Effect of Dispersion Forces on Dynamic Stability of Electrostatically Actuated Micro/Nano-Beams in Presence of Mechanical Shocks

2019 ◽  
Vol 11 (09) ◽  
pp. 1950085 ◽  
Author(s):  
Amin Hajarian ◽  
Mahdi Moghimi Zand ◽  
Naeem Zolfaghari
Keyword(s):  
Electrostatic Force ◽  
Stability Limit ◽  
Beam Theory ◽  
Dispersion Forces ◽  
Mechanical Shock ◽  
Electrostatically Actuated ◽  
Dimensional Parameters ◽  
Casimir Interactions ◽  
The Stability ◽  
External Forces

Dispersion forces such as van der Waals and Casimir interactions become important when the size of structures shrinks. Therefore, the effective design of micro and nano-sized structures depends on appropriate consideration of these forces. In the current research, we analyzed the effect of dispersion forces on the dynamic behavior of a micro/nanobeam actuated by electrostatic forces subject to a mechanical shock. We used the Euler–Bernoulli beam theory including nonlinearities due to mid-plane stretching in our model. The equation of motion is solved using time-dependent finite element method, and pull-in forces are calculated. The stability regimes are evaluated as the set of three force parameters in which the beam elasticity overcomes the external forces, and the beam is able to vibrate without hitting the substrate. Results show that the design of the beam should be such that the three sets of non-dimensional parameters that determine the intensity of shock, dispersion, and electrostatic force do not fall above the stability limit to avoid pull-in instability. Our results have applications in the design of electrostatically actuated micro/nanobeams in mechanical shock environments such as accelerometers.

Dynamic Analysis of Three Parallel Beams With Electrostatic Force Interaction

2011 ◽  
Author(s):  
Pezhman A. Hassanpour ◽  
Patricia M. Nieva ◽  
Amir Khajepour
Keyword(s):  
Time Domain ◽  
Stability Condition ◽  
Initial Conditions ◽  
Electrostatic Force ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Stability Margin ◽  
Modal Damping ◽  
The Stability ◽  
Euler Bernoulli Beam

In this paper, the dynamics of a micro-machined structure with three parallel cantilevers is investigated. The cantilevers are electrically charged and apply electrostatic force to each other. The governing equations of motion are derived using Euler-Bernoulli beam theory and considering structural modal damping. The stability condition of the beams for various electric charges is also studied. In addition, the equations of motion are integrated to obtain the response of the beams in time-domain for a range of initial conditions. This response is used to study the behavior of the beams at the stability margin. The end application of the structure under investigation is in the device characterization. The dynamic stability condition and time-domain responses are used to investigate the reliability of the characterization. Once translated back to physical quantities, these results can be used for improving the measurements.

scholarly journals Volcanic Lateral Collapse Processes in Mafic Arc Edifices: A Review of Their Driving Processes, Types and Consequences

2021 ◽  
Vol 9 ◽  
Author(s):  
Jorge E. Romero ◽  
Margherita Polacci ◽  
Sebastian Watt ◽  
Shigeru Kitamura ◽  
Daniel Tormey ◽  
...  
Keyword(s):  
Large Scale ◽  
Stability Limit ◽  
Hydrothermal Systems ◽  
Sector Collapse ◽  
Geological Evidence ◽  
Basaltic Rocks ◽  
Surrounding Landscape ◽  
The Stability ◽  
External Forces ◽  
Historical Accounts

Volcanic cones are frequently near their gravitational stability limit, which can lead to lateral collapse of the edifice, causing extensive environmental impact, property damage, and loss of life. Here, we examine lateral collapses in mafic arc volcanoes, which are relatively structurally simple edifices dominated by a narrow compositional range from basalts to basaltic andesites. This still encompasses a broad range of volcano dimensions, but the magma types erupted in these systems represent the most abundant type of volcanism on Earth and rocky planets. Their often high magma output rates can result in rapid construction of gravitationally unstable edifices susceptible both to small landslides but also to much larger-scale catastrophic lateral collapses. Although recent studies of basaltic shield volcanoes provide insights on the largest subaerial lateral collapses on Earth, the occurrence of lateral collapses in mafic arc volcanoes lacks a systematic description, and the features that make such structures susceptible to failure has not been treated in depth. In this review, we address whether distinct characteristics lead to the failure of mafic arc volcanoes, or whether their propensity to collapse is no different to failures in volcanoes dominated by intermediate (i.e., andesitic-dacitic) or silicic (i.e., rhyolitic) compositions? We provide a general overview on the stability of mafic arc edifices, their potential for lateral collapse, and the overall impact of large-scale sector collapse processes on the development of mafic magmatic systems, eruptive style and the surrounding landscape. Both historical accounts and geological evidence provide convincing proofs of recurrent (and even repetitive) large-scale (>0.5 km3) lateral failure of mafic arc volcanoes. The main factors contributing to edifice instability in these volcanoes are: (1) frequent sheet-like intrusions accompanied by intense deformation and seismicity; (2) shallow hydrothermal systems weakening basaltic rocks and reducing their overall strength; (3) large edifices with slopes near the critical angle; (4) distribution along fault systems, especially in transtensional settings, and; (5) susceptibility to other external forces such as climate change. These factors are not exclusive of mafic volcanoes, but probably enhanced by the rapid building of such edifices.

