Wave Propagation Analysis of Smart Nanostructures 1st Edition by Farzad Ebrahimi, Ali Dabbagh ISBN 0367226952 978-0367226954
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ISBN 10: 0367226952
ISBN 13: 978-0367226954
Author: Farzad Ebrahimi, Ali Dabbagh
Wave Propagation Analysis of Smart Nanostructures presents a mathematical framework for the wave propagation problem of small-scale nanobeams and nanoplates manufactured from various materials, including functionally graded composites, smart piezoelectric materials, smart magneto-electro-elastic materials, smart magnetostrictive materials, and porous materials. In this book, both classical and refined higher-order shear deformation beam and plate hypotheses are employed to formulate the wave propagation problem using the well-known Hamilton’s principle. Additionally, the influences of small-scale nanobeams on the mechanical behaviors of nanostructures are covered using both nonlocal elasticity and nonlocal strain gradient elasticity theories. Impacts of various terms, such as elastic springs of elastic foundation, damping coefficient of viscoelastic substrate, different types of temperature change, applied electric voltage and magnetic potential, and intensity of an external magnetic field on the dispersion curves of nanostructures, are included in the framework of numerous examples.
Table of contents:
1 An Introduction to Wave Theory and Propagation Analysis
1.1 Introduction
1.2 Practical Applications of Waves
1.3 Wave Propagation Solution
1.3.1 Beam-Type Solution
Classical Beams’ Solution
1.3.1.2 Shear Deformable Beams’ Solution
1.3.2 Plate-Type Solution
1.3.2.1 Classical Plates’ Solution
1.3.2.2 Shear Deformable Plates’ Solution
2 An Introduction to Nonlocal Elasticity Theories and Scale-Dependent Analysis in Nanostructures
2.1 Size Dependency: Fundamentals and Literature Review
2.2 Mathematical Formulation of the Nonlocal Elasticity
2.2.1 Constitutive Equation for Linear Elastic Solids
2.2.2 Constitutive Equations of Piezoelectric Materials
2.2.3 Constitutive Equations of Magnetoelectroelastic (MEE) Materials
2.3 Mathematical Formulation of the Nonlocal Strain Gradient Elasticity
2.3.1 Constitutive Equation for Linear Elastic Solids
2.3.2 Constitutive Equations of Piezoelectric Materials
2.3.3 Constitutive Equations of MEE Materials
3 Size-Dependent Effects on Wave Propagation in Nanostructures
3.1 Importance of Wave Dispersion in Nanostructures
3.2 Wave Dispersion in Smart Nanodevices
3.3 Crucial Parameters in Accurate Approximation of the Wave
Propagation Responses in Nanostructures
4 Wave Propagation Characteristics of Inhomogeneous Nanostructures
4.1 Introduction
4.1.1 Functionally Graded Materials (FGMs)
4.1.2 FG Nanostructures
4.2 Homogenization of FGMs
4.2.1 Power-Law Model
4.2.2 Mori-Tanaka Model
4.3 Analysis of FG Nanobeams
4.3.1 Kinematic Relations of Beams
4.3.1.1 Euler-Bernoulli Beam Theory
4.3.1.2 Refined Sinusoidal Beam Theory
4.3.2 Derivation of the Equations of Motion for Beams
4.3.2.1 Equations of Motion of Euler-Bernoulli Beams
4.3.2.2 Equations of Motion of Refined Sinusoidal Beams
