Vibration analysis of three-layered nanobeams based on nonlocal elasticity theory
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Laboratory of Mechanical Modeling and Production (LA2MP), National School of Engineers of Sfax
Laboratory of Applied Mechanics and Engineering (LR-May-ENIT), National School of Engineers of Tunis, Tunisia.
Publication date: 2017-10-15
Journal of Theoretical and Applied Mechanics 2017;55(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.