Nonlinear differential equations in micro/nano mechanics : application in micro/nano structures and electromechanical systems /

Nonlinear differential equations in micro/nano mechanics : application in micro/nano structures and electromechanical systems /

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Bibliographic Details
Main Author: Koochi, Ali
Other Authors: Abadyan, Mohamadreza
Format: Electronic eBook
Language:English
Published: Amsterdam : Elsevier, 2020.
Subjects:
Differential equations, Nonlinear.
Online Access:CONNECT
Table of Contents:
  • Front Cover
  • Nonlinear Differential Equations in Micro/nano Mechanics
  • Copyright
  • Contents
  • Preface
  • Acknowledgments
  • 1 Differential equations in miniature structures
  • 1.1 Introduction to miniature structures
  • 1.2 Physics of small-scale structures
  • 1.2.1 Electrostatic actuation
  • 1.2.2 Pull-in instability
  • 1.2.3 Dispersion forces
  • 1.2.4 Size dependency
  • 1.2.5 Surface effects
  • 1.2.6 Damping in NEMS/MEMS
  • 1.2.6.1 Drag force
  • 1.2.6.2 Squeezed lm damping
  • 1.2.6.3 Slide lm damping
  • 1.3 Modeling of small-scale structures
  • 1.3.1 Lumped parameter model
  • 1.3.2 Micro/nanoscale continuum mechanics
  • 1.3.2.1 Strain-displacement relations
  • 1.3.2.2 Constitutive equation
  • 1.4 Conclusion
  • References
  • 2 Semianalytical solution methods
  • 2.1 Introduction
  • 2.2 Homotopy perturbation method
  • 2.2.1 Cantilever nanoactuator in van der Waals regime
  • 2.3 Adomian decomposition methods
  • 2.3.1 Conventional Adomian decomposition method
  • 2.3.1.1 Nanoswitch in Casimir regime
  • 2.3.2 Modi ed Adomian decomposition method
  • 2.3.2.1 Size-dependent behavior of the NEMS with elastic boundary condition
  • 2.3.3 Comparison between the conventional and modi ed Adomian decomposition methods
  • 2.4 Green's function methods
  • 2.4.1 General Green's function
  • 2.4.1.1 Carbon-nanotube actuator close to graphite sheets
  • 2.4.2 Monotonic iteration method
  • 2.4.2.1 Size-dependent behavior of the nanowire manufactured nanoswitch
  • 2.5 Differential transformation method
  • 2.5.1 Size-dependent instability of a double-sided nanobridge
  • 2.6 Variation iteration methods
  • 2.6.1 Nanowire manufactured nanotweezers
  • 2.7 Galerkin method for static problems
  • 2.7.1 Circular micromembrane subjected to hydrostatic pressure and electrostatic force
  • 2.8 Conclusion
  • References
  • 3 Numerical solution methods
  • 3.1 Introduction
  • 3.2 Generalized differential quadrature method
  • 3.2.1 Impact of size and surface energies on the performance of nanotweezers
  • 3.2.2 U-shaped nanosensor
  • 3.3 Finite difference method
  • 3.3.1 Nanoactuator in ionic liquid media
  • 3.3.2 Paddle-type nanosensor
  • 3.4 Finite element method
  • 3.4.1 Double-sided nanobridge in Casimir regime
  • 3.4.2 Parallel-plates microcapacitor
  • 3.5 Conclusion
  • References
  • 4 Dynamic and time-dependent equations
  • 4.1 Introduction
  • 4.2 Reduced-order approaches
  • 4.2.1 Galerkin method for dynamic problems
  • 4.2.1.1 Dynamic analysis of narrow nanoactuators
  • 4.2.1.2 Dynamic analysis of narrow nanoactuators with AC actuation
  • 4.2.2 Rayleigh-Ritz method
  • 4.2.2.1 Dynamic analysis of nanowire-based sensor in the accelerating eld
  • 4.3 Runge-Kutta method
  • 4.3.1 Dynamic behavior of rotational nanomirror
  • 4.3.2 Torsion/bending dynamic analysis of a circular nanoscanner
  • 4.4 Homotopy perturbation method for time-dependent differential equations

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