Large amplitude free vibration of nanobeams with various boundary conditions based on the nonlocal elasticity theory

2014 ◽  
Vol 56 ◽  
pp. 621-628 ◽  
Author(s):  
Mesut Şimşek
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Elasticity Theory ◽  
Large Amplitude ◽  
Nonlocal Elasticity ◽  
Nonlocal Elasticity Theory ◽  
Various Boundary Conditions

Dynamic Analysis of a Viscoelastic Nanobeam

2019 ◽  
Vol 799 ◽  
pp. 223-229 ◽  
Author(s):  
Mustafa Arda ◽  
Metin Aydogdu
Keyword(s):  
Boundary Conditions ◽  
Dynamic Analysis ◽  
Elasticity Theory ◽  
Nonlocal Elasticity ◽  
Initial Conditions ◽  
Nonlocal Elasticity Theory ◽  
Equation Of Motion ◽  
Critical Buckling Load ◽  
Damping Effect ◽  
Material Equation

Vibration of an axially loaded viscoelastic nanobeam is analyzed in this study. Viscoelasticity of the nanobeam is modeled as a Kelvin-Voigt material. Equation of motion and boundary conditions for viscoelastic nanobeam are provided with help of Eringen’s Nonlocal Elasticity Theory. Initial conditions are used in solution of governing equation of motion. Damping effect of the viscoelastic nanobeam structure is investigated. Nonlocal effect on natural frequency and damping of nanobeam and critical buckling load is obtained.

scholarly journals Modeling of smart magnetically affected flexoelectric/piezoelectric nanostructures incorporating surface effects

2017 ◽  
Vol 7 ◽  
pp. 184798041771310 ◽  
Author(s):  
Farzad Ebrahimi ◽  
Mohammad Reza Barati
Keyword(s):  
Boundary Conditions ◽  
Elastic Foundation ◽  
Nonlocal Elasticity ◽  
Nonlocal Parameter ◽  
Surface Elasticity ◽  
Nonlocal Elasticity Theory ◽  
Surface Effects ◽  
Geometrical Parameters ◽  
Various Boundary Conditions ◽  
Buckling Behavior

In this article, electromechanical buckling behavior of size-dependent flexoelectric/piezoelectric nanobeams is investigated based on nonlocal and surface elasticity theories. Flexoelectricity represents the coupling between the strain gradients and electrical polarizations. Flexoelectric/piezoelectric nanostructures can tolerate higher buckling loads compared with conventional piezoelectric ones, especially at lower thicknesses. Nonlocal elasticity theory of Eringen is applied for analyzing flexoelectric/piezoelectric nanobeams for the first time. The flexoelectric/piezoelectric nanobeams are assumed to be in contact with a two-parameter elastic foundation which consists of infinite linear springs and a shear layer. The residual surface stresses which are usually neglected in modeling of flexoelectric nanobeams are incorporated into nonlocal elasticity to provide better understanding of the physics of the problem. Applying an analytical method which satisfies various boundary conditions, the governing equations obtained from Hamilton’s principle are solved. The reliability of the present approach is verified by comparing the obtained results with those provided in literature. Finally, the influences of nonlocal parameter, surface effects plate geometrical parameters, elastic foundation, and boundary conditions on the buckling characteristics of the flexoelectric/piezoelectric nanobeams are explored in detail.

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