The size effect on the free vibration and bending of a curved FG micro/nanobeam is studied in this paper. Using the Hamilton principle the differential equations and boundary conditions is derived for a nonlocal Euler-Bernoulli curved micro/nanobeam. The material properties vary through radius direction. Using the Navier approach an analytical solution for simply supported boundary conditions is obtained where the power index law of FGM, the curved micro/nanobeam opening angle, the effect of aspect ratio and nonlocal parameter on natural frequencies and the radial and tangential displacements were analyzed. It is concluded that increasing the curved micro/nanobeam opening angle results in decreasing and increasing the frequencies and displacements, respectively. To validate the natural frequencies of curved nanobeam, when the radius of it approaches to infinity, is compared with a straight FG nanobeam and showed a good agreement.
In this article, generalized differential quadrature method (GDQM) is used to study the free vibrational behavior of variable cross section nano beams. Eringen's nonlocal elastic theory is taken into account to model the small scale effects and nonuniformity is assumed by exponentially varying the width of nano beam. Governing equation of motion is solved using generalized differential quadrature method with different numbers of sampling points. Effects of increasing the sampling points in reaching more accurate results for first three frequency parameters are presented and it is shown that after a specific number of sampling points, results merge to a certain accurate number. It is concluded that generalized differential quadrature method is able to reach the correct answers comparing to analytical results. Moreover, due to the stiffness softening behavior of small-scale structures, necessity of using Eringen's nonlocal elastic theory to model the small scale effects due to the frequency variation is observed. |
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