjected to Electrostatics Actuation

“…The total deflection of the DWCNTs is composed of a static part, w sn (x, t), and a dynamic part, y n (x, t), where n = 1, 2. (10)(11)(12)14,15) The static and dynamic solutions are determined by the DC and AC voltages, respectively. To find the dynamic part, the AC and DC voltage components (V = V dc + V ac cos(Ωt)) must be entered into Eqs.…”

“…Similar studies were conducted on microbeams. (10)(11)(12) Hawwa and Al-Qahtani (13) simplified the electric forces acting on a DWCNTs under harmonic electric force with a harmonic force acting on only the outer tube. In this study, forced vibrations of clamped-clamped DWCNTs under axial force and AC-DC complex electrostatic actuations are investigated using nonlinear Euler-Bernoulli beam theory.…”

Analysis of Dynamic Behaviour of a Tensioned Carbon Nanotube in Thermal and Pressurized Environments

“…The impacts of piezoelectric and electrostatic actuators on the vibration characteristics of carbon nanotube were examined by Quakad and Younis [21]. and Zamanian et al [22]. In some further studies, Abdel-Rahman and Nayfeh [23], Hawwa and Al-Qahtani [24], Hajnayeb and Khaden [25] and Belhadj et al [26] presented different works on the vibration and instability of DWCNTs under the influence of electrostatic actuations.…”

Nonlinear vibrations of single- and double-walled carbon nanotubes resting on two-parameter foundation in a magneto-thermal environment

“…Few years later, Ouakad and Younis [21] investigated the nonlinear vibration of electrically actuated carbon nanotube resonators. In an earlier work, Zamanian et al [22] presented the non-linear vibrations analysis of a microresonator subjected to piezoelectric and electrostatic actuations. As a continuation of the tremendous work, Abdel-Rahman, Hawwa, Hajnayeb, and Belhadj [23][24][25][26] performed a vibration and instability studies of DWCNT using a nonlinear model and considering an electrostatic actuation as an external excitation agent.…”