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The free vibration of micro-beams is analyzed employing three different beam models. The previously obtained equations of motion for Bernoulli–Euler and Timoshenko models are solved analytically. A higher-order model is devised, which satisfies the lateral boundary conditions of micro-beams. The equations of motion with associated boundary conditions are derived by means of Hamilton's principle. The generalized differential quadrature method is used for the solution of the equations. The first five natural frequencies are obtained for micro-beams with three length-scale parameter/height ratios and five different boundary conditions.
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Noori et al. (2015) studied this question.
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