Nonlinear free vibration of nanotube with small scale effects embedded in viscous matrix

2014 ◽  
Vol 60 ◽  
pp. 45-51 ◽  
Author(s):  
Yi-Ze Wang ◽  
Feng-Ming Li
Keyword(s):  
Free Vibration ◽  
Scale Effects ◽  
Small Scale ◽  
Nonlinear Free Vibration

Nonlinear free vibration of skew nanoplates with surface and small scale effects

2014 ◽  
Vol 78 ◽  
pp. 48-56 ◽  
Author(s):  
P. Malekzadeh ◽  
M.R. Golbahar Haghighi ◽  
M. Shojaee
Keyword(s):  
Free Vibration ◽  
Scale Effects ◽  
Small Scale ◽  
Nonlinear Free Vibration

A Novel Refined Plate Theory for Free Vibration Analyses of Single-Layered Graphene Sheets Lying on Winkler-Pasternak Elastic Foundations

2019 ◽  
Vol 58 ◽  
pp. 151-164 ◽  
Author(s):  
Fatima Boukhatem ◽  
Aicha Bessaim ◽  
Abdelhakim Kaci ◽  
Abderrahmane Mouffoki ◽  
Mohammed Sid Ahmed Houari ◽  
...  
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Elastic Foundation ◽  
Displacement Field ◽  
Scale Effects ◽  
Plate Theory ◽  
Small Scale ◽  
Graphene Sheets ◽  
Refined Plate Theory ◽  
Foundation Parameters

In this article, the analyses of free vibration of nanoplates, such as single-layered graphene sheets (SLGS), lying on an elastic medium is evaluated and analyzed via a novel refined plate theory mathematical model including small-scale effects. The noteworthy feature of theory is that the displacement field is modelled with only four unknowns, which is even less than the other shear deformation theories. The present one has a new displacement field which introduces undetermined integral variables, the shear stress free condition on the top and bottom surfaces of the plate is respected and consequently, it is unnecessary to use shear correction factors. The theory involves four unknown variables, as against five in case of other higher order theories and first-order shear deformation theory. By using Hamilton’s principle, the nonlocal governing equations are obtained and they are solved via Navier solution method. The influences played by transversal shear deformation, plate aspect ratio, side-to-thickness ratio, nonlocal parameter, and elastic foundation parameters are all examined. From this work, it can be observed that the small-scale effects and elastic foundation parameters are significant for the natural frequency.

Nonlinear free vibration of orthotropic graphene sheets using nonlocal Mindlin plate theory

2011 ◽  
Vol 226 (7) ◽  
pp. 1896-1906 ◽  
Author(s):  
AR Setoodeh ◽  
P Malekzadeh ◽  
AR Vosoughi
Keyword(s):  
Free Vibration ◽  
Virtual Work ◽  
Plate Theory ◽  
Differential Quadrature Method ◽  
Nonlinear Partial Differential Equations ◽  
Mindlin Plate ◽  
Small Scale ◽  
Graphene Sheets ◽  
Nonlinear Free Vibration ◽  
Mindlin Plate Theory

This article deals with the small-scale effect on the nonlinear free vibration of orthotropic single-layered graphene sheets using the nonlocal elasticity plate theory. The formulations are based on the Mindlin plate theory, and von Karman-type nonlinearity is considered in strain displacement relations. Virtual work principle is used to derive the nonlinear nonlocal plate equations in which the effects of rotary inertia and transverse shear are included. The differential quadrature method is employed to reduce the governing nonlinear partial differential equations to a system of nonlinear algebraic eigenvalue equations. The efficiency and accuracy of the method are demonstrated by comparing the developed result with those available in literature. The methodology is capable of studying large-amplitude vibration characteristics of nanoplates with different sets of boundary conditions. The effects of various parameters on the nonlinear vibrations of nanoplates are presented.

scholarly journals Free Vibration Analysis of Simply Supported P-FGM Nanoplate Using a Nonlocal Four Variables Shear Deformation Plate Theory

