Nonlinear Differential Equations in Micro Nano Mechanics

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.

Produk Detail:

  • Author : Ali Koochi
  • Publisher : Elsevier
  • Pages : 123 pages
  • ISBN : 0128192356
  • Rating : 4/5 from 21 reviews
CLICK HERE TO GET THIS BOOKNonlinear Differential Equations in Micro Nano Mechanics

Nonlinear Differential Equations in Micro/Nano Mechanics

Nonlinear Differential Equations in Micro/Nano Mechanics
  • Author : Ali Koochi,Mohamadreza Abadyan
  • Publisher : Elsevier
  • Release : 29 May 2020
GET THIS BOOKNonlinear Differential Equations in Micro/Nano Mechanics

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

Application of Nonlinear Systems in Nanomechanics and Nanofluids

Application of Nonlinear Systems in Nanomechanics and Nanofluids
  • Author : Davood Domairry Ganji,Sayyid Habibollah Hashemi Kachapi
  • Publisher : William Andrew
  • Release : 19 March 2015
GET THIS BOOKApplication of Nonlinear Systems in Nanomechanics and Nanofluids

With Application of Nonlinear Systems in Nanomechanics and Nanofluids the reader gains a deep and practice-oriented understanding of nonlinear systems within areas of nanotechnology application as well as the necessary knowledge enabling the handling of such systems. The book helps readers understand relevant methods and techniques for solving nonlinear problems, and is an invaluable reference for researchers, professionals and PhD students interested in research areas and industries where nanofluidics and dynamic nano-mechanical systems are studied or applied. The book is

Introduction to Micromechanics and Nanomechanics

Introduction to Micromechanics and Nanomechanics
  • Author : Shaofan Li,Gang Wang
  • Publisher : World Scientific Publishing Company
  • Release : 05 December 2017
GET THIS BOOKIntroduction to Micromechanics and Nanomechanics

This book presents a systematic treatise on micromechanics and nanomechanics, which encompasses many important research and development areas such as composite materials and homogenizations, mechanics of quantum dots, multiscale analysis and mechanics, defect mechanics of solids including fracture and dislocation mechanics, etc. In this second edition, some previous chapters are revised, and some new chapters added — crystal plasticity, multiscale crystal defect dynamics, quantum force and stress, micromechanics of metamaterials, and micromorphic theory. The book serves primarily as a graduate textbook

Analytical Methods in Nonlinear Oscillations

Analytical Methods in Nonlinear Oscillations
  • Author : Ebrahim Esmailzadeh,Davood Younesian,Hassan Askari
  • Publisher : Springer
  • Release : 29 June 2018
GET THIS BOOKAnalytical Methods in Nonlinear Oscillations

This book covers both classical and modern analytical methods in nonlinear systems. A wide range of applications from fundamental research to engineering problems are addressed. The book contains seven chapters, each with miscellaneous problems and their detailed solutions. More than 100 practice problems are illustrated, which might be useful for students and researchers in the areas of nonlinear oscillations and applied mathematics. With providing real world examples, this book shows the multidisciplinary emergence of nonlinear dynamical systems in a wide range

Energy Methods for Free Boundary Problems

Energy Methods for Free Boundary Problems
  • Author : S.N. Antontsev,J.I. Diaz,S. Shmarev
  • Publisher : Springer Science & Business Media
  • Release : 06 December 2012
GET THIS BOOKEnergy Methods for Free Boundary Problems

For the past several decades, the study of free boundary problems has been a very active subject of research occurring in a variety of applied sciences. What these problems have in common is their formulation in terms of suitably posed initial and boundary value problems for nonlinear partial differential equations. Such problems arise, for example, in the mathematical treatment of the processes of heat conduction, filtration through porous media, flows of non-Newtonian fluids, boundary layers, chemical reactions, semiconductors, and so

Sixth International Conference on Nonlinear Mechanics (ICNM-6)

Sixth International Conference on Nonlinear Mechanics (ICNM-6)
  • Author : Zhe-wei Zhou
  • Publisher : DEStech Publications, Inc
  • Release : 30 August 2013
GET THIS BOOKSixth International Conference on Nonlinear Mechanics (ICNM-6)

Novel mathematical and modeling approaches to problems in graded materials, biological materials, fluid mechanics and more Covers nanomechanics, multi-scale modeling, interface mechanics and microstructure This series volume contains 128 not previously published research presentations on using nonlinear mechanics to understand and model a wide variety of materials, including polymers, metals and composites, as well as subcellular and cellular tissues. Focus is on numerical and physics approaches to representing multiscale relationships within complex solids and fluids systems, with applications in materials science,

Differential Transformation Method for Mechanical Engineering Problems

Differential Transformation Method for Mechanical Engineering Problems
  • Author : Mohammad Hatami,Davood Domairry Ganji,Mohsen Sheikholeslami
  • Publisher : Academic Press
  • Release : 17 November 2016
GET THIS BOOKDifferential Transformation Method for Mechanical Engineering Problems

Differential Transformation Method for Mechanical Engineering Problems focuses on applying DTM to a range of mechanical engineering applications. The authors modify traditional DTM to produce two additional methods, multi-step differential transformation method (Ms-DTM) and the hybrid differential transformation method and finite difference method (Hybrid DTM-FDM). It is then demonstrated how these can be a suitable series solution for engineering and physical problems, such as the motion of a spherical particle, nanofluid flow and heat transfer, and micropolar fluid flow and

Mathematical Modelling and Numerical Analysis of Size-Dependent Structural Members in Temperature Fields

Mathematical Modelling and Numerical Analysis of Size-Dependent Structural Members in Temperature Fields
  • Author : Jan Awrejcewicz,Vadim A. Krysko,Maxim V. Zhigalov,Anton V. Krysko
  • Publisher : Springer
  • Release : 17 December 2020
GET THIS BOOKMathematical Modelling and Numerical Analysis of Size-Dependent Structural Members in Temperature Fields

This book is devoted to researchers and teachers, as well as graduate students, undergraduates and bachelors in engineering mechanics, nano-mechanics, nanomaterials, nanostructures and applied mathematics. It presents a collection of the latest developments in the field of nonlinear (chaotic) dynamics of mass distributed-parameter nanomechanical structures, providing a rigorous and comprehensive study of modeling nonlinear phenomena. It is written in a unique pedagogical style particularly suitable for independent study and self-education. In addition, the book achieves a good balance between Western

Nonlinear Wave Dynamics of Materials and Structures

Nonlinear Wave Dynamics of Materials and Structures
  • Author : Holm Altenbach,Victor A. Eremeyev,Igor S. Pavlov,Alexey V. Porubov
  • Publisher : Springer Nature
  • Release : 22 April 2020
GET THIS BOOKNonlinear Wave Dynamics of Materials and Structures

This book marks the 60th birthday of Prof. Vladimir Erofeev – a well-known specialist in the field of wave processes in solids, fluids, and structures. Featuring a collection of papers related to Prof. Erofeev’s contributions in the field, it presents articles on the current problems concerning the theory of nonlinear wave processes in generalized continua and structures. It also discusses a number of applications as well as various discrete and continuous dynamic models of structures and media and problems of