Nonlinear differential equations in micro/nano mechanics application in micro/nano structures and electromechanical systems / Ali Koochi, Mohamadreza Abadyan.

Format:

Book

Author/Creator:

Koochi, Ali.

Contributor:

Abadyan, Mohamadreza.

ScienceDirect (Online service)

Language:

English

Subjects (All):

Differential equations, Nonlinear.

Physical Description:

1 online resource (272 pages)

Place of Publication:

Amsterdam : Elsevier, 2020.

System Details:

text file

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

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

Notes:

Description based upon print version of record.

4.4.1 Dynamic behavior of a nonlocal nanobridge with the surface effect

Includes index.

Electronic reproduction. Amsterdam Available via World Wide Web.

Other Format:

Print version: Koochi, Ali Nonlinear Differential Equations in Micro/nano Mechanics : Application in Micro/Nano Structures and Electromechanical Systems

ISBN:

9780128192368

0128192364

Publisher Number:

99987442916

Access Restriction:

Restricted for use by site license.