Limit Points Behavior in Electrostatically Actuated Initially Curved Micro Plate

2016 ◽  
Author(s):  
Lior Medina ◽  
Rivka Gilat ◽  
Slava Krylov
Keyword(s):  
Degrees Of Freedom ◽  
Mechanical Load ◽  
Electrostatic Force ◽  
Equilibrium Path ◽  
Buckling Modes ◽  
Reduced Order ◽  
Electrostatically Actuated ◽  
Base Functions ◽  
Three Degrees Of Freedom ◽  
Good Agreement

The axisymmetric snap-through of an initially curved circular micro plate, subjected to a transversal distributed electrostatic force is studied. The analysis is based on a reduced order (RO) model resulting from the Galerkin decomposition, with buckling modes of a flat plate used as the base functions. In order to check the validity of the RO model, the corresponding problem for a displacement-independent (“mechanical”) load is solved, and a comparison between the RO model and those obtained using finite elements (FE) analysis is carried out. It is shown, that the two are in good agreement, indicating that the RO model can be used for a plate undergoing electrostatic loading. However, the study shows that at least three degrees of freedom (DOF) are required for an accurate prediction of the equilibrium path and bistability. The coupled electromechanical analysis shows that due to the nonlinearity of the electrostatic load, the snap-through occurs at a lower displacement than in the case of the “mechanical” load. Moreover, the study concludes that actuation of plates of realistic dimensions can be achieved by reasonably low voltages.

Symmetry Breaking in an Initially Curved Micro Beam Loaded by a Distributed Electrostatic Force

2012 ◽  
Author(s):  
Lior Medina ◽  
Rivka Gilat ◽  
Slava Krylov
Keyword(s):  
Symmetry Breaking ◽  
Degrees Of Freedom ◽  
Electrostatic Force ◽  
Reduced Order ◽  
Electrostatically Actuated ◽  
Straight Beam ◽  
Base Functions ◽  
Approximate Expressions ◽  
Symmetric Response ◽  
Good Agreement

The asymmetric buckling of a shallow initially curved stress-free micro beam subjected to distributed nonlinear deflection-dependent electrostatic force is studied. The analysis is based on a two degrees of freedom reduced order (RO) model, resulting from the Galerkin decomposition with linear undamped eigen-modes of a straight beam used as the base functions. Simple approximate expressions are derived defining the geometric parameters of beams for which an asymmetric response bifurcates from the symmetric one. The necessary criterion establishes the conditions for the appearance of bifurcation points on the unstable branch of the symmetric response curve; the sufficient criterion assures a realistic asymmetric buckling bifurcating from the stable branches of the curve. It is shown that while the symmetry breaking conditions are affected by the nonlinearity of the electrostatic force, its influence is less pronounced than in the case of the symmetric snap-through criterion. A comparison between the RO model results and those obtained by direct numerical analysis shows good agreement between the two and indicates that the obtained criteria can be used to predict non-symmetric buckling in electrostatically actuated bistable micro beams.

Latching Criteria in Bistable Prestressed Curved Micro Beams

2015 ◽  
Author(s):  
Lior Medina ◽  
Rivka Gilat ◽  
Slava Krylov
Keyword(s):  
Response Curve ◽  
Transverse Force ◽  
Curved Beams ◽  
Buckling Modes ◽  
Reduced Order ◽  
Electrostatically Actuated ◽  
Straight Beam ◽  
Base Functions ◽  
Symmetric Response ◽  
Good Agreement

Curved beams subjected to transverse force may exhibit a latching phenomena, namely remain in their buckled configuration under zero force such that an opposite force is required for their release. In this study, we investigate the latching in bistable electrostatically actuated prestressed curved beams. The analysis is based on a reduced order (RO) model resulting from the Galerkin decomposition with buckling modes of a straight beam as base functions. Criteria for the existence of latching are derived in terms of the beam geometric parameters and the axial load. Two conditions are formulated: A necessary criterion establishes the appearance of latching on the symmetric response curve and a sufficient condition which assures the existence of latching in the presence of bifurcations. A comparison between the model results and those obtained by numerical analysis shows good agreement up to a certain elevation. It is noted that as the latching is not affected by the nonlinear electrostatic load, the obtained criteria stand for all types of loading.

Tristable Properties in Electrostatically Actuated Initially Curved Coupled Micro Beams

2021 ◽  
Author(s):  
Lior Medina ◽  
Ashwin A. Seshia
Keyword(s):  
Degrees Of Freedom ◽  
Geometrical Parameters ◽  
Curved Beams ◽  
Buckling Modes ◽  
Reduced Order ◽  
Electrostatically Actuated ◽  
Critical Thresholds ◽  
All Solutions ◽  
Base Functions

Abstract A limit point behaviour analysis of a metastructure, composed of two double clamped, initially curved beams, coupled via a rigid truss at their respective centres, is carried out when subjected to a distributed electrostatic load. The analysis is based on a reduced order (RO) model resulting from Galerkin’s decomposition, with symmetric buckling modes taken as the base functions, for either beam. All solutions employed the implicit arc-length “Riks” method to accommodate for winding equilibrium paths, while validation of the said results were carried out against finite differences (FD) direct solutions. In addition, local stability analysis via the energy method, conducted on the primary beam was instrumental in clarifying the role of the various extremum points by characterising which branches are stable, and which are not. The combined analysis has shown that the driving beam, which directly encounters the load, is able to possess bistable as well as tristable properties, provided that the metastructure meets certain geometrical parameters. Several variations of tristability are disclosed in the study. The analysis indicates that a model with at least three degrees of freedom (DOF) is needed to predict such configurations, as well as the various critical thresholds, with reasonable errors of around one percent when compared against FD. In so doing, the model can be used to provide static characterisation of the structure.

