Size-dependent vibration of functionally graded rotating nanobeams with different boundary conditions based on nonlocal elasticity theory

2021 ◽  
pp. 095440622110380
Author(s):  
Jianshi Fang ◽  
Bo Yin ◽  
Xiaopeng Zhang ◽  
Bin Yang
Keyword(s):  
Angular Velocity ◽  
Boundary Conditions ◽  
Elasticity Theory ◽  
Nonlocal Elasticity ◽  
Slenderness Ratio ◽  
Nonlocal Parameter ◽  
Nonlocal Elasticity Theory ◽  
Functionally Graded ◽  
Different Boundary Conditions ◽  
Gradient Variation

The free vibration of rotating functionally graded nanobeams under different boundary conditions is studied based on nonlocal elasticity theory within the framework of Euler-Bernoulli and Timoshenko beam theories. The thickness-wise material gradient variation of the nanobeam is considered. By introducing a second-order axial shortening term into the displacement field, the governing equations of motion of the present new nonlocal model of rotating nanobeams are derived by the Hamilton’s principle. The nonlocal differential equations are solved through the Galerkin method. The present nonlocal models are validated through the convergence and comparison studies. Numerical results are presented to investigate the influences of the nonlocal parameter, angular velocity, material gradient variation together with slenderness ratio on the vibration of rotating FG nanobeams with different boundary conditions. Totally different from stationary nanobeams, the rotating nanobeams with relatively high angular velocity could produce larger fundamental frequencies than local counterparts. Additionally, the axial stretching-transverse bending coupled vibration is perfectly shown through the frequency loci veering and modal conversion.

Wave propagation analysis of size-dependent rotating inhomogeneous nanobeams based on nonlocal elasticity theory

2017 ◽  
Vol 24 (17) ◽  
pp. 3809-3818 ◽  
Author(s):  
Farzad Ebrahimi ◽  
Mohammad Reza Barati ◽  
Parisa Haghi
Keyword(s):  
Elasticity Theory ◽  
Nonlocal Elasticity ◽  
Nonlocal Parameter ◽  
Beam Theory ◽  
Nonlocal Elasticity Theory ◽  
Wave Dispersion ◽  
Functionally Graded ◽  
Wave Number ◽  
Graded Material ◽  
Fg Nanobeam

The present research deals with the wave dispersion behavior of a rotating functionally graded material (FGMs) nanobeam applying nonlocal elasticity theory of Eringen. Material properties of rotating FG nanobeam are spatially graded according to a power-law model. The governing equations as functions of axial force due to centrifugal stiffening and displacements are obtained by employing Hamilton’s principle based on the Euler–Bernoulli beam theory. By using an analytical model, the dispersion relations of the FG nanobeam are derived by solving an eigenvalue problem. Numerical results clearly show that various parameters, such as angular velocity, gradient index, wave number and nonlocal parameter, are significantly effective to characteristics of wave propagations of rotating FG nanobeams. The results can be useful for next generation study and design of nanomachines, such as nanoturbines, nanoscale molecular bearings and nanogears, etc.

Size-Dependent Buckling and Postbuckling Analyses of First-Order Shear Deformable Magneto-Electro-Thermo Elastic Nanoplates Based on the Nonlocal Elasticity Theory

2017 ◽  
Vol 17 (01) ◽  
pp. 1750014 ◽  
Author(s):  
R. Ansari ◽  
R. Gholami
Keyword(s):  
Boundary Conditions ◽  
Elasticity Theory ◽  
Shear Deformation ◽  
Nonlocal Elasticity ◽  
Nonlocal Parameter ◽  
Nonlocal Elasticity Theory ◽  
Small Scale ◽  
First Order ◽  
Size Dependent ◽  
Shear Deformable

This paper presents a nonlocal nonlinear first-order shear deformable plate model for investigating the buckling and postbuckling of magneto-electro-thermo elastic (METE) nanoplates under magneto-electro-thermo-mechanical loadings. The nonlocal elasticity theory within the framework of the first-order shear deformation plate theory along with the von Kármán-type geometrical nonlinearity is used to derive the size-dependent nonlinear governing partial differential equations and associated boundary conditions, in which the effects of shear deformation, small scale parameter and thermo-electro-magneto-mechanical loadings are incorporated. The generalized differential quadrature (GDQ) method and pseudo arc-length continuation algorithm are used to determine the critical buckling loads and postbuckling equilibrium paths of the METE nanoplates with various boundary conditions. Finally, the influences of the nonlocal parameter, boundary conditions, temperature rise, external electric voltage and external magnetic potential on the critical buckling load and postbuckling response are studied.

scholarly journals Double mode model of size-dependent chaotic vibrations of nanoplates based on the nonlocal elasticity theory

2021 ◽  
Author(s):  
Jan Awrejcewicz ◽  
Grzegorz Kudra ◽  
Olga Mazur
Keyword(s):  
Elasticity Theory ◽  
Nonlocal Elasticity ◽  
Scale Effects ◽  
Plate Theory ◽  
Nonlocal Parameter ◽  
Nonlocal Elasticity Theory ◽  
Phase Portraits ◽  
Small Scale ◽  
Governing System ◽  
Account Due

AbstractIn this paper vibrations of the isotropic micro/nanoplates subjected to transverse and in-plane excitation are investigated. The governing equations of the problem are based on the von Kármán plate theory and Kirchhoff–Love hypothesis. The small-size effect is taken into account due to the nonlocal elasticity theory. The formulation of the problem is mixed and employs the Airy stress function. The two-mode approximation of the deflection and application of the Bubnov–Galerkin method reduces the governing system of equations to the system of ordinary differential equations. Varying the load parameters and the nonlocal parameter, the bifurcation analysis is performed. The bifurcations diagrams, the maximum Lyapunov exponents, phase portraits as well as Poincare maps are constructed based on the numerical simulations. It is shown that for some excitation conditions the chaotic motion may occur in the system. Also, the small-scale effects on the character of vibrating regimes are illustrated and discussed.

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.

Sign in / Sign up

Export Citation Format

Share Document