Dynamics of Microbeams under Multi-Frequency Excitations

Micro functionally graded material (FGM) structures are able to have proper functions in vast environments. In this paper, nonlinear governing equations of the size-dependent micro-switch are derived using modified couple stress theory. Effective external forces including fringing field of electrostatic force and Casimir force are considered. Two electrodes cooperate to track the in-plane motions of the micro continuous system by tuning the supply voltages of the electrostatic force. An adaptive projection law is proposed to compensate for the effect of error in the initial estimates of system parameters. To achieve more reliability, a robust active vibration strategy is presented to withstand external disturbances. At any time, just one electrode is operational, and optimization is performed to decrease the controller gains. The highly nonlinear inputs have a singularity in the dynamics of the system, which are known as pull-in instability, so for safety, the controller gains are chosen such that the pull-in voltage is avoided. The dynamic response of the system is simulated using a single mode or multiple modes to validate the effectiveness of the presented vibration control approaches. The effects of error of the initial estimate of system parameters, the effect of impulse and the influences of various volume fractions are studied.

show abstract

“…Ebrahim et al [ 50 ] found the maximum amplitude of a clamped-clamped micro-beam of

length. The applied voltage is

, in which

is the oscillation frequency.…”

Section: Simulations and Discussionmentioning

confidence: 99%

“… Comparison of the results of numerical simulations in this paper with the experimental results [ 50 ]. …”

Section: Figurementioning

confidence: 99%

Nonlinear Robust Adaptive Multi-Modal Vibration Control of Bi-Electrode Micro-Switch with Constraints on the Input

et al. 2017

View full text Add to dashboard Cite

show abstract

“…However, the difficulty lies in matching vibration frequencies to the harvester's resonance frequency, and the sensing range is limited in low bandwidth. As a potential solution, researchers have explored the use of nonlinear mechanical resonators to expand the power bandwidth and sensing range [22,23]. More specifically, for wireless ME antennas [24,25], enhancing data transmission speed involves utilizing a nonlinear signal component to effectively separate information bandwidth and radiation from the antenna's limited bandwidth.…”

Section: Introductionmentioning

confidence: 99%

Modeling of Magnetoelectric Microresonator Using Numerical Method and Simulated Annealing Algorithm

Sadeghi,

Bazrafkan,

Rutner

et al. 2023

Micromachines

View full text Add to dashboard Cite

A comprehensive understanding of the linear/nonlinear dynamic behavior of wireless microresonators is essential for micro-electromechanical systems (MEMS) design optimization. This study investigates the dynamic behaviour of a magnetoelectric (ME) microresonator, using a finite element method (FEM) and machine learning algorithm. First, the linear/nonlinear behaviour of a fabricated thin-film ME microactuator is assessed in both the time domain and frequency spectrum. Next, a data driven system identification (DDSI) procedure and simulated annealing (SA) method are implemented to reconstruct differential equations from measured datasets. The Duffing equation is employed to replicate the dynamic behavior of the ME microactuator. The Duffing coefficients such as mass, stiffness, damping, force amplitude, and excitation frequency are considered as input parameters. Meanwhile, the microactuator displacement is taken as the output parameter, which is measured experimentally via a laser Doppler vibrometer (LDV) device. To determine the optimal range and step size for input parameters, the sensitivity analysis is conducted using Latin hypercube sampling (LHS). The peak index matching (PIM) and correlation coefficient (CC) are considered assessment criteria for the objective function. The data-driven developed models are subsequently employed to reconstruct/predict mode shapes and the vibration amplitude over the time domain. The effect of driving signal nonlinearity and total harmonic distortion (THD) is explored experimentally under resonance and sub-resonance conditions. The vibration measurements reveal that as excitation levels increase, hysteresis variations become more noticeable, which may result in a higher prediction error in the Duffing array model. The verification test indicates that the first bending mode reconstructs reasonably with a prediction accuracy of about 92 percent. This proof-of-concept study demonstrates that the simulated annealing approach is a promising tool for modeling the dynamic behavior of MEMS systems, making it a strong candidate for real-world applications.

show abstract

“…However, the multi-harmonic excitation in MEMS mixer-filters (Ramini et al, 2016) gives a positive effect in down-conversion and filtering frequencies from radio frequencies to intermediate frequency signals. Vibration of clamped-clamped microbeams in MEMS with periodic excitations are theoretically (Jaber et al, 2016a,b) and experimentally (Ibrahim et al, 2017) investigated. It is shown that there is a benefit of multi-frequency excitations in conversion of the signal in a wide frequency band.…”

Section: Introductionmentioning

confidence: 99%

Steady state vibration of the periodically forced and damped pure nonlinear two-degrees-of-freedom oscillator

Cvetićanin

Zukowic

Cveticanin³

2019

Journal of Theoretical and Applied Mechanics

View full text Add to dashboard Cite

In the paper, a pure nonlinear and damped two-mass oscillator excited with a periodical force is considered. The oscillator is modelled with a system of two coupled second order nonlinear and non-homogenous equations. Using the model, two problems are investigated: one, identification of the excitation force for the known vibrating response of the system, and the second, determination of vibrations of the system excited with the known periodical force. Using the steady-state motion of the nonlinear oscillator, a method for identification of the excitation force is developed. For the pure nonlinear oscillator, it is obtained that the forcing function has the form of the Ateb function. However, if the excitation force is known, the procedure for computing the steady-state vibration of the system is introduced. The solution corresponds to steady-state vibrations of the free oscillator, but the amplitude and phase are assumed to be time variable. The averaged solutions are obtained for the pure nonlinear oscillator with an additional linear elastic force and for the van der Pol oscillator. Analytically obtained solutions are compared with numerical ones. They are in good agreement.

show abstract

Dynamics of Microbeams under Multi-Frequency Excitations

Cited by 9 publications

References 25 publications

Nonlinear Robust Adaptive Multi-Modal Vibration Control of Bi-Electrode Micro-Switch with Constraints on the Input

Nonlinear Robust Adaptive Multi-Modal Vibration Control of Bi-Electrode Micro-Switch with Constraints on the Input

Modeling of Magnetoelectric Microresonator Using Numerical Method and Simulated Annealing Algorithm

Steady state vibration of the periodically forced and damped pure nonlinear two-degrees-of-freedom oscillator

Contact Info

Product

Resources

About