Experimental and Theoretical Investigation of the Nonlinear Dynamics of an Electrostatically-Actuated Device

2008 ◽  
Author(s):  
Fadi M. Alsaleem ◽  
Mohammad I. Younis ◽  
Hassen M. Ouakad
Keyword(s):  
Nonlinear Dynamics ◽  
Experimental Data ◽  
Natural Frequency ◽  
Primary Resonance ◽  
Resonance Excitation ◽  
Squeeze Film ◽  
Nonlinear Phenomena ◽  
Harmonic Load ◽  
Mems Devices ◽  
Electrostatically Actuated

We present modeling, analysis, and experimental investigation for dynamic instabilities and bifurcations in electrostatically actuated resonators. These instabilities are induced by exciting a microstructure with a nonlinear forcing composed of a DC parallel-plate electrostatic load superimposed to an AC harmonic load. Because of the dominant effect of the electrostatic nonlinearity, several resonances and nonlinear phenomena are induced. Examples of these are the excitation of secondary-resonances, superharmonic and subharmonic, at half and twice the natural frequency of the microstructure. Also, local bifurcations, such as saddle-node and pitchfork, and global bifurcations, such as the escape phenomenon and the homoclinic tangling may occur. These lead to undesirable jumps, hysteresis, and dynamic pull-in instabilities in MEMS devices and structures. The present work represents an attempt to explore these topics in more depth. The first part of this paper is focused on analyzing and studying the nonlinear dynamics of a capacitive device both theoretically and experimentally with a focus on the case of primary-resonance excitation (near the fundamental natural frequency of the structure). The device is made up of two cantilever beams with a proof mass attached to their tips. A nonlinear spring-mass-damper model is utilized, which accounts for squeeze-film damping. Long-time integration for the equation of motion is used to compare with the obtained experimental data. Then, global dynamic analysis is conducted using a finite difference method (primary resonance) and shooting method (subharmonic resonance) combined with the Floquet theory to capture periodic orbits and analyze their stability. The domains of attraction (basins of attraction) for selected data are calculated numerically. Experimental data revealing primary and sub-harmonic resonances, dynamic pull-in, and the escape-from-a-potential-well phenomenon are shown and compared with the theoretical results.

Nonlinear Dynamics of Electrically-Actuated Carbon Nanotube Resonator

2008 ◽  
Author(s):  
Hassen M. Ouakad ◽  
Mohammad I. Younis
Keyword(s):  
Nonlinear Dynamics ◽  
Carbon Nanotube ◽  
Natural Frequency ◽  
Primary Resonance ◽  
Beam Model ◽  
Harmonic Load ◽  
Shooting Technique ◽  
The Galerkin Method ◽  
Euler Bernoulli Beam ◽  
Bernoulli Beam Model

This paper presents an investigation into the nonlinear dynamics of a carbon nanotube (CNT) actuated electrically by a DC force and an AC harmonic load. The CNT is described by an Euler Bernoulli beam model that accounts for the system nonlinearities due to mid-plane stretching and electrostatic forcing. A reduced-order model based on the Galerkin method is developed and utilized to simulate the static and dynamic response of the CNT. The static deflection of the CNT and its pull-in voltage are calculated and validated by comparing them to published results. It was found that mid-plane stretching has a major impact on the pull-in prediction of CNT. Dynamic analysis is conducted to explore the nonlinear oscillation of the CNT near its fundamental natural frequency (primary resonance) and near one half, twice, and three times its natural frequency (secondary resonances). The nonlinear analysis is carried out using a shooting technique combined with the Floquet theory to capture periodic orbits and analyze their stability. The results show that these resonances can lead to complex nonlinear dynamics phenomena such as hysteresis, dynamic pull-in, hardening and softening behaviors, and frequencies bands with an inevitable escape from a potential well.

An Experimental and Theoretical Investigation of Dynamic Pull-In in MEMS Devices Actuated Electrostatically

2009 ◽  
Author(s):  
Fadi M. Alsaleem ◽  
Mohammad I. Younis
Keyword(s):  
Natural Frequency ◽  
Escape Behavior ◽  
Experimental Testing ◽  
Stable State ◽  
Primary Resonance ◽  
Excitation Amplitude ◽  
Lumped Parameter Model ◽  
Mems Devices ◽  
Electrostatically Actuated ◽  
Capacitive Accelerometer

