Statics and Dynamics of MEMS Arches Under Axial Forces

2013 ◽  
Vol 135 (2) ◽  
Author(s):  
Sami A. Alkharabsheh ◽  
Mohammad I. Younis
Keyword(s):  
Natural Frequency ◽  
Stable Operation ◽  
Electrostatic Forces ◽  
Order Model ◽  
Reduced Order ◽  
Electrostatically Actuated ◽  
Axial Forces ◽  
Compressive Loads ◽  
Statics And Dynamics ◽  
Static Equation

This works aims to investigate the effect of axial forces on the static behavior and the fundamental natural frequency of electrostatically actuated MEMS arches. The analysis is based on a nonlinear equation of motion of a shallow arch under axial and electrostatic forces. The static equation is solved using a reduced-order model based on the Galerkin procedure. The effects of the axial and electrostatic forces on the static response are examined. Then, the eigenvalue problem of the arch is solved for various equilibrium positions. Several results are shown for the variations of the natural frequency and equilibrium position of the arch under axial forces ranging from compressive loads beyond buckling to tensile loads and for voltage loads starting from small values to large values near the pull-in instability. It is found that the dynamics of MEMS arches are very sensitive to axial forces, which may be induced unintentionally through microfabrication processes or due to temperature variations while in use. On the other hand, it is shown that axial forces can be used deliberately to control the dynamics of MEMS arches to achieve desirable functions, such as extending their stable operation range and tuning their natural frequencies.

Reduced Order Model of MEMS Sensors Near Natural Frequency

2011 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Jose C. Solis Silva
Keyword(s):  
Natural Frequency ◽  
Nonlinear Response ◽  
Casimir Effect ◽  
Electrostatic Force ◽  
Reduced Order Model ◽  
Mass Detection ◽  
Order Model ◽  
Reduced Order ◽  
First Order ◽  
Electrostatically Actuated

The nonlinear response of an electrostatically actuated cantilever beam microresonator sensor for mass detection is investigated. The excitation is near the natural frequency. A first order fringe correction of the electrostatic force, viscous damping, and Casimir effect are included in the model. The dynamics of the resonator is investigated using the Reduced Order Model (ROM) method, based on Galerkin procedure. Steady-state motions are found. Numerical results for uniform microresonators with mass deposition and without are reported.

Reduced Order Model for MEMS Cantilever Resonators Under Soft AC Voltage Near Natural Frequency

2012 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Israel Martinez
Keyword(s):  
Natural Frequency ◽  
Nonlinear Response ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Electrostatic Force ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
First Order ◽  
Electrostatically Actuated

The nonlinear response of an electrostatically actuated cantilever beam microresonator is investigated. The AC voltage is of frequency near resonator’s natural frequency. A first order fringe correction of the electrostatic force and viscous damping are included in the model. The dynamics of the resonator is investigated using the Reduced Order Model (ROM) method, based on Galerkin procedure. Steady-state motions are found. Numerical results for the uniform microresonator are compared with those obtained via the Method of Multiple Scales (MMS).

Reduced Order Model Analysis of Frequency Response of Alternating Current Near Half Natural Frequency Electrostatically Actuated MEMS Cantilevers

2012 ◽  
Vol 8 (3) ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Israel Martinez ◽  
Martin W. Knecht
Keyword(s):  
Natural Frequency ◽  
Microelectromechanical Systems ◽  
Multiple Scales ◽  
Alternating Current ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
Electrostatically Actuated ◽  
Mems Resonator ◽  
Fringe Effect