Atomic disruption beam theory

2016 ◽  
pp. 3524-3528
Author(s):  
Casey Ray McMahon
Keyword(s):  
Neutron Beam ◽  
Beam Theory ◽  
Solid Material ◽  
Material Matter ◽  
Solid Matter ◽  
Plasma Generation ◽  
Resulting Effect ◽  
Drilling Operations ◽  
The Stability

In this paper, I discuss the theory behind the use of a dense, concentrated neutron particle-based beam. I look at the particle based physics behind such a beam, when it is focused against solid material matter. Although this idea is still only theoretical, it appears that such a beam may be capable of disrupting the stability of the atoms within solid matter- in some cases by passing great volumes of neutrons between the electron and nucleus thus effectively “shielding” the electron from the charge of the nucleus. In other cases, by disrupting the nucleus by firing neutrons into it, disrupting the nucleus and weakening its bond on electrons. In either case- the resulting effect would be a disruption of the atom, which in the case of material matter would cause said material matter to fail, which would appear to the observer as liquification with some plasma generation. Thus, a dense neutron particle based beam could be used to effectively liquefy material matter. Such a beam could bore through rock, metal, or even thick, military grade armour, like that used on tanks- causing such materials to rapidly liquefy. The denser and thicker the neutron beam, the more devastating the effect of the beam- thus the faster material matter will liquefy and the greater the area of liquification. Such a beam would have applications in Defence, mining and drilling operations.

Optimization of the Robust Stability Limit for Multi-Cutter Turning Processes

2015 ◽  
Author(s):  
Marta J. Reith ◽  
Daniel Bachrathy ◽  
Gabor Stepan
Keyword(s):  
Robust Stability ◽  
Optimal Parameter ◽  
Stability Limit ◽  
Boundary Function ◽  
Lower Envelope ◽  
Computation Method ◽  
Parameter Region ◽  
Dynamical Parameters ◽  
The Stability ◽  
Machining Parameter

Multi-cutter turning systems bear huge potential in increasing cutting performance. In this study we show that the stable parameter region can be extended by the optimal tuning of system parameters. The optimal parameter regions can be identified by means of stability charts. Since the stability boundaries are highly sensitive to the dynamical parameters of the machine tool, the reliable exploitation of the so-called stability pockets is limited. Still, the lower envelope of the stability lobes is an appropriate upper boundary function for optimization purposes with an objective function taken for maximal material removal rates. This lower envelope is computed by the Robust Stability Computation method presented in the paper. It is shown in this study, that according to theoretical results obtained for optimally tuned cutters, the safe stable machining parameter region can significantly be extended, which has also been validated by machining tests.

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.

Some difficulties associated with the limit equilibrium method of slices

1983 ◽  
Vol 20 (4) ◽  
pp. 661-672 ◽  
Author(s):  
R. K. H. Ching ◽  
D. G. Fredlund
Keyword(s):  
Slope Stability ◽  
Factor Of Safety ◽  
Limit Equilibrium ◽  
Stability Limit ◽  
Limit Equilibrium Method ◽  
Soil Conditions ◽  
Side Force ◽  
Limit Equilibrium Methods ◽  
Equilibrium Method ◽  
The Stability

Several commonly encountered problems associated with the limit equilibrium methods of slices are discussed. These problems are primarily related to the assumptions used to render the inherently indeterminate analysis determinate. When these problems occur in the stability computations, unreasonable solutions are often obtained. It appears that problems occur mainly in situations where the assumption to render the analysis determinate seriously departs from realistic soil conditions. These problems should not, in general, discourage the use of the method of slices. Example problems are presented to illustrate these difficulties and suggestions are proposed to resolve these problems. Keywords: slope stability, limit equilibrium, method of slices, factor of safety, side force function.