2019 ◽  
Vol 69 (4) ◽  
pp. 9-24 ◽  
Author(s):  
Chikh Abdelbaki
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Power Law ◽  
Material Properties ◽  
Scale Effects ◽  
Plate Theory ◽  
Functionally Graded ◽  
Small Scale ◽  
Simply Supported ◽  
Shear Deformation Plate Theory

AbstractThis paper shows an analysis of the free vibration of functionally graded simply supported nanoplate. The nonlocal four variables shear deformation plate theory is used to predict the free vibration frequencies of functionally graded nanoplate simply supported using non-local elasticity theory with the introduction of small-scale effects. The effect of the material properties, thickness-length ratio, aspect ratio, the exponent of the power law, the vibration mode is presented, the current solutions are compared to those obtained by other researchers. Equilibrium equations are obtained using the virtual displacements principle. P-FGM Power law is used to have a distribution of material properties that vary across the thickness. The results are in good agreement with those of the literature.

Effects of couple stresses on the in-plane vibration of micro-rotating disks

2020 ◽  
Vol 26 (13-14) ◽  
pp. 1246-1259
Author(s):  
Emadoddin Bagheri ◽  
Mostafa Jahangiri ◽  
Mohsen Asghari
Keyword(s):  
Free Vibration ◽  
Mechanical Behavior ◽  
Couple Stress ◽  
Scale Effects ◽  
Couple Stress Theory ◽  
Modified Couple Stress Theory ◽  
Small Scale ◽  
Rotating Disks ◽  
Stress Theory ◽  
Modified Couple Stress

Micro-rotating disks are extensively used in micro-electromechanical systems such as micro-gyroscopes and micro-rotors. Because of the sensitivity of these elements, enough knowledge about the mechanical behavior of these structures is an essential matter for designers and fabricators. The small-scale effects on the in-plane free vibration of such micro-disks present an important aspect of the mechanical behavior of these elements. The small-scale effects on the in-plane free vibration of these micro-disks are investigated in this study using the modified couple stress theory. By using the Hamilton principle, the partial differential equations governing the coupled radial and tangential motion of the disk particles with their corresponding boundary conditions are derived. Then, the solution for the boundary value problem is analytically presented. The effects of the angular speed of the micro-disks and the length scale parameter of the modified couple stress theory on the steady radial and tangential displacements, and on the natural frequencies are investigated. Those results are compared with the ones previously obtained from the classical continuum mechanics analysis.

Differential quadrature solutions for the nonconservative instability of a class of single-walled carbon nanotubes

2018 ◽  
Vol 35 (1) ◽  
pp. 251-267 ◽  
Author(s):  
Maria Anna De Rosa ◽  
Maria Lippiello ◽  
Stefania Tomasiello
Keyword(s):  
Free Vibration ◽  
Scale Effects ◽  
Nonlocal Parameter ◽  
Added Mass ◽  
Differential Quadrature ◽  
Small Scale ◽  
Numerical Schemes ◽  
Content Type ◽  
Single Walled Carbon ◽  
Integration Schemes

Purpose The purpose of the present paper is to investigate the nonconservative instability of a single-walled carbon nanotube (SWCNT) with an added mass through nonlocal theories. The governing equations are discretized by means of the differential quadrature (DQ) rules, as introduced by Bellman and Casti. DQ rules have been largely used in engineering and applied sciences. Recently, they were applied to enhance some numerical schemes, such as step-by-step integration schemes and Picard-like numerical schemes. Design/methodology/approach In the present paper, the DQ rules are used to investigate the nonconservative instability of a SWCNT through nonlocal theories. Findings To show the sensitivity of the SWCNT to the values of added mass and the influence of nonlocal parameter on the fundamental frequencies values, some numerical examples have been performed and discussed. Yet, the effect of the different boundary conditions on the instability behaviour has been investigated. The validity of the present model has been confirmed by comparing some results against the ones available in literature. Originality/value Applying the nonlocal elasticity theory, this paper presents a re-formulation of Hamilton’s principle for the free vibration analysis of a uniform Euler–Bernoulli nanobeam. The main purpose of this paper is to investigate the free vibration response of an SWCNT with attached mass and for various values of small scale effects.

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.

Sign in / Sign up

Export Citation Format

Share Document