4.3.3 Constitutive Equations of FG Nanobeams
4.3.4 The Nonlocal Governing Equations of FG Nanobeams
4.3.5 Wave Solution for FG Nanobeams
4.3.5.1 Solution of Euler-Bernoulli FG Nanobeams
4.3.5.2 Solution of Refined Sinusoidal FG Nanobeams
4.3.6 Numerical Results and Discussion
4.4 Analysis of FG Nanoplates
4.4.1 Kinematic Relations of Plates
4.4.1.1 Classical Plate Theory
4.4.1.2 Refined Sinusoidal Plate Theory
4.4.2 Derivation of the Equations of Motion for Plates
4.4.2.1 Equations of Motion for Classical Plates.
4.4.2.2 Equations of Motion for Refined Sinusoidal Plates
4.4.3 Constitutive Equations of FG Nanoplates
4.4.4 The Nonlocal Governing Equations of FG Nanoplates
4.4.5 Wave Solution for FG Nanoplates
4.4.5.1 Solution of Classical FG Nanoplates
4.4.5.2 Solution of Refined Sinusoidal FG Nanoplates
4.4.6 Numerical Results and Discussion
5 Porosity Effects on Wave Propagation Characteristics of Inhomogeneous Nanostructures
5.1 Introduction
5.1.1 Porous FGM Structures
5.1.2 Porous FGM Nanostructures
5.2 Homogenization of Porous FGMs
5.2.1 Modified Power-Law Porous Model
5.2.2 Coupled Elastic-Kinetic Porous Model.
5.3 Wave Propagation in Porous FG Nanostructures
5.3.1 Analysis of Porous FG Nanobeams
5.3.2 Analysis of Porous FG Nanoplates
6 Wave Propagation Analysis of Smart Heterogeneous Piezoelectric Nanostructures
6.1 Introduction
6.2 Analysis of Piezoelectric FG Nanobeams
6.2.1 Euler-Bemoulli Piezoelectric Nanobeams
6.2.1.1 Motion Equations of Piezoelectric Euler-Bernoulli Beams.
6.2.1.2 Nonlocal Strain Gradient Piezoelectricity for Euler-Bernoulli Nanobeams
6.2.1.3 Governing Equations of Piezoelectric Euler-Bernoulli Nanobeams
6.2.1.4 Wave Solution of the Euler-Bernoulli Piezoelectric Nanobeams
6.2.2 Refined Sinusoidal Piezoelectric Nanobeams
6.2.2.1 Motion Equations of Piezoelectric Refined Shear Deformable Beams
6.2.2.2 Nonlocal Strain Gradient Piezoelectricity for Refined Sinusoidal Nanobeams.
6.2.2.3 Governing Equations of Piezoelectric Refined Sinusoidal Nanobeams
6.2.2.4 Wave Solution of the Refined Piezoelectric Nanobeams
6.2.3 Numerical Results for Piezoelectric Nanobeams
6.3 Analysis of FG Piezoelectric Nanoplates
6.3.1 Classical Piezoelectric Nanoplates
6.3.1.1 Motion Equations of Piezoelectric Kirchhoff-Love Nanoplates
6.3.1.2 Nonlocal Strain Gradient Piezoelectricity for Kirchhoff-Love Nanoplates
6.3.1.3 Governing Equations of Piezoelectric Kirchhoff-Love Nanoplates
6.3.1.4 Wave Solution for the Kirchhoff-Love Piezoelectric Nanoplates
6.3.2 Refined Sinusoidal Piezoelectric Nanoplates
6.3.2.1 Equations of Motion of Piezoelectric Refined Sinusoidal Nanoplates
6.3.2.2 Nonlocal Strain Gradient Piezoelectricity for Refined Sinusoidal Nanoplates
6.3.2.3 Governing Equations of Piezoelectric Refined Sinusoidal Nanoplates
6.3.2.4 Wave Solution for the Refined Sinusoidal Piezoelectric Nanoplates
6.3.3 Numerical Results for Piezoelectric Nanoplates
7 Wave Dispersion Characteristics of Magnetostrictive Nanostructures
7.1 Magnetostriction and Magnetostrictive Materials
7.2 Velocity Feedback Control System
7.3 Constitutive Equations of Magnetostrictive Nanostructures
7.4 Derivation of the Governing Equations
