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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

4.4.1 Dynamic behavior of a nonlocal nanobridge with the surface effect

Includes index.