The Effect of Membrane Load on the Usage of Berger’s Model in Electrostatically Actuated Pre-Stressed Circular Curved Micro Plates

2021 ◽  
Author(s):  
Lior Medina ◽  
Rami Eliasi ◽  
Rivka Gilat ◽  
Slava Krylov
Keyword(s):  
Finite Elements ◽  
Degrees Of Freedom ◽  
Mechanical Load ◽  
Fe Model ◽  
Buckling Modes ◽  
Reduced Order ◽  
Electrostatically Actuated ◽  
All Solutions ◽  
Convergence Study ◽  
Micro Plates

Abstract The effect of membrane load on the behaviour of axisymmetric bistable circular curved microplates on Berger’s based axisymmetric reduced order (RO) model, incorporating radial prestress, is studied. The model is first validated for a “mechanical” load, against a Föppl-von-Kármán’s RO model with twenty degrees of freedom (DOF), a finite differences (FD) solution and a finite elements (FE) model, serving as the reference. All solutions implement the “Riks” method to track possible unstable branches, which can swerve in due to the presence of higher buckling modes. A convergence study is carried out for the snap-through location and load, as well as for the critical elevation and prestress required for bistability. Based on validated results of the analysis, the reliability of the model for predicting the effect of prestress on the plate behaviour under nonlinear electrostatic load is then investigated while using FD solutions as the reference. The study furnishes a reliable expended RO model, which includes prestress on the as-fabricated curved plate. The resulting model can further be used to estimate the value of residual prestress, present in an electrostatically actuated curved plate, based on its response.

On the Usage of Berger’s Model for Electrostatically Actuated Circular Curved Micro Plates

2017 ◽  
Author(s):  
Lior Medina ◽  
Rivka Gilat ◽  
Slava Krylov
Keyword(s):  
Flat Plate ◽  
Continuous Method ◽  
Structural Elements ◽  
Buckling Modes ◽  
Reduced Order ◽  
Electrostatically Actuated ◽  
Significant Interest ◽  
Base Functions ◽  
Galerkin Models ◽  
Micro Plates

Micro- and nanolectromechanical systems (MEMS/NEMS) incorporating two-dimensional structural elements such as plates attracted significant interest in recent years. In this work, we explore implementation of a model based on Berger’s approximation, which significantly simplifies the formulation of a curved plate and describes it by a single governing equation. The solution of this equation is based on the Galerkin decomposition with buckling modes of an initially flat plate used as the base functions. To track the unstable branches of the equilibrium curve, a continuous method based on the Riks algorithm is implemented. The validation of the models is conducted for two loading cases, “mechanical” deflection-independent load, and electrostatic displacement-dependent load. In the case of an initially flat plate, results provided by the reduced order (RO) Galerkin models were compared to results available in the literature. In the case of a curved plate undergoing “mechanical” loading, results of a direct finite elements (FE) analysis, as well as of a finite differences (FD) analysis, were used as a reference. We show that the DOF Berger RO model can be conveniently used for analysis of plates with small curvature, as it provides satisfactory accuracy. Further more, a single DOF model can be used for the development of a bistability criterion.

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).

Nonlinear Dynamics of MEMS Arches

2010 ◽  
Author(s):  
Sami Alkharabsheh ◽  
Mohammad Younis
Keyword(s):  
Electrostatic Force ◽  
Equations Of Motion ◽  
Amplitude Dependence ◽  
Harmonic Load ◽  
Order Model ◽  
Shooting Technique ◽  
Reduced Order ◽  
Electrostatically Actuated ◽  
Dynamic Phenomena ◽  
Unstable States

In this paper, the dynamic response of electrostatically actuated clamped-clamped arch microbeam is investigated when excited by a DC load superimposed to an AC harmonic load. The dynamic analysis is carried out using a Galerkin-based reduced order model along with a shooting technique to find periodic motions and analyzing its stability using a Floquet theory. Results are presented for the cases of primary and super harmonic resonances. We found several nonlinear dynamic phenomena due to the inherent nonlinear electrostatic force and geometric nonlinearity of the arch. These include frequency-amplitude dependence, jumps, tangent bifurcations, coexistence of solutions, and softening and hardening behaviors. The shooting technique showed high robustness in capturing both the stable and unstable states of the system. Hence, it helped clarify vague behaviors that were previously reported using longtime integration of the equations of motion.

Reduced Order Model on DC Bias Effect on the Frequency Response of Electrostatically Actuated Biosensor Microplates

2016 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Christian Reyes
Keyword(s):  
Frequency Response ◽  
Electrostatic Force ◽  
Alternate Current ◽  
Reduced Order Model ◽  
Order Model ◽  
Bias Effect ◽  
Reduced Order ◽  
Electrostatically Actuated ◽  
Ground Plate ◽  
Dc Bias

This paper investigates the frequency response of microplates under electrostatic actuation. The microplate is parallel to a fixed ground plate. The electrostatic force that actuates the system is given by both Alternate Current (AC) and Direct Current (DC) voltages. The AC frequency is set to be near half natural frequency of the structure. Damping influence is also investigated in this paper. The method of investigation is Reduced Order Model. The effects of various parameters on the response of the structure are reported.

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.

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