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Volume 6, Number 3, September 2018

In the present research, wave propagation characteristics of a rotating FG nanobeam undergoing rotation is studied based on nonlocal strain gradient theory. Material properties of nanobeam are assumed to change gradually across the thickness of nanobeam according to Mori-Tanaka distribution model. The governing partial differential equations are derived for the rotating FG nanobeam by applying the Hamilton's principle in the framework of Euler-Bernoulli beam model. An analytical solution is applied to obtain wave frequencies, phase velocities and escape frequencies. It is observed that wave dispersion characteristics of rotating FG nanobeams are extremely influenced by angular velocity, wave number, nonlocal parameter, length scale parameter, temperature change and material graduation.

Key Words
functionally graded materials; nonlocal strain gradient theory; wave dispersion characteristics; rotating nanobeam

Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University, 3414916818, Qazvin, Iran.

In this study, static bending of an edge cracked cantilever nanobeam composed of functionally graded material (FGM) subjected to transversal point load at the free end of the beam is investigated based on modified couple stress theory. Material properties of the beam change in the height direction according to exponential distributions. The cracked nanobeam is modelled using a proper modification of the classical cracked-beam theory consisting of two sub-nanobeams connected through a massless elastic rotational spring. The inclusion of an additional material parameter enables the new beam model to capture the size effect. The new non-classical beam model reduces to the classical beam model when the length scale parameter is set to zero. The considered problem is investigated within the Euler-Bernoulli beam theory by using finite element method. In order to establish the accuracy of the present formulation and results, the deflections are obtained, and compared with the published results available in the literature. Good agreement is observed. In the numerical study, the static deflections of the edge cracked FGM nanobeams are calculated and discussed for different crack positions, different lengths of the beam, different length scale parameter, different crack depths, and different material distributions. Also, the difference between the classical beam theory and modified couple stress theory is investigated for static bending of edge cracked FGM nanobeams. It is believed that the tabulated results will be a reference with which other researchers can compare their results.

Key Words
open edge crack; modified couple stress theory; functionally graded materials; nanobea

Department of Civil Engineering, Bursa Technical University, Bursa, Turkey.

Polystyrene granules were combined with nanosilver to form a nanocomposite film. One-side migration was conducted to test into three food simulants (3% acetic acid, 10% ethanol and 95% ethanol) at 40

Key Words
migration; nanosilver; simulants; concentration; diffusion coefficient

(1) Jaber Soleimani:
Agricultural Engineering Research Department, East Azarbaijan Agricultural and Natural Resources Educational and Research Center, Agricultural Research, Educational and Extension Organization (AREEO), Tabriz, Iran;
(2) Babak Ghanbarzadeh, Jalal Dehgannya:
Department of Food Science and Technology, Faculty of Agriculture, University of Tabriz, Tabriz, Iran;
(3) Sima Baheri Islami:
Faculty of Mechanical Engineering, Department of Mechanical Engineering, University of Tabriz, Tabriz, Iran;
(4) Saeed M. Sorouraddin:
Department of Analytical Chemistry, Faculty of Chemistry, University of Tabriz, Tabriz, Iran.

Vibration of axially functionally graded nano-rods and beams is investigated. It is assumed that the material properties change along the rod and beam length. The Ritz method with algebraic polynomials is used in the formulation of the problems. Stress gradient elasticity theory is utilized in order to include the nonlocal effects. Frequencies are obtained for different boundary conditions, geometrical and material properties. Nonlocal parameter is assumed as changing linearly or quadratically along the length of the nanostructure. Frequencies are compared to constant nonlocal parameter cases and considerable differences are observed between constant and variable nonlocal parameter cases. Mode shapes in various cases are depicted in order to explain the effects of axial grading.

Key Words
vibration; axially functionally graded; nanorod; nanobeam; nonlocal elasticity

(1) Metin Aydogdu, Mustafa Arda:
Department of Mechanical Engineering, Trakya University, 22130 Edirne, Turkey;
(2) Seckin Filiz:
Corlu Vocational School, Namik Kemal University, 59860 Tekirdag, Turkey.

Present investigation deals with the free vibration characteristics of nanoscale-beams resting on elastic Pasternak\'s foundation based on nonlocal strain-gradient theory and a higher order hyperbolic beam model which captures shear deformation effect without using any shear correction factor. The nanobeam is lying on twoparameters elastic foundation consist of lower spring layers as well as a shear layer. Nonlocal strain gradient theory takes into account two scale parameters for modeling the small size effects of nanostructures more accurately. Hamilton\'s principal is utilized to derive the governing equations of embedded strain gradient nanobeam and, after that, analytical solutions are provided for simply supported conditions to solve the governing equations. The obtained results are compared with those predicted by the previous articles available in literature. Finally, the impacts of nonlocal parameter, length scale parameter, slenderness ratio, elastic medium, on vibration frequencies of nanosize beams are all evaluated.

Key Words
nanobeam; dynamic; nonlocal strain gradient elasticity; pasternak foundation

(1) Ismail Bensaid, Ahmed Bekhadda:
IS2M Laboratory, Mechanical engineering Department, Faculty of Technology, University of Abou Beckr Belkaid (UABT), Tlemcen, Algeria;
(2) Bachir Kerboua:
Mechanical engineering Department, Faculty of Technology, University of Abou Beckr Belkaid (UABT), Tlemcen, Algeria.

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