Pull-In Dynamics of an Elastic Beam Actuated by Distributed Electrostatic Force

2003 ◽  
Author(s):  
Slava Krylov ◽  
Ronen Maimon
Keyword(s):  
Nonlinear Dynamics ◽  
Dynamic Instability ◽  
Electrostatic Force ◽  
Normal Modes ◽  
Elastic Beam ◽  
Nonlinear Damping ◽  
Rotational Inertia ◽  
Electrostatic Forces ◽  
Spatial Region ◽  
Electrically Actuated

A detailed study of the transient nonlinear dynamics of an electrically actuated micron scale beam is presented. A model developed using the Galerkin procedure with normal modes as a basis accounts for the distributed nonlinear electrostatic forces, nonlinear distributed squeezed film damping forces, and rotational inertia of a mass carried by the beam. Special attention is paid to the dynamics of the beam near instability points. Results generated by the model and confirmed experimentally show that nonlinear damping leads to shrinkage of the spatial region where stable motion is realizable. The voltage that causes dynamic instability, in turn, approaches the static pull-in value.

Pull-in Dynamics of an Elastic Beam Actuated by Continuously Distributed Electrostatic Force

2004 ◽  
Vol 126 (3) ◽  
pp. 332-342 ◽  
Author(s):  
Slava Krylov ◽  
Ronen Maimon
Keyword(s):  
Nonlinear Dynamics ◽  
Dynamic Instability ◽  
Electrostatic Force ◽  
Normal Modes ◽  
Elastic Beam ◽  
Nonlinear Damping ◽  
Rotational Inertia ◽  
Electrostatic Forces ◽  
Spatial Region ◽  
Electrically Actuated

A detailed study of the transient nonlinear dynamics of an electrically actuated micron scale beam is presented. A model developed using the Galerkin procedure with normal modes as a basis accounts for the distributed nonlinear electrostatic forces, nonlinear squeezed film damping, and rotational inertia of a mass carried by the beam. Special attention is paid to the dynamics of the beam near instability points. Results generated by the model and confirmed experimentally show that nonlinear damping leads to shrinkage of the spatial region where stable motion is realizable. The voltage that causes dynamic instability, in turn, approaches the static pull-in value.

scholarly journals Nonlinear Dynamics of Carbon Nanotubes Under Large Electrostatic Force

2015 ◽  
Author(s):  
Tiantian Xu ◽  
Mohammad I. Younis
Keyword(s):  
Nonlinear Dynamics ◽  
Carbon Nanotubes ◽  
Electrostatic Force ◽  
Small Diameter ◽  
Dynamic Responses ◽  
Cylindrical Shape ◽  
Beam Model ◽  
Electrostatic Forces ◽  
Complicated Form ◽  
The Impact

Because of the inherent nonlinearities involving the behavior of CNTs when excited by electrostatic forces, modeling and simulating their behavior is challenging. The complicated form of the electrostatic force describing the interaction of their cylindrical shape, forming upper electrodes, to lower electrodes poises serious computational challenges. This presents an obstacle against applying and using several nonlinear dynamics tools typically used to analyze the behavior of complicated nonlinear systems, such as shooting, continuation, and integrity analysis techniques. This works presents an attempt to resolve this issue. We present an investigation of the nonlinear dynamics of carbon nanotubes when actuated by large electrostatic forces. We study expanding the complicated form of the electrostatic force into enough number of terms of the Taylor series. Then, we utilize this form along with an Euler–Bernoulli beam model to study the static and dynamic behavior of CNTs. The geometric nonlinearity and the nonlinear electrostatic force are considered. An efficient reduced-order model (ROM) based on the Galerkin method is developed and utilized to simulate the static and dynamic responses of the CNTs. Several results are generated demonstrating softening and hardening behavior of the CNTs near their primary and secondary resonances. The effect of DC voltage load and AC voltage load on the nonlinearity has been studied. We also investigated the impact of initial slack level on the natural frequency and the nonlinearity. Small diameter and large initial slacked CNTs has been considered.

scholarly journals Nonlinear Dynamics of Carbon Nanotubes Under Large Electrostatic Force

2015 ◽  
Vol 11 (2) ◽  
Author(s):  
Tiantian Xu ◽  
Mohammad I. Younis
Keyword(s):  
Nonlinear Dynamics ◽  
Carbon Nanotubes ◽  
Electrostatic Force ◽  
Dynamic Responses ◽  
Cylindrical Shape ◽  
Beam Model ◽  
Electrostatic Forces ◽  
Complicated Form ◽  
The Galerkin Method ◽  
Integrity Analysis

