This paper develops a micro-scale vibration analysis of micro-plates using higher-order shear and normal deformable plate theory in conjunction with modiﬁed couple stress theory. The present model includes one material length scale parameter which takes into account the size effects. The equations of motions and boundary conditions are derived using Hamilton’s principle. Analytical solutions for the free vibration problem of simply supported rectangular micro-plates are obtained. Numerical results are presented to illustrate the effect of small scale on the dynamic response of functionally graded micro- plates. The results show that the size-dependent effect increases the stiffness of the micro-plate and consequently increases the natural frequencies. Keywords Functionally graded Modiﬁed couple stress theory Higher-order shear and normal deformable plate theory Thick micro-plates 1 Introduction reduce to the micron scales, the stiffness and strength of materials increase because of material size effect. It is well Functionally graded materials (FGMs) are non-homoge- known that classical continuum theories do not include the neous composites that identify with their smooth and size effect in micro-scale structures. In order to overcome continuous variations in one or more directions. They are this deﬁciency, many higher-order theories such as classi- usually a combination of two
Iranian Journal of Science and Technology, Transactions of Mechanical Engineering – Springer Journals
Published: Jun 4, 2018
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