Free vibration analysis of functionally graded folded plates under thermal environment

Abstract

Functionally graded materials (FGMs) are new materials whose properties change gradually in respect to their dimensions. This group of materials shows a tremendous improvement of previously used composite materials. FGM consists of two or more materials whose combination enables the achievement of specified properties in accordance with the desired application. The Ceramic-Metal FGMs can be designed to reduce thermal stresses and take advantage of the corrosion and heat resistances of ceramic and the mechanical strength, good machinability, high toughness and bonding capability of metals without severe internal thermal stresses. Use of folded plates are common nowadays for many types of structures. Judicial use of folds increases the stiffness of the structure and hence its load carrying capacity. As the FGMs are most likely to be used in the high thermal environments, the free vibration analysis, a fundamental dynamic characteristic, of FGM flat and folded plates under thermal environment holds significant importance in understanding their mechanical behaviour and potential applications. Modal analysis of all side clamped (CCCC) FGM rectangular flat and folded plates in the thermal environment is done based on the First-order transverse shear deformation theory (FSDT). Material properties are assumed to be dependent on temperature and vary continuously in thickness direction according to power law distribution. A finite element program in MATLAB environment is developed for the present study applying folded plate transformation considering 8-noded isoparametric elements with 6 degrees of freedom per node. The effect of various parameters like crank angle β, different side to thickness ratios (b/h ratio), temperature field (uniform/linear/non-linear temperature rise) and gradient indices on the natural frequencies of FG rectangular flat and folded plates is studied. It is observed that increasing thermal load reduces the stiffness of the structure considerably. Stiffer sections can withstand more temperature than thinner sections. Presence of ridge line in folded plates make the structure stiffer compared to flat plate and hence is capable of resisting higher thermal load. The calculated results have been validated with the existing literature. The thesis also gives an overview of the existing literature on the area of different classifications, various fabrication methods and applications of the FGMs. In recent decades, the exploration of FGMs' free vibration behavior has attracted the attention of researchers across mechanical, aerospace, civil, and biomedical engineering disciplines. The inherent complexity stemming from varying material properties within FGM plates, coupled with diverse boundary conditions and geometric configurations, necessitates advanced computational techniques for accurate analysis.