Because of the inherent nonlinearities involving the behavior of carbon nanotubes (CNTs) when excited by electrostatic forces, modeling and simulating their behavior are challenging. The complicated form of the electrostatic force describing the interaction of their cylindrical shape, forming upper electrodes, to lower electrodes poises serious computational challenges. This presents an obstacle against applying and using several nonlinear dynamics tools typically used to analyze the behavior of complicated nonlinear systems undergoing large motion, such as shooting, continuation, and integrity analysis techniques. This work presents an attempt to resolve this issue. We present an investigation of the nonlinear dynamics of CNTs when actuated by large electrostatic forces. We study by expanding the complicated form of the electrostatic force into enough number of terms of the Taylor series. Then, we utilize this form along with an Euler–Bernoulli beam model to study for the first time the dynamic behavior of CNTs when excited by large electrostatic force. The geometric nonlinearity and the nonlinear electrostatic force are considered. An efficient reduced-order model (ROM) based on the Galerkin method is developed and utilized to simulate the static and dynamic responses of the CNTs. Several results are generated demonstrating softening and hardening behavior of the CNTs near their primary and secondary resonances. The effects of the DC and AC voltage loads on the behavior have been studied. The impacts of the initial slack level and CNT diameter are also demonstrated.

The Primary Nonlinear Dynamics of Modal and Nonmodal Perturbations of Monochromatic Inertia–Gravity Waves

2007 ◽  
Vol 64 (1) ◽  
pp. 74-95 ◽  
Author(s):  
Ulrich Achatz
Keyword(s):  
Nonlinear Dynamics ◽  
Dynamic Instability ◽  
Normal Modes ◽  
Large Degree ◽  
Small Scale ◽  
Turbulent Dissipation ◽  
Static And Dynamic Instability ◽  
Boussinesq Fluid ◽  
Secondary Instabilities ◽  
Elliptically Polarized

Abstract The breaking of an inertia–gravity wave (IGW), initiated by its leading normal modes (NMs) or singular vectors (SVs), and the resulting small-scale eddies are investigated by means of direct numerical simulations of a Boussinesq fluid characterizing the upper mesosphere. The focus is on the primary nonlinear dynamics, neglecting the effect of secondary instabilities. It is found that the structures with the strongest impact on the IGW and also the largest turbulence amplitudes are the NM (for a statically unstable IGW) or short-term SV (statically and dynamically stable IGW) propagating horizontally transversely with respect to the IGW, possibly in agreement with observations of airglow ripples in conjunction with statically unstable IGWs. In both cases these leading structures reduce the IGW amplitude well below the static and dynamic instability thresholds. The resulting turbulent dissipation rates are within the range of available estimates from rocket soundings, even for IGWs at amplitudes low enough precluding NM instabilities. Thus SVs can help explain turbulence occurring under conditions not amenable for the classic interpretation via static and dynamic instability. Because of the important role of the statically enhanced roll mechanism in the energy exchange between IGW and eddies, the turbulent velocity fields are often conspicuously anisotropic. The spatial turbulence distribution is determined to a large degree by the elliptically polarized horizontal velocity field of the IGW.

Electrostatic Forces on Particles Floating Within the Interface Between Two Immiscible Fluids

2007 ◽  
Author(s):  
Nadine Aubry ◽  
Pushpendra Singh
Keyword(s):  
Dielectric Properties ◽  
Field Strength ◽  
Electric Field ◽  
Electric Field Strength ◽  
External Electric Field ◽  
Capillary Force ◽  
Electrostatic Force ◽  
Immiscible Fluids ◽  
Electrostatic Forces ◽  
Dipole Interactions

The objective of this paper is to study the dependence of the electrostatic force that act on a particle within the interface between two immiscible fluids on the parameters such as the dielectric properties of the fluids and particles, the particle’s position within the interface, and the electric field strength. It is shown that the component of electrostatic force normal to the interface varies as a2, where a is the particle radius, and since in equilibrium it is balanced by the vertical capillary force, the interfacial deformation caused by the particle changes when an external electric field is applied. In addition, there are lateral electrostatic forces among the particles due to the dipole-dipole interactions which, when the distance between two particles is O(a), vary as a2, and remain significant for submicron sized particles.

