Synopsis "Nonlinear Differential Equations in Micro (in English)"
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