This paper uses the reduced order model (ROM) method to investigate the nonlinear-parametric dynamics of electrostatically actuated microelectromechanical systems (MEMS) cantilever resonators under soft alternating current (AC) voltage of frequency near half natural frequency. This voltage is between the resonator and a ground plate and provides the actuation for the resonator. Fringe effect and damping forces are included. The resonator is modeled as a Euler-Bernoulli cantilever. ROM convergence shows that the five terms model accurately predicts the steady states of the resonator for both small and large amplitudes and the pull-in phenomenon either when frequency is swept up or down. It is found that the MEMS resonator loses stability and undergoes a pull-in phenomenon (1) for amplitudes about 0.5 of the gap and a frequency less than half natural frequency, as the frequency is swept up, and (2) for amplitudes of about 0.87 of the gap and a frequency about half natural frequency, as the frequency is swept down. It also found that there are initial amplitudes and frequencies lower than half natural frequency for which pull-in can occur if the initial amplitude is large enough. Increasing the damping narrows the escape band until no pull-in phenomenon can occur, only large amplitudes of about 0.85 of the gap being reached. If the damping continues to increase the peak amplitude decreases and the resonator experiences a linear dynamics like behavior. Increasing the voltage enlarges the escape band by shifting the sweep up bifurcation frequency to lower values; the amplitudes of losing stability are not affected. Fringe effect affects significantly the behavior of the MEMS resonator. As the cantilever becomes narrower the fringe effect increases. This slightly enlarges the escape band and increases the sweep up bifurcation amplitude. The method of multiple scales (MMS) fails to accurately predict the behavior of the MEMS resonator for any amplitude greater than 0.45 of the gap. Yet, for amplitudes less than 0.45 of the gap MMS predictions match perfectly ROM predictions.

Response of Electrostatically Actuated Sensors Near Half of the Natural Frequency

2009 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Martin W. Knecht
Keyword(s):  
Natural Frequency ◽  
Governing Equation ◽  
Multiple Scales ◽  
Equation Of Motion ◽  
Casimir Forces ◽  
Order Model ◽  
Reduced Order ◽  
Electrostatically Actuated ◽  
Micro Sensor ◽  
Phase Amplitude

A cantilever micro-resonator electrostatically actuated near half of the natural frequency is investigated. Hamilton’s principle is used to derive the partial-differential equation of motion for a general non-uniform sensor. Nonlinearities arise due to the electrostatic and Casimir forces. The electrostatic actuation introduces parametric coefficients in both linear and nonlinear parts of the governing equation. A direct approach is taken using the method of multiple scales resulting in a phase-amplitude relationship for the system. Numerical results for a uniform capacitive resonator micro-sensor are provided and tested numerically using a reduced-order model of the governing equation of motion.

Reduced Order Model of CNT Cantilever Resonators Under AC Voltage Near Half Natural Frequency

2013 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Le Luo
Keyword(s):  
Natural Frequency ◽  
Multiple Scales ◽  
Electrostatic Force ◽  
Reduced Order Model ◽  
Order Model ◽  
Damping Force ◽  
Reduced Order ◽  
Electrostatically Actuated ◽  
Carbon Nano Tubes ◽  
Ground Plate

This paper deals with electrostatically actuated Carbon Nano-Tubes (CNT) cantilevers using Reduced Order Model method. The system consists of a CNT parallel to a ground plate. An alternating current (AC) voltage is considered between the two. The CNT undergoes an oscillatory motion due to the electrostatic force generated by the voltage. Another two forces act on the CNT, namely a damping force, and a van der Waals force due to gaps less than 50 nm. The Method of Multiple Scales (MMS) and the Reduced Order Model (ROM) method (using AUTO solver) are used to investigate the system under soft excitations and/or weak nonlinearities. The frequency response is found in the case of AC near half natural frequency.

ON NONLINEAR RESPONSE NEAR-HALF NATURAL FREQUENCY OF ELECTROSTATICALLY ACTUATED MICRORESONATORS

2011 ◽  
Vol 11 (04) ◽  
pp. 641-672 ◽  
Author(s):  
DUMITRU I. CARUNTU ◽  
MARTIN KNECHT
Keyword(s):  
Natural Frequency ◽  
Nonlinear Response ◽  
Multiple Scales ◽  
Casimir Effect ◽  
Electrostatic Force ◽  
Order Model ◽  
Reduced Order ◽  
First Order ◽  
Electrostatically Actuated ◽  
Fringe Effect

This paper deals with the nonlinear response of electrostatically actuated cantilever beam microresonators near-half natural frequency. A first-order fringe correction of the electrostatic force, viscous damping, and Casimir effect are included in the model. Both forces, electrostatic and Casimir, are nonlinear. The dynamics of the resonator is investigated using the method of multiple scales (MMS) in a direct approach of the problem. The reduced order model (ROM) method, based on Galerkin procedure, is used as well. Steady-state motions are found. Numerical simulations are conducted for uniform microresonators. The influences of damping, actuation, and fringe effect on the resonator response are found.