In this work, we investigate dynamic pull-in in MEMS devices actuated with a DC voltage superimposed to an AC harmonic voltage. We focus on the role of the AC frequency and amplitude in triggering instabilities. Dynamic pull-in is treated here in the context of a broader concept in nonlinear dynamics, which is the escape-from-potential-well phenomenon. The escape is defined where, for specific AC frequency and amplitude, the system exhibits the pull-in instability. We investigate dynamic pull-in experimentally in a polysilicon microcantilever beam, a cantilever and clamped-clamped microbeams made of gold, and a capacitive accelerometer. It is found experimentally that, despite the differences in their structures, the tested devices exhibit similar escape behavior near their fundamental natural frequency (primary resonance). A series of experiments are conducted using the capacitive accelerometer to study the effect of pressure (damping), excitation amplitude and frequency, resonance type (primary and subharmonic at twice the device’s natural frequency), and sweeping type (sweeping the AC amplitude or sweeping the AC frequency) on the escape zones. It is found that, except for the sweeping type, these factors have significant effect on shaping the escape zones. A nonlinear lumped-parameter model is used to capture the dynamics of the capacitive accelerometer. A shooting method is utilized to predict the theoretical zones of inevitable escape, where it is impossible for a resonator to oscillate in a stable state. An attempt has been made to relate the inevitable escape bands to the pull-in bands measured experimentally. We found that both pull-in bands and inevitable escape bands are correlated. However, we concluded that experimental testing is still needed to estimate accurately the instability bounds of each electrostatically actuated resonator.

Exploration of New Concepts for Mass Detection in Electrostatically-Actuated Structures Based on Nonlinear Phenomena

2009 ◽  
Vol 4 (2) ◽  
Author(s):  
Mohammad I. Younis ◽  
Fadi Alsaleem
Keyword(s):  
Natural Frequency ◽  
Equations Of Motion ◽  
Primary Resonance ◽  
Electrical Signal ◽  
Nonlinear Phenomena ◽  
Harmonic Load ◽  
Mass Sensor ◽  
Mass Detection ◽  
Mass Sensing ◽  
Fundamental Natural Frequency

This study presents an effort to explore the exploitation of dynamic instabilities and bifurcations in micro-electro-mechanical systems to realize novel methods and functionalities for mass sensing and detection. These instabilities are induced by exciting a microstructure with a nonlinear forcing composed of a dc parallel-plate electrostatic load and an ac harmonic load. The frequency of the ac load is tuned to be near the fundamental natural frequency of the structure (primary resonance) or its multiples (subharmonic resonance). For each excitation method, local bifurcations, such as saddle-node and pitchfork, and global bifurcations, such as the escape phenomenon, may occur. This work aims to explore the utilization of these bifurcations to design novel mass sensors and switches of improved characteristics. One explored concept of a device is a switch triggered by mass threshold. The basic idea of this device is based on the phenomenon of escape from a potential well. This device has the potential of serving as a smart switch that combines the functions of two devices: a sensitive gas/mass sensor and an electromechanical switch. The switch can send a strong electrical signal as a sign of mass detection, which can be used to actuate an alarming system or to activate a defensive or a security system. A second type of explored devices is a mass sensor of amplified response. The basic principle of this device is based on the jump phenomena encountered in pitchfork bifurcations during mass detection. This leads to an amplified response of the excited structure making the sensor more sensitive and its signal easier to be measured. As case studies, these device concepts are first demonstrated by simulations on clamped-clamped and cantilever microbeams. Results are presented using long-time integration for the equations of motion of a reduced-order model. An experimental case study of a capacitive sensor is presented illustrating the proposed concepts. It is concluded that exciting a microstructure at twice its fundamental natural frequency produces the most promising results for mass sensing and detection.

The Static and Dynamic Behavior of MEMS Arches Under Electrostatic Actuation

2009 ◽  
Author(s):  
Hassen M. Ouakad ◽  
Mohammad I. Younis ◽  
Fadi M. Alsaleem ◽  
Ronald Miles ◽  
Weili Cui
Keyword(s):  
Multiple Scales ◽  
Perturbation Technique ◽  
Dynamical Behavior ◽  
Primary Resonance ◽  
Reduced Order Model ◽  
Harmonic Load ◽  
Order Model ◽  
Reduced Order ◽  
Electrostatically Actuated ◽  
Model Equations

In this paper, we investigate theoretically and experimentally the static and dynamic behaviors of electrostatically actuated clamped-clamped micromachined arches when excited by a DC load superimposed to an AC harmonic load. A Galerkin based reduced-order model is used to discretize the distributed-parameter model of the considered shallow arch. The natural frequencies of the arch are calculated for various values of DC voltages and initial rises of the arch. The forced vibration response of the arch to a combined DC and AC harmonic load is determined when excited near its fundamental natural frequency. For small DC and AC loads, a perturbation technique (the method of multiple scales) is also used. For large DC and AC, the reduced-order model equations are integrated numerically with time to get the arch dynamic response. The results show various nonlinear scenarios of transitions to snap-through and dynamic pull-in. The effect of rise is shown to have significant effect on the dynamical behavior of the MEMS arch. Experimental work is conducted to test polysilicon curved microbeam when excited by DC and AC loads. Experimental results on primary resonance and dynamic pull-in are shown and compared with the theoretical results.

