Coupled extensional-flexural vibration behaviour of a system of elastically connected functionally graded micro-scale panels
Keywords:
functionally graded plate, modified couple stress, vibration, size effectAbstract
This study is concerned with the free vibration behaviour of a system of elastically connected functionally graded micro-scale panels. The mechanical properties of the micro-panel are assumed to have a through-thickness variation and governed by a power-law relation in terms of the constituents’ volume fractions. The biharmonic equations governing the motion of each micro-panel are formulated through the adoption of the energy method along with the postulates of the Kirchhoff–Love plate theory. Concentrating on the asynchronous motion of the connected micropanels, the study investigates the shift of the natural frequencies of the system as a result of variation in the: aspect ratio of the micro-panel, span-to-thickness ratio of the micro-panel; gradient index; small-scale effect; and the ratio of the Young’s modulus. Estimates of the natural frequencies, under the assumption of simplysupported edges of the micro-panels, are provided by the Navier’s solution method. The qualitative assessment of the model’s parameters indicates that the effect of the gradient index is stifled by the presence of the size effect. Moreover, it is observed that higher values of the ratio of the constituents’ Young’s modulus generate a stiffer response of the micro-panel than higher values of the connectors’ stiffness and the constituents’ density ratio.
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