Coupled extensional-flexural vibration behaviour of a system of elastically connected functionally graded micro-scale panels

Abstract

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 micro-panels, 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 simply-supported edges of the micro-panels, are provided by the Navier’s solution method. The qualitative assessment of the mode...