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2 Journal of Theoretical and Applied Mechanics

2 2017

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Vibration analysis of three-layered nanobeams based on nonlocal elasticity theory

Kammoun N., Jrad H., Bouaziz S., Soula M., Haddar M.

Journal of Theoretical and Applied Mechanics

2017

Vol. 55 nr 4

1299--1312

In this paper, the first investigation on free vibration analysis of three-layered nanobeams with the shear effect incorporated in the mid-layer based on the nonlocal theory and both Euler Bernoulli and Timoshenko beams theories is presented. Hamilton’s formulation is applied to derive governing equations and edge conditions. In order to solve differential equations of motions and to determine natural frequencies of the proposed three-layered nanobeams with different boundary conditions, the generalized differential quadrature (GDQM) is used. The effect of the nanoscale parameter on the natural frequencies and deflection modes shapes of the three layered-nanobeams is discussed. It appears that the nonlocal effect is important for the natural frequencies of the nanobeams. The results can be pertinent to the design and application of MEMS and NEMS.

Numerical creep analysis of FGM rotating disc with GDQ method

Zharfi H., Toussi H. E.

Journal of Theoretical and Applied Mechanics

2017

Vol. 55 nr 1

331--341

Rotating discs are the vital part of many kinds of machineries. Usually, they are operating at relatively high angular velocity and temperature conditions. Accordingly, in practice, the creep analysis is an essential necessity in the study of rotating discs. In this paper, the time dependent creep analysis of a thin Functionally Graded Material (FGM) rotating disc investigated using the Generalized Differential Quadrature (GDQ) method. Creep is described with Sherby’s constitutive model. Secondary creep governing equations are derived and solved for a disc with two various boundary conditions and with linear distribution of SiC particles in pure Aluminum matrix. Since the creep rates are a function of stresses, time and temperature, there is not a closed form solution to these equations. Using a solution algorithm and the GDQ method, a solution procedure for these nonlinear equations is presented. Comparison of the results with other existing creep studies in literature reveals the robustness, precision and high efficiency beside rapid convergence of the present approach.