EFFECTS OF CASIMIR AND VAN DER WAALS FORCES ON THE PULL-IN INSTABILITY OF THE NONLINEAR MICRO AND NANO-BRIDGE GYROSCOPES

2014 ◽  
Vol 14 (02) ◽  
pp. 1350059 ◽  
Author(s):  
M. MOJAHEDI ◽  
M. T. AHMADIAN ◽  
K. FIROOZBAKHSH
Keyword(s):  
Numerical Methods ◽  
Nonlinear Equations ◽  
Proof Mass ◽  
Van Der Waals ◽  
Van Der Waals Forces ◽  
System Of Nonlinear Equations ◽  
Coriolis Forces ◽  
Homotopy Perturbation ◽  
Extended Hamilton’S Principle ◽  
Fringing Field

The influence of Casimir and van der Waals forces on the instability of vibratory micro and nano-bridge gyroscopes with proof mass attached to its midpoint is studied. The gyroscope subjected to the base rotation, Casimir and van der Waals attractions is actuated and detected by electrostatic methods. The system has two coupled bending motions actuated by the electrostatic and Coriolis forces. First a system of nonlinear equations for the flexural-flexural deflection of beam gyroscopes is derived using the extended Hamilton's principle. In modeling, the nonlinearities due to mid-plane stretching, electrostatic forces, including fringing field, Casimir and van der Waals attractions, are considered. The method of homotopy perturbation is used to solve the equations of equilibrium, with the solution validated by numerical methods. In addition, the effect of nondimensional parameters on the instability and deflection of the gyroscope is investigated. The data presented can be used in the design of vibratory micro/nano gyroscopes.

Oscillatory Behavior of the Nonlinear Clamped-Free Beam Microgyroscopes Under Electrostatic Actuation and Detection

2013 ◽  
Author(s):  
Mahdi Mojahedi ◽  
Mohammad Taghi Ahmadian ◽  
Keikhosrow Firoozbakhsh ◽  
Ahmad Barari
Keyword(s):  
Proof Mass ◽  
Angular Rate ◽  
Longitudinal Axis ◽  
Oscillatory Behavior ◽  
Structural Vibration ◽  
System Of Nonlinear Equations ◽  
Angular Rotation ◽  
Electrostatically Actuated ◽  
Fringing Field ◽  
Tip Mass

Vibratory Micromachined gyroscopes use suspending mechanical parts to measure rotation. They have no gyratory component that require bearings, and for this reason they can be easily miniaturized and batch production using micromachining methods. They operate based on the energy interchange between two modes of structural vibration. The objective of this paper is to study the oscillatory behavior of an electrostatically actuated vibrating microcantilever gyroscope with proof mass at its end. In the modelling, the effects of different nonlinearities, fringing field and base rotation are considered. The microgyroscope is subjected to coupled bending oscillations around the static deflection which are coupled by base rotation. The primary oscillation is generated in drive direction of microgyroscope by applying a pair of DC and AC voltages in the tip mass. Secondary oscillation in sense direction is induced by Coriolis coupling when the beam has the input angular rate along longitudinal axis. Input angular rotation can be measured by sensing oscillation tuned by another DC voltage applied to the proof mass. First a system of nonlinear equations which describes flexural-flexural motion of electrostatically actuated microbeam gyroscopes under input rotation, is derived by extended Hamilton principle. The oscillatory behavior of microgyroscopes is then analytically investigated, where the microgyroscopes are predeformed by DC voltages in both directions. The effects of the nondimensional parameters on the natural frequencies of the system are discussed at the end of the paper.

OSCILLATORY BEHAVIOR OF AN ELECTROSTATICALLY ACTUATED MICROCANTILEVER GYROSCOPE

2013 ◽  
Vol 13 (06) ◽  
pp. 1350030 ◽  
Author(s):  
M. MOJAHEDI ◽  
M. T. AHMADIAN ◽  
K. FIROOZBAKHSH
Keyword(s):  
Natural Frequencies ◽  
Proof Mass ◽  
Angular Rate ◽  
Oscillatory Behavior ◽  
System Of Nonlinear Equations ◽  
Angular Rotation ◽  
Electrostatically Actuated ◽  
Fringing Field ◽  
Tip Mass ◽  
Secondary Oscillation

This paper is concerned with the study of the oscillatory behavior of an electrostatically actuated microcantilever gyroscope with a proof mass attached to its free end. In mathematical modeling, the effects of different nonlinearities such as electrostatic forces, fringing field, inertial terms and geometric nonlinearities are considered. The microgyroscope is subjected to bending oscillations around the static deflection coupled with base rotation. The primary oscillation is generated in drive direction of the microgyroscope by a pair of DC and AC voltages on the tip mass. The secondary oscillation occurring in the sense direction is induced by the Coriolis coupling caused by the input angular rate of the beam along its axis. The input angular rotation can be measured by sensing the oscillation tuned to another DC voltage of the proof mass. First, a system of nonlinear equations governing the flexural–flexural motion of electrostatically actuated microbeam gyroscopes subjected to input rotations is derived by the extended Hamilton principle. The oscillatory behavior of the microgyroscopes subjected to DC voltages in both directions is then analytically investigated. Finally, the effects of the geometric parameters, base rotation and fringing field on the natural frequencies of the system are assessed.

