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.

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.

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.

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.

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.

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.

scholarly journals Static and Dynamic Analysis of Electrostatically Actuated MEMS Shallow Arches for Various Air-Gap Configurations

Micromachines ◽  
2021 ◽  
Vol 12 (8) ◽  
pp. 930
Author(s):  
Hassen M. Ouakad ◽  
Nouha Alcheikh ◽  
Mohammad I. Younis
Keyword(s):  
Expansion Method ◽  
Geometrical Parameters ◽  
Parallel Plates ◽  
Reduced Order ◽  
Shallow Arches ◽  
Static And Dynamic Analysis ◽  
Electrostatically Actuated ◽  
Static Responses ◽  
Wide Range ◽  
Electrically Actuated

In this research, we investigate the structural behavior, including the snap-through and pull-in instabilities, of in-plane microelectromechanical COSINE-shaped and electrically actuated clamped-clamped micro-beams resonators. The work examines various electrostatic actuation patterns including uniform and non-uniform parallel-plates airgap arrangements, which offer options to actuate the arches in the opposite and same direction of their curvature. The nonlinear equation of motion of a shallow arch is discretized into a reduced-order model based on the Galerkin’s expansion method, which is then numerically solved. Static responses are examined for various DC electrostatic loads starting from small values to large values near pull-in and snap-through instability ranges, if any. The eigenvalue problem of the micro-beam is solved revealing the variations of the first four natural frequencies as varying the DC load. Various simulations are carried out for several case studies of shallow arches of various geometrical parameters and airgap arrangements, which demonstrate rich and diverse static and dynamic behaviors. Results show few cases with multi-states and hysteresis behaviors where some with only the pull-in instability and others with both snap-through buckling and pull-in instabilities. It is found that the micro-arches behaviors are very sensitive to the electrode’s configuration. The studied configurations reveal different possibilities to control the pull-in and snap-through instabilities, which can be used for improving arches static stroke range as actuators and for realizing wide-range tunable micro-resonators.

On the Use of Quantum Thermal Bath in Unimolecular Fragmentation Simulations

2019 ◽  
Author(s):  
Riccardo Spezia ◽  
Hichem Dammak
Keyword(s):  
Degrees Of Freedom ◽  
Molecular Simulations ◽  
Zero Point ◽  
Thermal Bath ◽  
Unimolecular Dissociation ◽  
Point Energy ◽  
Rotational Degrees Of Freedom ◽  
The Difference ◽  
Nuclear Effects

<div> <div> <div> <p>In the present work we have investigated the possibility of using the Quantum Thermal Bath (QTB) method in molecular simulations of unimolecular dissociation processes. Notably, QTB is aimed in introducing quantum nuclear effects with a com- putational time which is basically the same as in newtonian simulations. At this end we have considered the model fragmentation of CH4 for which an analytical function is present in the literature. Moreover, based on the same model a microcanonical algorithm which monitor zero-point energy of products, and eventually modifies tra- jectories, was recently proposed. We have thus compared classical and quantum rate constant with these different models. QTB seems to correctly reproduce some quantum features, in particular the difference between classical and quantum activation energies, making it a promising method to study unimolecular fragmentation of much complex systems with molecular simulations. The role of QTB thermostat on rotational degrees of freedom is also analyzed and discussed. </p> </div> </div> </div>

scholarly journals Dzyaloshinskii–Moriya interaction in noncentrosymmetric superlattices

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Woo Seung Ham ◽  
Abdul-Muizz Pradipto ◽  
Kay Yakushiji ◽  
Kwangsu Kim ◽  
Sonny H. Rhim ◽  
...  
Keyword(s):  
Heavy Metal ◽  
Degrees Of Freedom ◽  
Orbit Coupling ◽  
Inversion Symmetry ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Band Formation ◽  
Research Activities ◽  
Moriya Interaction

AbstractDzyaloshinskii–Moriya interaction (DMI) is considered as one of the most important energies for specific chiral textures such as magnetic skyrmions. The keys of generating DMI are the absence of structural inversion symmetry and exchange energy with spin–orbit coupling. Therefore, a vast majority of research activities about DMI are mainly limited to heavy metal/ferromagnet bilayer systems, only focusing on their interfaces. Here, we report an asymmetric band formation in a superlattices (SL) which arises from inversion symmetry breaking in stacking order of atomic layers, implying the role of bulk-like contribution. Such bulk DMI is more than 300% larger than simple sum of interfacial contribution. Moreover, the asymmetric band is largely affected by strong spin–orbit coupling, showing crucial role of a heavy metal even in the non-interfacial origin of DMI. Our work provides more degrees of freedom to design chiral magnets for spintronics applications.

scholarly journals A Superfluid Perspective on Neutron Star Dynamics

Universe ◽  
2021 ◽  
Vol 7 (1) ◽  
pp. 17
Author(s):  
Nils Andersson
Keyword(s):  
Neutron Star ◽  
Degrees Of Freedom ◽  
Temperature Scale ◽  
Fluid System ◽  
Fluid Core ◽  
State Of Matter ◽  
Entrainment Effect ◽  
Neutron Component ◽  
The Impact

As mature neutron stars are cold (on the relevant temperature scale), one has to carefully consider the state of matter in their interior. The outer kilometre or so is expected to freeze to form an elastic crust of increasingly neutron-rich nuclei, coexisting with a superfluid neutron component, while the star’s fluid core contains a mixed superfluid/superconductor. The dynamics of the star depend heavily on the parameters associated with the different phases. The presence of superfluidity brings new degrees of freedom—in essence we are dealing with a complex multi-fluid system—and additional features: bulk rotation is supported by a dense array of quantised vortices, which introduce dissipation via mutual friction, and the motion of the superfluid is affected by the so-called entrainment effect. This brief survey provides an introduction to—along with a commentary on our current understanding of—these dynamical aspects, paying particular attention to the role of entrainment, and outlines the impact of superfluidity on neutron-star seismology.

scholarly journals Higher spins from exotic dualisations

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Nicolas Boulanger ◽  
Victor Lekeu
Keyword(s):  
Infinite Number ◽  
Arbitrary Number ◽  
Degrees Of Freedom ◽  
Young Tableaux ◽  
Spacetime Dimension ◽  
Massless Field ◽  
Free Level ◽  
Higher Spins

Abstract At the free level, a given massless field can be described by an infinite number of different potentials related to each other by dualities. In terms of Young tableaux, dualities replace any number of columns of height hi by columns of height D − 2 − hi, where D is the spacetime dimension: in particular, applying this operation to empty columns gives rise to potentials containing an arbitrary number of groups of D − 2 extra antisymmetric indices. Using the method of parent actions, action principles including these potentials, but also extra fields, can be derived from the usual ones. In this paper, we revisit this off-shell duality and clarify the counting of degrees of freedom and the role of the extra fields. Among others, we consider the examples of the double dual graviton in D = 5 and two cases, one topological and one dynamical, of exotic dualities leading to spin three fields in D = 3.

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