Free Vibration analysis of a rectangular functionally graded plate reinforced with carbon nanotubes with simply supported condition on elastic foundation and using a novel trigonometric higher-order theory

This study explores the free vibration analysis of a functionally-graded rectangular plate which has been reinforced by carbon nanotubes (CNT) using the novel theory of trigonometric higher-order shear deformation. Carbon nano-tubes have been distributed through the thickness direction in a linear, symmetric and non-symmetric fashion. The foundation pertaining to Pasternak , or rather duo-parameter, has been utilized in the modeling; moreover, the new mixtures rule has been used for estimating the plate properties. The governing equations have been derived using the Hamilton’s principle, and the Navier’s solution has been used for dealing with a rectangular plate boundary conditions. Lastly, the effects of diverse parameters have been examined upon the vibrational behavior of the plate, such as the different distributions of CNT and the geometric properties of the plate. The results show that the amount of natural frequencies rise in proportion with an increase in the ratio of thickness to the width of the plate (h/b); a decrease in the ratio of length to the width of the plate (a/b); as well as an increase in the coefficients of the elastic foundation, such that the changes in the amounts of natural frequencies will be tremendously decreased in proportion with K> 10000 and K> 1000, and such changes will not be tangible.Furthermore, the highest amounts of frequencies will be pertinent to the X distribution, and the lowest amounts of frequencies will be pertinent to the O distribution