In-Plane Functionally Graded Plates: A Study on the Free Vibration and Dynamic Instability Behaviours

Abstract Functionally graded materials are well-known composite materials, characterized by a continuously varying mixture of materials’ phases, tailored to meet structures operating requirements while contributing to minimize abrupt stress transitions at dissimilar materials’ interfaces, as occur in composite laminates. Hence, designing a functionally graded material to comply with these objectives constitutes an important modelling tool to improve structures’ functionality. These graded composite materials present more commonly a mixture variation through the structures’ thickness direction. However, when dealing with thin structures this solution may present evident limitations, both from the manufacturing perspective as well as from the through-thickness distribution influence on the structure response. It is therefore important to explore other spatial mixture distributions’ possibilities. To this purpose, the present work considers thin graded materials’ plates which constitution is defined by a set of different in-plane volume fraction distributions. The influence of these distributions on the free vibrations and dynamic instability of thin plates is assessed through a comprehensive set of parametric studies. The free vibration problem and the dynamic instability problem’ solutions are respectively obtained by Rayleigh-Ritz and Bolotin’s methods. As a complementary analysis contribution, image correlation studies are also developed for a set of fundamental mode shapes.