Frequency Analysis of Nano Sandwich Structure with Nonlocal Effect

2013 ◽  
Vol 829 ◽  
pp. 231-235 ◽  
Author(s):  
Omid Rahmani ◽  
Solmaz Ghaffari
Keyword(s):  
Frequency Analysis ◽  
Sandwich Structure ◽  
Scale Effects ◽  
Nonlocal Elasticity Theory ◽  
Free Vibrations ◽  
Nonlocal Effect ◽  
Small Scale ◽  
Vibration Characteristic ◽  
Sandwich Core ◽  
Scale Coefficient

This study deals with the frequency analysis of Nano-sandwich-structure with nonlocal effect. The model takes into account the flexibility of the sandwich core while the faces are treat as beams. The different stiffness of core will impart different vibration characteristic of the structure. To examine free vibrations of Nano-sandwich-structure, nonlocal elasticity theory has been applied. In this paper an investigation is carried out to understand the small-scale effects in the free vibration. The boundary conditions of simply-supported conditions are described here. Further the effects of scale coefficient and stiffness parameter are studied in this manuscript.

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.

scholarly journals Nonlinear magneto-thermo-elastic vibration of mass sensor armchair carbon nanotube resting on an elastic substrate

2020 ◽  
Vol 7 (1) ◽  
pp. 153-165
Author(s):  
Rajendran Selvamani ◽  
M. Mahaveer Sree Jayan ◽  
Rossana Dimitri ◽  
Francesco Tornabene ◽  
Farzad Ebrahimi
Keyword(s):  
Carbon Nanotube ◽  
Mechanical Response ◽  
Scale Effects ◽  
Nonlocal Elasticity Theory ◽  
Wave Dispersion ◽  
Elastic Vibration ◽  
Ultrasonic Waves ◽  
Small Scale ◽  
Dimensionless Frequency ◽  
Mass Sensors

AbstractThe present paper aims at studying the nonlinear ultrasonic waves in a magneto-thermo-elastic armchair single-walled (SW) carbon nanotube (CNT) with mass sensors resting on a polymer substrate. The analytical formulation accounts for small scale effects based on the Eringen’s nonlocal elasticity theory. The mathematical model and its differential equations are solved theoretically in terms of dimensionless frequencies while assuming a nonlinear Winkler-Pasternak-type foundation. The solution is obtained by means of ultrasonic wave dispersion relations. A parametric work is carried out to check for the effect of the nonlocal scaling parameter, together with the magneto-mechanical loadings, the foundation parameters, the attached mass, boundary conditions and geometries, on the dimensionless frequency of nanotubes. The sensitivity of the mechanical response of nanotubes investigated herein, could be of great interest for design purposes in nano-engineering systems and devices.

scholarly journals Parametric vibrations of graphene sheets based on the double mode model and the nonlocal elasticity theory

2021 ◽  
Author(s):  
Jan Awrejcewicz ◽  
Grzegorz Kudra ◽  
Olga Mazur
Keyword(s):  
Elasticity Theory ◽  
Nonlocal Elasticity ◽  
Nonlinear Oscillations ◽  
Scale Effects ◽  
Equations Of Motion ◽  
Nonlocal Elasticity Theory ◽  
Small Scale ◽  
Largest Lyapunov Exponent ◽  
Graphene Sheets ◽  
Parametric Vibrations

AbstractParametric vibrations of the single-layered graphene sheet (SLGS) are studied in the presented work. The equations of motion govern geometrically nonlinear oscillations. The appearance of small effects is analysed due to the application of the nonlocal elasticity theory. The approach is developed for rectangular simply supported small-scale plate and it employs the Bubnov–Galerkin method with a double mode model, which reduces the problem to investigation of the system of the second-order ordinary differential equations (ODEs). The dynamic behaviour of the micro/nanoplate with varying excitation parameter is analysed to determine the chaotic regimes. As well the influence of small-scale effects to change the nature of vibrations is studied. The bifurcation diagrams, phase plots, Poincaré sections and the largest Lyapunov exponent are constructed and analysed. It is established that the use of nonlocal equations in the dynamic analysis of graphene sheets leads to a significant alteration in the character of oscillations, including the appearance of chaotic attractors.