7.4.1 Goveming Equations of Magnetostrictive Nanobeams
7.4.2 Governing Equations of Magnetostrictive Nanoplates
7.5 Solution Procedure
7.5.1 Arrays of Damping Matrix of Nanobeams
7.5.2 Arrays of Damping Matrix of Nanoplates
7.6 Numerical Results and Discussion
8 Wave Propagation Analysis of Magnetoelectroelastic Heterogeneous
Nanostructures
8.1 Introduction
8.2 Analysis of MEE-FG Nanobeams
8.2.1 Euler-Bernoulli MEE Nanobeams
8.2.1.1 Motion Equations of MEE Euler-Bernoulli Beams
8.2.1.2 Nonlocal Strain Gradient Magnetoelectroelasticity Euler-Bernoulli Nanobeams
for
8.2.1.3 Governing Equations of MEE Euler-Bernoulli Nanobeams
8.2.1.4 WaveSolution of the MEE Euler-Bernoulli Nanobeams
8.2.2 Refined Sinusoidal MEE Nanobeams
8.2.2.1 Equations of Motion of MEE Refined Sinusoidal Beams
8.2.2.2 Nonlocal Strain Gradient Magnetoelectroelasticity for Refined Sinusoidal Nanobeams
8.2.2.3 Governing Equations of MEE Refined Sinusoidal Nanobeams
8.2.2.4 Wave Solution of MEE Refined Sinusoidal Nanobeams
8.2.3 Numerical Results about MEE Nanobeams
8.3 Analysis of MEE-FG Nanoplates
8.3.1 Kirchhoff-Love MEE Nanoplates
8.3.1.1 Equations of Motion of MEE Kirchhoff-Love Plates
8.3.1.2 Nonlocal Strain Gradient Magnetoelectroelasticity for Kirchhoff-Love Nanoplates
8.3.1.3 Governing Equations of MEE Kirchhoff-Love Nanoplates
8.3.1.4 Wave Solution of MEE Kirchhoff-Love Nanoplates
8.3.2 Refined Sinusoidal MEE Nanoplate.
8.3.2.1 Equations of Motion of MEE Refined Sinusoidal Plates
8.3.2.2 Nonlocal Strain Gradient Magnetoelectroelasticity for Refined Sinusoidal Nanoplates
8.3.2.3 Governing Equations of MEE Refined Sinusoidal Nanoplates
8.3.2.4 Wave Solution of MEE Refined Sinusoidal Nanoplates
8.3.3 Numerical Results for MEE Nanoplates
9 Effect of Various Resting Media on Wave Dispersion Characteristics of Smart Nanostructures
9.1 Winkler Foundation
9.1.1 Analysis of Nanobeams Embedded on Winkler Foundation
9.1.2 Analysis of Nanoplates Embedded on Winkler Foundation
9.2 Winkler-Pasternak Foundation
9.2.1 Analysis of Nanobeams Embedded on Winkler-Pasternak Foundation
9.2.2 Analysis of Nanoplates Embedded on Winkler-Pasternak Foundation
9.3 visco-Pasternak Foundation
9.3.1 Analysis of Nanobeams Embedded on visco-Pasternak Foundation
9.3.2 Analysis of Nanoplates Embedded on visco-Pasternak Foundation
9.4 Numerical Results and Discussion
10 Thermal Effects on Wave Propagation Characteristics of Smart Nanostructures
10.1 Introduction
10.2 Analysis of FG Nanobeams
10.3 Analysis of FG Nanoplates
10.4 Different Types of Temperature Raise
10.4.1 Uniform Temperature Raise (UTR)
10.4.2 Linear Temperature Raise (LTR)
10.4.3 Sinusoidal Temperature Raise (STR)
10.4.4 Nonlinear Temperature Raise (NLTR)
10.5 Numerical Results and Discussion
11 Magnetic Field Effects on Wave Propagation Characteristics of Smart
Nanostructures
11.1 Introduction
11.2 Maxwell’s Relations
11.3 Analysis of FG Nanobeams
11.4 Analysis of FG Nanoplates
11.5 Numerical Results and Discussion
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Tags: Farzad Ebrahimi, Ali Dabbagh, Wave Propagation, Analysis of Smart Nanostructures