Microresonators Based on 1:2 Internal Resonance

2005 ◽  
Author(s):  
Ashwin Vyas ◽  
Anil K. Bajaj
Keyword(s):  
Internal Resonance ◽  
Unique Feature ◽  
Rf Mems ◽  
Primary Resonance ◽  
Mems Devices ◽  
Beam Structure ◽  
Electrostatically Actuated ◽  
Autoparametric Resonance ◽  
Second Mode ◽  
T Beam

A nonlinear autoparametric resonance based microresonator concept is explored in this study. The concept is illustrated by modelling an electrostatically actuated T-beam structure, with the first two modes of the structure in 1:2 internal resonance. The response of the system to primary resonance of the first and second mode is presented. When the second mode is resonantly actuated, the second mode in turn excites the first mode due to 1:2 internal resonance and the nonlinear coupling between the two modes. The structure therefore oscillates in first mode with half the frequency of excitation voltage. This is a unique feature of this microresonator, and as a result of this feature, the resonator can serve as a filter as well as a mixer in RF MEMS devices. When the first mode is excited, the structure oscillates in both the first and the second mode and thus has an output signal with frequency twice the input signal. The response also showed Hopf-bifurcations for higher actuation voltages.

Investigation of 3:1 Internal Resonance of Electrostatically Actuated Microbeams With Flexible Supports

2020 ◽  
Author(s):  
Praveen Kumar ◽  
Mandar M. Inamdar ◽  
Dnyanesh N. Pawaskar
Keyword(s):  
Internal Resonance ◽  
Multiple Scales ◽  
Time Integration ◽  
External Source ◽  
Mems Devices ◽  
Electrode Gap ◽  
Dynamical Equations ◽  
Electrostatically Actuated ◽  
Second Mode ◽  
Flexible Supports

Abstract Interaction between modes due to internal resonance has many applications in MEMS devices. In this paper, we investigate the modal interaction through 3 : 1 internal resonance of an electrostatically actuated microbeam with flexible supports in the form of rotational and transversal springs. The static displacement and the first three modal frequencies are obtained at the applied DC voltage by a reduced order model for a specified ratio of electrode gap and thickness. We then obtain the value of applied voltage for which 3 : 1 internal resonance exists for four different combinations of unequal end support stiffnesses. We calculate the coefficients of the coupled dynamical equations of first two modes for all the four cases and solve them by using numerical time integration and the method of multiple scales. We observe the interaction between the first and the second mode when each of the modes is independently excited by an external source. When the second mode is externally excited, interestingly, we also find that the undriven mode response amplitude is twice that of the driven mode.

scholarly journals Utilization of 2:1 Internal Resonance in Microsystems

Micromachines ◽  
2018 ◽  
Vol 9 (9) ◽  
pp. 448 ◽  
Author(s):  
Navid Noori ◽  
Atabak Sarrafan ◽  
Farid Golnaraghi ◽  
Behraad Bahreyni
Keyword(s):  
Internal Resonance ◽  
Mode Coupling ◽  
Equations Of Motion ◽  
Low Frequency ◽  
Nonlinear Behavior ◽  
Excitation Amplitude ◽  
Beam Structure ◽  
Nonlinear Mode Coupling ◽  
T Beam ◽  
Low Frequency Mode

In this paper, the nonlinear mode coupling at 2:1 internal resonance has been studied both analytically and experimentally. A modified micro T-beam structure is proposed, and the equations of motion are developed using Lagrange’s energy method. A two-variable expansion perturbation method is used to describe the nonlinear behavior of the system. It is shown that in a microresonator with 2:1 internal resonance, the low-frequency mode is autoparametrically excited after the excitation amplitude reaches a certain threshold. The effect of damping on the performance of the system is also investigated.

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.

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.

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.

Design of Electrostatic Micro Mirrors for Improved Stability Though Surface Contact

1998 ◽  
Author(s):  
Timothy Moulton ◽  
G. K. Ananthasuresh
Keyword(s):  
Design Method ◽  
Electrostatic Force ◽  
Electrostatic Actuation ◽  
Mems Devices ◽  
Complex Dynamic ◽  
Micro Electro Mechanical Systems ◽  
Electrostatically Actuated ◽  
Surface Contact ◽  
Improved Stability ◽  
Mems Process

Abstract There exists a need to stabilize the electrostatic actuation commonly used in Micro-Electro-Mechanical Systems (MEMS). Most electrostatically actuated MEMS devices act as variable capacitors with varying gap between the charged conductors. Electrostatic force in these devices is a nonlinear attractive force between the conductors resulting in a complex dynamic system. These systems are stable for only a small portion of the initial gap. In this paper a design method is presented for electrostatic micro-mirrors with improved stability. Controllable, stable electrostatic actuation can be achieved through surface contact between the two conductors. Once in contact with the surface, the compliance of the structure is used to stabilize the electrostatic actuation over a long range of motion. Beam based variable angle mirrors were designed and fabricated using the Multi-User MEMS Process at MCNC technology center. The design methods for stable electrostatic actuation were tested on these mirrors. Some characteristics are noted and their implementation into future designs is discussed.

MEMS-Enabled Smart Beam-Steering Antennas

2014 ◽  
pp. 183-203
Author(s):  
Hadi Mirzajani ◽  
Habib Badri Ghavifekr ◽  
Esmaeil Najafi Aghdam
Keyword(s):  
Microelectromechanical Systems ◽  
Rf Mems ◽  
Beam Steering ◽  
Smart Antennas ◽  
Phase Shifters ◽  
Rapid Rate ◽  
Mems Devices ◽  
Batch Fabrication ◽  
Mems Technology ◽  
Smart Beam

In recent years, Microelectromechanical Systems (MEMS) technology has seen a rapid rate of evolution because of its great potential for advancing new products in a broad range of applications. The RF and microwave devices and components fabricated by this technology offer unsurpassed performance such as near-zero power consumption, high linearity, and cost effectiveness by batch fabrication in respect to their conventional counterparts. This chapter aims to give an in-depth overview of the most recently published methods of designing MEMS-based smart antennas. Before embarking into the different techniques of beam steering, the concept of smart antennas is introduced. Then, some fundamental concepts of MEMS technology such as micromachining technologies (bulk and surface micromachining) are briefly discussed. After that, a number of RF MEMS devices such as switches and phase shifters that have applications in beam steering antennas are introduced and their operating principals are completely explained. Finally, various configurations of MEMS-enabled beam steering antennas are discussed in detail.

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