Nonlinear Dynamics of an Electrically Actuated MEMS Device: Experimental and Theoretical Investigation

2013 ◽  
Author(s):  
Laura Ruzziconi ◽  
Abdallah H. Ramini ◽  
Mohammad I. Younis ◽  
Stefano Lenci
Keyword(s):  
Nonlinear Dynamics ◽  
Theoretical Investigation ◽  
Initial Conditions ◽  
Micro Electro Mechanical System ◽  
Mass Model ◽  
Design Guideline ◽  
Electrically Actuated ◽  
Theoretical Predictions ◽  
Frequency Sweeps ◽  
Safe Condition

This study deals with an experimental and theoretical investigation of an electrically actuated micro-electro-mechanical system (MEMS). The experimental nonlinear dynamics are explored via frequency sweeps in a neighborhood of the first symmetric natural frequency, at increasing values of electrodynamic excitation. Both the non-resonant branch, the resonant one, the jump between them, and the presence of a range of inevitable escape (dynamic pull-in) are observed. To simulate the experimental behavior, a single degree-of-freedom spring mass model is derived, which is based on the information coming from the experimentation. Despite the apparent simplicity, the model is able to catch all the most relevant aspects of the device response. This occurs not only at low values of electrodynamic excitation, but also at higher ones. Nevertheless, the theoretical predictions are not completely fulfilled in some aspects. In particular, the range of existence of each attractor is smaller in practice than in the simulations. This is because, under realistic conditions, disturbances are inevitably encountered (e.g. discontinuous steps when performing the sweeping, approximations in the modeling, etc.) and give uncertainties to the operating initial conditions. A reliable prediction of the actual (and not only theoretical) response is essential in applications. To take disturbances into account, we develop a dynamical integrity analysis. Integrity profiles and integrity charts are performed. They are able to detect the parameter range where each branch can be reliably observed in practice and where, instead, becomes vulnerable. Moreover, depending on the magnitude of the expected disturbances, the integrity charts can serve as a design guideline, in order to effectively operate the device in safe condition, according to the desired outcome.

scholarly journals Electrostatic forces alter particle size distributions in atmospheric dust

2020 ◽  
Vol 20 (5) ◽  
pp. 3181-3190 ◽  
Author(s):  
Joseph R. Toth III ◽  
Siddharth Rajupet ◽  
Henry Squire ◽  
Blaire Volbers ◽  
Jùn Zhou ◽  
...  
Keyword(s):  
Electric Field ◽  
Size Distribution ◽  
Long Range ◽  
Electric Fields ◽  
Electrostatic Force ◽  
Small Scale ◽  
Size Distributions ◽  
Electrostatic Forces ◽  
Atmospheric Dust ◽  
Airborne Dust

Abstract. Large amounts of dust are lofted into the atmosphere from arid regions of the world before being transported up to thousands of kilometers. This atmospheric dust interacts with solar radiation and causes changes in the climate, with larger-sized particles having a heating effect, and smaller-sized particles having a cooling effect. Previous studies on the long-range transport of dust have found larger particles than expected, without a model to explain their transport. Here, we investigate the effect of electric fields on lofted airborne dust by blowing sand through a vertically oriented electric field, and characterizing the size distribution as a function of height. We also model this system, considering the gravitational, drag, and electrostatic forces on particles, to understand the effects of the electric field. Our results indicate that electric fields keep particles suspended at higher elevations and enrich the concentration of larger particles at higher elevations. We extend our model from the small-scale system to long-range atmospheric dust transport to develop insights into the effects of electric fields on size distributions of lofted dust in the atmosphere. We show that the presence of electric fields and the resulting electrostatic force on charged particles can help explain the transport of unexpectedly large particles and cause the size distribution to become more uniform as a function of elevation. Thus, our experimental and modeling results indicate that electrostatic forces may in some cases be relevant regarding the effect of atmospheric dust on the climate.

Nonlinear Dynamics of a Beam-Rigid Body Microgyroscope

2014 ◽  
Author(s):  
S. A. M. Lajimi ◽  
G. R. Heppler ◽  
E. Abdel-Rahman
Keyword(s):  
Nonlinear Dynamics ◽  
Rigid Body ◽  
Shooting Method ◽  
Electrostatic Force ◽  
Time Integration ◽  
Primary Resonance ◽  
Longitudinal Axis ◽  
Response Curves ◽  
Long Time ◽  
Long Time Integration

The nonlinear dynamics of a cantilever-beam-rigid-body MEMS gyroscope near primary resonance are studied by using a shooting method and long time integration. The microsensor includes a square beam carrying an eccentric end-rigid-body rotating about the longitudinal axis and under an electrostatic force. The mathematical model of the system is reduced by using the method of assumed modes. Using a shooting method and long time integration, the dynamic characteristics of the system are investigated and presented in terms of frequency-response plots and force-response curves. The bifurcation points are discussed and the regions of instability are characterized.

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