A Dynamical Model for Studying the Stability of Thermo-Solutal Convection Under the Effect of Vertical Vibration

2005 ◽  
Author(s):  
Y. P. Razi ◽  
M. Mojtabi ◽  
K. Maliwan ◽  
M. C. Charrier-Mojtabi ◽  
A. Mojtabi
Keyword(s):  
Stability Analysis ◽  
Mechanical Vibration ◽  
Stability Limit ◽  
Lewis Number ◽  
Vertical Vibration ◽  
Wave Number ◽  
Dimensionless Wave Number ◽  
Non Linear ◽  
Linear Differential ◽  
The Stability

This paper concerns the thermal stability analysis of porous layer saturated by a binary fluid under the influence of mechanical vibration. The linear stability analysis of this thermal system leads us to study the following damped coupled Mathieu equations: BH¨+B(π2+k2)+1H˙+(π2+k2)−k2k2+π2RaT(1+Rsinω*t*)H=k2k2+π2(NRaT)(1+Rsinω*t*)Fε*BF¨+Bπ2+k2Le+ε*F˙+π2+k2Le−k2k2+π2NRaT(1+Rsinω*t*)F=k2k2+π2RaT(1+Rsinω*t*)H where RaT is thermal Rayleigh number, R is acceleration ratio (bω2/g), Le is the Lewis number, k is the dimensionless wave-number, ε* is normalized porosity and N is the buoyancy ratio (H and F are perturbations of temperature and concentration fields). In the follow up, the non-linear behavior of the problem is studied via a generalization of the Lorenz model (five coupled non-linear differential equations with periodic coefficients). In the presence or absence of gravity, the stability limit for the onset of stationary as well as Hopf bifurcations is determined.

Added Fluid Mass and the Equations of Motion of a Parachute

1983 ◽  
Vol 34 (3) ◽  
pp. 226-242 ◽  
Author(s):  
John A. Eaton
Keyword(s):  
Equations Of Motion ◽  
Added Mass ◽  
Unsteady Forces ◽  
Fluid Mass ◽  
Mass Tensor ◽  
Body Shapes ◽  
The Stability ◽  
External Forces ◽  
Six Degree Of Freedom ◽  
Nonlinear Solutions

SummaryWhile it has long been known that added fluid mass may be important in the dynamics of parachutes, due to inadequate or incorrect derivation and/or implementation of the added mass tensor its full significance in the stability of parachutes has yet to be appreciated. The concept of added mass is outlined and some general conditions for its significance are presented. Its implementation in the parachute equations of motion is reviewed, and the equations used in previous treatments are shown to be erroneous. A general method for finding the equivalent external forces and moments due to added mass is given, and the correct, anisotropic forms of the added mass tensor are derived for the six degree-of-freedom motion in an ideal fluid of rigid body shapes with planar-, twofold- and axisymmetry, These derivations may also be useful in dynamic stability studies of other low relative density bodies such as airships, balloons, submarines and torpedoes. Full nonlinear solutions of the equations of motion for the axisymmetric parachute have been obtained, and results indicate that added mass effects are more significant than previously predicted. In particular, the component of added mass along the axis of symmetry has a strong influence on stability. Better data on unsteady forces and moments on parachutes are needed.

Stability of Heat Pipes in Vapor-Dominated Systems

1999 ◽  
Author(s):  
Pouya Amili ◽  
Yanis C. Yortsos
Keyword(s):  
Rayleigh Number ◽  
Linear Stability ◽  
Oil Recovery ◽  
Critical Rayleigh Number ◽  
Stability Limit ◽  
Wave Number ◽  
Nuclear Waste Repository ◽  
Geothermal Systems ◽  
Dimensionless Numbers ◽  
The Stability

Abstract We study the linear stability of a two-phase heat pipe zone (vapor-liquid counterflow) in a porous medium, overlying a superheated vapor zone. The competing effects of gravity, condensation and heat transfer on the stability of a planar base state are analyzed in the linear stability limit. The rate of growth of unstable disturbances is expressed in terms of the wave number of the disturbance, and dimensionless numbers, such as the Rayleigh number, a dimensionless heat flux and other parameters. A critical Rayleigh number is identified and shown to be different than in natural convection under single phase conditions. The results find applications to geothermal systems, to enhanced oil recovery using steam injection, as well as to the conditions of the proposed Yucca Mountain nuclear waste repository. This study complements recent work of the stability of boiling by Ramesh and Torrance (1993).

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