An effective analytical approach to nonlinear free vibration of elastically actuated microtubes
- PDF / 772,244 Bytes
- 11 Pages / 547.087 x 737.008 pts Page_size
- 26 Downloads / 213 Views
(0123456789().,-volV) (0123456789().,-volV)
MODELLING AND ANALYSIS OF MECHANICAL SYSTEMS DYNAMICS
An effective analytical approach to nonlinear free vibration of elastically actuated microtubes Nicolae Herisanu
. Vasile Marinca
Received: 1 March 2020 / Accepted: 20 August 2020 Ó Springer Nature B.V. 2020
Abstract Based on Hamiltonian principle and a modified couple stress theory, a nonlinear differential equation of motion of electrostatically actuated microbeams is presented. The method of Galerkin– Bubnov decomposition is employed to convert the established system into reduced discrete modal equation. The analytical approximate solution to nonlinear free vibration is obtained by means of the optimal auxiliary functions method. The influence of internal material length scale parameter and outer diameter on the dynamic behavior is considered. The proposed procedure is effective, convenient and does not require linearization or small parameters assumption. The main advantage of this technique consists in that it provides a convenient way to control the convergence of the approximate solution in a very rigorous way. Keywords Optimal auxiliary functions method Elastically actuated microtube Nonlinear differential equation Optimal convergence-control parameters
N. Herisanu (&) Politehnica University of Timisoara, Timisoara, Romania e-mail: [email protected] N. Herisanu V. Marinca Centre for Advanced Technical Research, Romanian Academy, Timisoara, Romania e-mail: [email protected]
1 Introduction In the last years microtubes received an increased importance in a large variety of applications related to capacitive switches, signal filtering, semiconductor technology or resonant sensors. Electrically actuated microtubes are studied by the MEMS community and there are many potential applications in optical, aerospace and biomedical engineering. There are known several actuation methods for MEMS devices, but electrostatic actuation is the most well established actuation method because of its simplicity and high efficiency. Younis and Nayfeh [1] presented the response of resonant nanobeams to an electric actuation. They used a nonlinear model to account for the mid-plane stretching, a DC electrostatic force and an AC harmonic force including in the model design parameters by lumping them into nondimensional parameters. The influence of Casimir force on the nonlinear behavior of nanoscale electrostatic actuators is studied by Lin and Zhao [2]. Stability analysis showed that one equilibrium point is Hopf point and the other is unstable saddle point when there are two equilibrium points. Nayfeh et al. [3] studied the pull-in instability in MEMS resonators and find that characteristics of the pull-in phenomenon in the presence of AC loads differ from these under purely DC loads. The frequency or the amplitude of the AC loading can be adjusted to reduce the driving voltage and switching time. Chao
123
Meccanica
et al. [4] discussed the prediction of the DC dynamic pull-in voltages of a double clamped
Data Loading...