Self-Assembly of a Chiral Cubic Three-Connected Net from the High Symmetry Molecules C60 and SnI4

2020 ◽  
Author(s):  
Daniel B. Straus ◽  
Robert J. Cava
Keyword(s):  
Organic Synthesis ◽  
Self Assembly ◽  
Van Der Waals ◽  
Van Der Waals Forces ◽  
High Symmetry ◽  
Molecular Chirality ◽  
Chiral Materials ◽  
Self Assembled ◽  
Chiral Centers

The design of new chiral materials usually requires stereoselective organic synthesis to create molecules with chiral centers. Less commonly, achiral molecules can self-assemble into chiral materials, despite the absence of intrinsic molecular chirality. Here, we demonstrate the assembly of high-symmetry molecules into a chiral van der Waals structure by synthesizing crystals of C<sub>60</sub>(SnI<sub>4</sub>)<sub>2</sub> from icosahedral buckminsterfullerene (C<sub>60</sub>) and tetrahedral SnI4 molecules through spontaneous self-assembly. The SnI<sub>4</sub> tetrahedra template the Sn atoms into a chiral cubic three-connected net of the SrSi<sub>2</sub> type that is held together by van der Waals forces. Our results represent the remarkable emergence of a self-assembled chiral material from two of the most highly symmetric molecules, demonstrating that almost any molecular, nanocrystalline, or engineered precursor can be considered when designing chiral assemblies.

Solving System of Nonlinear Equations using Genetic Algorithm

2019 ◽  
Vol 10 (4) ◽  
pp. 877-886 ◽  
Author(s):  
Chhavi Mangla ◽  
Musheer Ahmad ◽  
Moin Uddin
Keyword(s):  
Genetic Algorithm ◽  
Nonlinear Equations ◽  
System Of Nonlinear Equations

scholarly journals Nanotube‐Based 1D Heterostructures Coupled by van der Waals Forces

Small ◽  
2021 ◽  
pp. 2102585
Author(s):  
Sofie Cambré ◽  
Ming Liu ◽  
Dmitry Levshov ◽  
Keigo Otsuka ◽  
Shigeo Maruyama ◽  
...  
Keyword(s):  
Van Der Waals ◽  
Van Der Waals Forces

scholarly journals Tuning adlayer-substrate interactions of graphene/h-BN heterostructures on Cu(111)–Ni and Ni(111)–Cu surface alloys

RSC Advances ◽  
2021 ◽  
Vol 11 (4) ◽  
pp. 1916-1927
Author(s):  
Jianmei Huang ◽  
Qiang Wang ◽  
Pengfei Liu ◽  
Guang-hui Chen ◽  
Yanhui Yang
Keyword(s):  
Long Range ◽  
Van Der Waals ◽  
Van Der Waals Forces ◽  
Alloy Surface ◽  
Surface Alloys ◽  
Substrate Interactions

The evolution of the interface and interaction of h-BN and graphene/h-BN (Gr/h-BN) on Cu(111)–Ni and Ni(111)–Cu surface alloys versus the Ni/Cu atomic percentage on the alloy surface were comparatively studied by DFT-D2, including critical long-range van der Waals forces.

scholarly journals A Comparative Analysis of Fractional-Order Gas Dynamics Equations via Analytical Techniques

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1735
Author(s):  
Shuang-Shuang Zhou ◽  
Nehad Ali Shah ◽  
Ioannis Dassios ◽  
S. Saleem ◽  
Kamsing Nonlaopon
Keyword(s):  
Homotopy Perturbation Method ◽  
Graphical Representation ◽  
Analytical Techniques ◽  
Variational Iteration Method ◽  
Computational Techniques ◽  
System Of Nonlinear Equations ◽  
Gas Dynamics Equations ◽  
Homotopy Perturbation ◽  
Fractional System ◽  
Modified Forms

This article introduces two well-known computational techniques for solving the time-fractional system of nonlinear equations of unsteady flow of a polytropic gas. The methods suggested are the modified forms of the variational iteration method and the homotopy perturbation method by the Elzaki transformation. Furthermore, an illustrative scheme is introduced to verify the accuracy of the available techniques. A graphical representation of the exact and derived results is presented to show the reliability of the suggested approaches. It is also shown that the findings of the current methodology are in close harmony with the exact solutions. The comparative solution analysis via graphs also represents the higher reliability and accuracy of the current techniques.

Sign in / Sign up

Export Citation Format

Share Document