Effects of DNA Encapsulation on Buckling Instability of Carbon Nanotube Based on Nonlocal Elasticity Theory

2014 ◽  
Author(s):  
Jacob Rafati ◽  
Mohsen Asghari ◽  
Sachin Goyal
Keyword(s):  
Elasticity Theory ◽  
Nonlocal Elasticity ◽  
Scale Effects ◽  
Nonlocal Elasticity Theory ◽  
Van Der Waals Interactions ◽  
Small Scale ◽  
Elastic Rod ◽  
Nano Structure ◽  
Buckling Instability ◽  
Nano Structures

Carbon nanotubes (CNTs) are capable to absorb and encapsulate some molecules to create new hybrid nano-structures providing a variety of functionally useful properties. CNTs functionalized by encapsulaitng single-stranded deoxy-ribonucleic acid (ssDNA) promise great potentials for applications in nanotechnology and nano-biotechnology. In this paper, buckling instability of ssDNA@CNT i.e. hybrid nano-structure composed of ssDNA encapsulated inside CNT has been investigated using the nonlocal elasticity theory. The nonlocal elasticity theory is capable to capture the small scale effects due to the discontinuity of nano-structures at atomic scales. The nonlocal elastic rod and shell equations are derived for modeling ssDNA and CNT respectively. Providing numerical examples, it is predicted that, ssDNA@(10,10) CNT is more resistant than the pristine (10,10) CNT against the buckling instability under radial pressure due to the inter-atomic van der Waals interactions between DNA and CNT. Furthermore, nonlocal elasticity theory predicts lower critical buckling pressure than does the local elasticity theory.

Nonlinear Vibration Analysis of Nano-Disks Based on Nonlocal Elasticity Theory Using Homotopy Perturbation Method

2019 ◽  
Vol 11 (02) ◽  
pp. 1950011 ◽  
Author(s):  
Mohammad Shishesaz ◽  
Mojtaba Shariati ◽  
Amin Yaghootian ◽  
Ali Alizadeh
Keyword(s):  
Perturbation Method ◽  
Elasticity Theory ◽  
Nonlocal Elasticity ◽  
Scale Effects ◽  
Plate Theory ◽  
Free Field ◽  
Nonlocal Elasticity Theory ◽  
Polar Coordinates ◽  
Small Scale ◽  
Classical Plate Theory

This paper introduces a novel approach for small-scale effects on nonlinear free-field vibration of a nano-disk using nonlocal elasticity theory. The formulation of a nano-disk is based on the nonlinear model of von Kármán strain in polar coordinates and classical plate theory. To analyze the nonlinear geometric and small-scale effects, the differential equation based on nonlocal elasticity theory was extracted from Hamilton principle, while the inertial and shear-stress effects were neglected. The equation of motion was discretized using the Galerkin method on selecting an appropriate function based on the boundary condition used for the nano-disk. Due to presence of nonlinear terms, the homotopy method was used in conjunction with the perturbation method (HPM) to ease up the solution and completely solve the problem. For further comparison, the nonlinear equations were solved by the fourth-order Runge–Kutta method, the solution of which was compared with that of HPM. Excellent agreements in results were observed between the two methods, indicating that the latter method can simplify the solution, and hence, can be applied to nonlinear nano-disk problems to seek their solution with a high accuracy.

Buckling Analysis of Orthotropic Nanoscale Plates Resting on Elastic Foundations

2018 ◽  
Vol 55 ◽  
pp. 42-56 ◽  
Author(s):  
Belkacem Kadari ◽  
Aicha Bessaim ◽  
Abdelouahed Tounsi ◽  
Houari Heireche ◽  
Abdelmoumen Anis Bousahla ◽  
...  
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Scale Effects ◽  
Plate Theory ◽  
Constitutive Relations ◽  
Shear Deformation Theory ◽  
Nonlocal Elasticity Theory ◽  
Higher Order ◽  
Small Scale ◽  
Classical Plate Theory