Reduced Order Model of CNT Cantilever Resonators Under AC Voltage Near Half Natural Frequency

2012 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Le Luo
Keyword(s):  
Natural Frequency ◽  
Multiple Scales ◽  
Van Der Waals ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
Electrostatically Actuated ◽  
Carbon Nano Tubes ◽  
Ground Plate ◽  
Phase Behaviors

This paper deals with electrostatically actuated Carbon Nano-Tubes (CNT) cantilevers using Reduced Order Model method. There are three kinds of forces acting on the CNT cantilever: electrostatic, elastostatic, and van der Waals. The van der Waals forces are significant for values of 50 nm or lower of the gap between the CNT and the ground plate. As both forceselectrostatic and van der Waals are nonlinear, and the CNT electrostatic actuation is given by AC voltage, the CNT undergoes nonlinear parametric dynamics. The Method of Multiple Scales (MMS), Reduced Order Model (ROM) and AUTO are used to investigate the system under soft excitations and/or weak nonlinearities. The frequency-amplitude and frequency-phase behaviors are found in the case of resonance near half natural frequency.

ROM of Electrostatically Actuated MEMS Resonators Under Simultaneous Resonances

2014 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Christian Reyes
Keyword(s):  
Frequency Response ◽  
Natural Frequency ◽  
Electrostatic Actuation ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
Electrostatically Actuated ◽  
Mems Resonator ◽  
Mems Resonators ◽  
Simultaneous Resonances

This paper deals with MEMS resonator sensors under double electrostatic actuation. The system consists of a MEMS cantilever between two parallel fixed plates. The frequencies of actuation are near natural frequency and near half natural frequency. The frequency response of the simultaneous resonance of the structure is investigated using Reduced Order Model (ROM) method.

Reduced Order Model of Electrostatically Actuated MEMS Resonators Resonance Near Half Natural Frequency

2012 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Israel Martinez ◽  
Martin W. Knecht
Keyword(s):  
Frequency Response ◽  
Natural Frequency ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
Electrostatically Actuated ◽  
Amplitude Frequency Response ◽  
Mems Resonators

This paper uses the Reduced Order Model (ROM) method to investigate the influence of nonlinearities from parametric electrostatic excitation due to soft AC voltage of frequency near half natural frequency of the MEMS cantilever resonator on its frequency response. Most of the analysis in literature investigates pull-in phenomenon, stability, amplitude–frequency relations, or finds time responses of such systems. In this work it is showed that the bifurcation points in the amplitude-frequency response occur at lower frequencies and amplitudes than predicted by the Method of Multiple Scales (MMS), a perturbation method. This result is extremely important for predicting pull-in phenomena. Also the ROM predicts pull-in instability for large initial amplitudes and AC frequencies less than half natural frequency of the resonator. MMS fails to predict this behavior. Increasing the damping and/or decreasing the voltage increases the frequency at which the system undergoes into a pull-in phenomenon.

scholarly journals Statics and Dynamics of V-shaped Micro-beams Under Axial Forces

2021 ◽  
Author(s):  
Hassen Ouakad ◽  
Nouha Alcheikh ◽  
Sofiane Ben Mbarek ◽  
Rodrigo Rocha ◽  
Mohammad Younis
Keyword(s):  
High Performance ◽  
Axial Loads ◽  
Electrostatically Actuated ◽  
High Tunability ◽  
Axial Forces ◽  
Initial Rise ◽  
Statics And Dynamics ◽  
Static Equation ◽  
Dc Bias

Abstract We present an investigation into the static and dynamic behaviors of electrostatically actuated in-plane micro-electro-mechanical V-shaped micro-beam under axial loads. The micro-beams are actuated with two separate electrodes of uniform air-gap across their length. The effects of the initial rise and DC bias voltage are examined while varying the axial loads ranging from compressive to tensile. The numerical analysis is based on a nonlinear equation of motion of a shallow V-shaped micro-beam. The static equation is solved using a reduced-order model based on the Galerkin procedure. Then, the eigenvalue problem of the structure is solved for various equilibrium positions. The analytical model is validated by comparing to an experimental case study. The results show rich and diverse static and dynamic behavior. It is shown that the micro-beam may exhibit only pull-in or snap-through and pull-in instabilities. Various multi-state and hysterics behaviors are demonstrated when varying the actuation forces and the initial rise. High tunability is demonstrated when varying the axial and DC loads for the first two symmetric vibration modes. Such rich behavior can be very useful for high performance micro-scale applications designs.

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