scholarly journals On the Application of the Multiple Scales Method on Electrostatically Actuated Resonators

2019 ◽  
Vol 14 (4) ◽  
Author(s):  
Saad Ilyas ◽  
Feras K. Alfosail ◽  
Mohammad I. Younis
Keyword(s):  
Analytical Solution ◽  
Multiple Scales ◽  
Excitation Frequency ◽  
Primary Resonance ◽  
Equation Of Motion ◽  
Higher Order ◽  
Resonance Excitation ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Electrostatically Actuated

We investigate modeling the dynamics of an electrostatically actuated resonator using the perturbation method of multiple time scales (MTS). First, we discuss two approaches to treat the nonlinear parallel-plate electrostatic force in the equation of motion and their impact on the application of MTS: expanding the force in Taylor series and multiplying both sides of the equation with the denominator of the forcing term. Considering a spring–mass–damper system excited electrostatically near primary resonance, it is concluded that, with consistent truncation of higher-order terms, both techniques yield same modulation equations. Then, we consider the problem of an electrostatically actuated resonator under simultaneous superharmonic and primary resonance excitation and derive a comprehensive analytical solution using MTS. The results of the analytical solution are compared against the numerical results obtained by long-time integration of the equation of motion. It is demonstrated that along with the direct excitation components at the excitation frequency and twice of that, higher-order parametric terms should also be included. Finally, the contributions of primary and superharmonic resonance toward the overall response of the resonator are examined.

A study of the nonlinear primary resonances of a micro-system under electrostatic and piezoelectric excitations

2014 ◽  
Vol 229 (10) ◽  
pp. 1904-1917 ◽  
Author(s):  
Ali K Hoshiar ◽  
Hamed Raeisifard
Keyword(s):  
Multiple Scales ◽  
Primary Resonance ◽  
Nonlinear Behavior ◽  
Nonlinear Effects ◽  
Resonance Excitation ◽  
Smart Device ◽  
Perturbation Approach ◽  
Softening Effect ◽  
Electrostatically Actuated ◽  
The Galerkin Method

In this article, a nonlinear analysis for a micro-system under electrostatic and piezoelectric excitations is presented. The micro-system beam is assumed as an elastic Euler-Bernoulli beam with clamped-free end conditions. The dynamic equations of this model have been derived by using the Hamilton method and considering the nonlinear inertia, curvature, piezoelectric and electrostatic terms. The static and dynamic solutions have been achieved by using the Galerkin method and the multiple-scales perturbation approach, respectively. The results are compared with numerical and other existing experimental results. By studying the primary resonance excitation, the effects of different parameters such as geometry, material, and excitations voltage on the system’s softening and hardening behaviors are evaluated. In an electrostatically actuated micro-system, it was showed that the nonlinear behavior occurs in frequency response as softening effect. In this paper, it is demonstrated that by applying a suitable piezoelectric DC voltage, this nonlinear effects can be controlled and altered to a linear domain. This model can be used to design a nano- or micro-scale smart device.

scholarly journals Nonlinear dynamics of a functionally graded piezoelectric micro-resonator in the vicinity of the primary resonance

2016 ◽  
Vol 23 (3) ◽  
pp. 400-413 ◽  
Author(s):  
Meysam T Chorsi ◽  
Saber Azizi ◽  
Firooz Bakhtiari-Nejad
Keyword(s):  
Nonlinear Dynamics ◽  
Shooting Method ◽  
Primary Resonance ◽  
Basins Of Attraction ◽  
Functionally Graded ◽  
Power Law Distribution ◽  
Electrostatically Actuated ◽  
Micro Resonator ◽  
Functionally Graded Piezoelectric ◽  
Damped Systems

This research is on the nonlinear dynamics of a two-sided electrostatically actuated capacitive micro-beam. The micro-resonator is composed of silicon and PZT as a piezoelectric material. PZT is functionally distributed along the height of the micro-beam according to the power law distribution. The micro-resonator is simultaneously subjected to DC piezoelectric and two-sided electrostatic actuations. The DC piezoelectric actuation leads to the generation of an axial force along the length of the micro-beam and this is used as a tuning tool to shift the primary resonance of the micro-resonator. The governing equation of the motion is derived by the minimization of the Hamiltonian and generalized to the viscously damped systems. The periodic solutions in the vicinity of the primary resonance are detected by means of the shooting method and their stability is investigated by determining the so-called Floquet exponents of the perturbed motions. The basins of attraction corresponding to three individual periodic orbits are determined. The results depict that the higher the amplitude of the periodic orbit, the smaller is the area of the attractor.

