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Nonlinear Differential Equations in Micro/nano Mechanics

  • ID: 5018820
  • Book
  • May 2020
  • Region: Global
  • 270 Pages
  • Elsevier Science and Technology
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Small-scale continuum mechanics theories are powerful tools for modelling miniature structures. By solving the governing equations of structural motion, the physical behaviour of these systems such as static behaviour, vibration and instability can be studied. However, this approach leads to strongly nonlinear ordinary or partial differential equations; there are usually no analytical solutions for these equations.

This book presents a variety of various efficient methods, including Homotopy methods, Adomian methods, reduced order methods, numerical methods, for solving the nonlinear governing equation of micro/nanostructures. Various structures including beam type micro/nano-electromechanical systems (MEMS/NEMS), carbon nanotube and graphene actuators, nano-tweezers, nano-bridges, plate-type microsystems and rotational micromirrors are modelled. Nonlinearity due to physical phenomena such as dispersion forces, damping, surface energies, microstructure-dependency, non-classic boundary conditions and geometry, fluid-solid interactions, elctromechanical instability, electromagnetic instability, nonlocal and size-dependency, are considered in the governing equations. For each solution method several examples are solved in order to better understanding the proposed methods.

This is an important resource for both materials scientists and mechanical engineers, who want to understand more about the underlying theories of nanostructure mechanical behaviour.

  • Establishes the theoretical foundation required for the modeling, simulation, and theoretical analysis of micro/nanostructures and MEMS/NEMS (continuum-based solid mechanics)
  • Covers various solution methods for investigating the behavior of nanostructures (applied mathematics)
  • Provides the simulation of different physical phenomena of the nanostructures

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1. Differential equations in miniature structures 2. Semi-analytical solution methods 3. Numerical methods 4. Dynamic and time-dependent equations

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Koochi, Ali
Dr. Ali Koochi is currently an assistant professor of Mechanical Engineering at the University of Torbat Heydarieh, Iran. He obtained his Ph.D. (2016) from Amirkabir University of Technology (AUT), M.S. degree (2009) from Sharif University of Technology (SUT) and his undergraduate B.S. degree (2006) from AUT. His general academic areas of interest include MEMS/NEMS, Dynamic Instability, Piezo/Magneto Materials, and Applied Mathematics.
Abadyan, Mohamadreza
Dr. Mohamadreza Abadyan received the M.Sc. and Ph.D. degrees in aerospace engineering from Sharif University of Technology, Iran, in 2004 and 2010, respectively. His current research interests include the pull-in performance of MEMS/NEMSnd mechanical behavior of polymer/composites.
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