This work presents the buckling investigation of embedded orthotropic nanoplates by using a new hyperbolic plate theory and nonlocal small-scale effects. The main advantage of this theory is that, in addition to including the shear deformation effect, the displacement field is modeled with only three unknowns and three governing equation as the case of the classical plate theory (CPT) and which is even less than the first order shear deformation theory (FSDT) and higher-order shear deformation theory (HSDT). A shear correction factor is, therefore, not required. Nonlocal differential constitutive relations of Eringen is employed to investigate effects of small scale on buckling of the rectangular nanoplate. The elastic foundation is modeled as two-parameter Pasternak foundation. The equations of motion of the nonlocal theories are derived and solved via Navier's procedure for all edges simply supported boundary conditions. The proposed theory is compared with other plate theories. Analytical solutions for buckling loads are obtained for single-layered graphene sheets with isotropic and orthotropic properties. The results presented in this study may provide useful guidance for design of orthotropic graphene based nanodevices that make use of the buckling properties of orthotropic nanoplates. Verification studies show that the proposed theory is not only accurate and simple in solving the buckling nanoplates, but also comparable with the other higher-order shear deformation theories which contain more number of unknowns. Keywords: Buckling; orthotropic nanoplates; a simple 3-unknown theory; nonlocal elasticity theory; Pasternak’s foundations. * Corresponding author; [email protected]

scholarly journals Buckling and Free Vibrations of Nanoplates – Comparison of Nonlocal Strain and Stress Approaches

2019 ◽  
Vol 9 (7) ◽  
pp. 1409 ◽  
Author(s):  
Małgorzata Chwał ◽  
Aleksander Muc
Keyword(s):  
Eigenvalue Problems ◽  
Scale Effects ◽  
Ritz Method ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Free Vibrations ◽  
Small Scale ◽  
Governing Equations ◽  
First Order ◽  
Fundamental Equations

The buckling and free vibrations of rectangular nanoplates are considered in this paper. The refined continuum transverse shear deformation theory (third and first order) is introduced to formulate the fundamental equations of the nanoplate. In addition, the analysis involves the nonlocal strain and stress theories of elasticity to take into account the small-scale effects encountered in nanostructures/nanocomposites. Hamilton’s principle is used to establish the governing equations of the nanoplate. The Rayleigh-Ritz method is proposed to solve eigenvalue problems dealing with the buckling and free vibration analysis of the nanoplates considered. Some examples are presented to investigate and illustrate the effects of various formulations.

scholarly journals Thermo-Mechanical Vibration of Short Carbon Nanotubes Embedded in Pasternak Foundation Based on Nonlocal Elasticity Theory

2013 ◽  
Vol 20 (4) ◽  
pp. 821-832 ◽  
Author(s):  
B. Amirian ◽  
R. Hosseini-Ara ◽  
H. Moosavi
Keyword(s):  
Carbon Nanotubes ◽  
High Temperature ◽  
Aspect Ratio ◽  
Elastic Medium ◽  
Scale Effects ◽  
Mechanical Vibration ◽  
Nonlocal Elasticity Theory ◽  
Small Scale ◽  
Beam Model ◽  
Short Carbon

This study is concerned with the thermal vibration analysis of a short single-walled carbon nanotube embedded in an elastic medium based on nonlocal Timoshenko beam model. A Winkler- and Pasternak-type elastic foundation is employed to model the interaction of short carbon nanotubes and the surrounding elastic medium. Influence of all parameters such as nonlocal small-scale effects, high temperature change, Winkler modulus parameter, Pasternak shear parameter, vibration mode and aspect ratio of short carbon nanotubes on the vibration frequency are analyzed and discussed. The present study shows that for high temperature changes, the effect of Winkler constant in different nonlocal parameters on nonlocal frequency is negligible. Furthermore, for all temperatures, the nonlocal frequencies are always smaller than the local frequencies in short carbon nanotubes. In addition, for high Pasternak modulus, by increasing the aspect ratio, the nonlocal frequency decreases. It is concluded that short carbon nanotubes have the higher frequencies as compared with long carbon nanotubes.

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