A Novel Expression for the Effective Viscosity to Model Squeeze-Film Damping at Low Pressure

2013 ◽  
Vol 390 ◽  
pp. 76-80 ◽  
Author(s):  
Maria F. Pantano ◽  
Salvatore Nigro ◽  
Franco Furgiuele ◽  
Leonardo Pagnotta
Keyword(s):  
Experimental Data ◽  
Effective Viscosity ◽  
Squeeze Film ◽  
Navier Stokes ◽  
Fluid Viscosity ◽  
The Novel ◽  
Mems Devices ◽  
Navier Stokes Equation ◽  
Experimental Procedure ◽  
Squeeze Film Damping

The Navier-Stokes equation is currentlyconsidered for modelling of squeeze-film damping in MEMS devices, also when the fluid flow associated to it is rarefied.In order to include rarefaction effects in such equation, a common approach consists of replacing the ordinary fluid viscosity with a scaled quantity, known as effective viscosity.The literature offers different expressions for the effective viscosity as a function of the Knudsen number (Kn). Such expressions were shown to work well whenKn<1, but theyresulted to be lessaccurate in case ofKn>1. In this paper a new expression is proposed to evaluate the effective viscosity for 1<Kn<40with increased reliability. Such anexpression was derivedfrom an optimized numerical-experimental procedure,developed in MATLAB® environment, using a finite element code and experimental data extracted from the literature. A comparison is finally reported and discussed between the results, in terms of damping coefficient, obtained considering previously reported effective viscosity expressions and the novel one,with reference to different squeeze film damping layouts, for which experimental data are already available.

Nonlinear Dynamics of Electrically Actuated Carbon Nanotube Resonators

2009 ◽  
Vol 5 (1) ◽  
Author(s):  
Hassen M. Ouakad ◽  
Mohammad I. Younis
Keyword(s):  
Nonlinear Dynamics ◽  
Carbon Nanotube ◽  
Natural Frequency ◽  
Reduced Order Model ◽  
Plane Boundary ◽  
Beam Model ◽  
Harmonic Load ◽  
Order Model ◽  
Reduced Order ◽  
Wide Range

This work presents an investigation of the nonlinear dynamics of carbon nanotubes (CNTs) when actuated by a dc load superimposed to an ac harmonic load. Cantilevered and clamped-clamped CNTs are studied. The carbon nanotube is described by an Euler–Bernoulli beam model that accounts for the geometric nonlinearity and the nonlinear electrostatic force. A reduced-order model based on the Galerkin method is developed and utilized to simulate the static and dynamic responses of the carbon nanotube. The free-vibration problem is solved using both the reduced-order model and by solving directly the coupled in-plane and out-of-plane boundary-value problems governing the motion of the nanotube. Comparison of the results generated by these two methods to published data of a more complicated molecular dynamics model shows good agreement. Dynamic analysis is conducted to explore the nonlinear oscillation of the carbon nanotube near its fundamental natural frequency (primary-resonance) and near one-half, twice, and three times its natural frequency (secondary-resonances). The nonlinear analysis is carried out using a shooting technique to capture periodic orbits combined with the Floquet theory to analyze their stability. The nonlinear resonance frequency of the CNTs is calculated as a function of the ac load. Subharmonic-resonances are found to be activated over a wide range of frequencies, which is a unique property of CNTs. The results show that these resonances can lead to complex nonlinear dynamics phenomena, such as hysteresis, dynamic pull-in, hardening and softening behaviors, and frequency bands with an inevitable escape from a potential well.

An Experimental and Theoretical Investigation of Double Resonance Activation in Electrostatic MEMS Resonators

2018 ◽  
Author(s):  
Mohammad H. Hasan ◽  
Hassen M. Ouakad ◽  
Nizar R. Jaber ◽  
Md Abdullah Al Hafiz ◽  
Fadi Alsaleem ◽  
...  
Keyword(s):  
Experimental Data ◽  
Double Resonance ◽  
Input Voltage ◽  
Micro Electro Mechanical System ◽  
Resonance Excitation ◽  
Beam Model ◽  
Mems Devices ◽  
Theoretical Simulation ◽  
Mems Resonators ◽  
Electrical Resonance

Electrostatic micro-electro-mechanical-system (MEMS) devices show great potential in a variety of applications such as sensing and actuation; however, they are hindered by their high input voltage requirement. Double resonance excitation, which activates the system’s mechanical and electrical resonances simultaneously, was recently demonstrated experimentally to alleviate this problem. In this work, we present a mathematical model, based on the Euler Bernoulli beam model coupled with a circuit model, to simulate double resonance in MEMS devices and to shed light more onto the previously published experimental data. We show good agreement between the theoretical simulation and experimental data when the electrical resonance frequency band is sufficiently high.

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