Article Vibration analysis of functionally graded circular plates of variable thickness under thermal environment by generalized differential quadrature method Roshan Lal and Rahul Saini Abstract The vibration of functionally graded circular plates of variable thickness under a thermal environment is analyzed when the nodal lines are concentric circles by using the generalized differential quadrature method for the nonlinear tem- perature distribution in the thickness direction. The parabolic variation in thickness along the radial direction is con- trolled by a taper constant. The plate material is graded in the transverse direction and its mechanical properties are temperature-dependent. The thermal environment over the top and bottom surfaces of the plate is assumed to be uniform. Hamilton’s principle has been used in obtaining the governing differential equations for thermo-elastic equili- brium and axisymmetric motion for such a plate model employing Kirchhoff plate theory. Numerical results for thermal displacements and natural frequencies of clamped and simply supported plates have been obtained using MATLAB. The effect of the taper constant, volume fraction index, and temperature difference on the vibration characteristics has been analyzed for the lowest three modes of vibration. A study in which the plate material has temperature-independent properties has also been performed. The accuracy of the present technique is verified by comparing the results with those available in the literature. Keywords Vibration, functionally graded circular plates, temperature-dependent properties, nonlinear thickness and temperature distribution, generalized differential quadrature method 1. Introduction The search for stronger and stronger materials has always been a subject of interest to engineers for building machines and structures, e.g. in the aerospace, automotive, and naval industries, and in thermal plants. Composite materials, tailored by mixing two or more conventional materials, have been used to ful- fill these requirements, and also to provide the desired mechanical properties along one or more directions. Owing to such characteristics as lighter weight, high stiffness, corrosion resistance, and super efficiency, these materials are extensively used in various techno- logical situations, such as in commercial and military aircraft, oil sucker rods used in lifting underground oil, printed circuit boards, sail boats, floor beams, power transmission shafts, oxygen tanks, and circular annular plates stiffened with radial and circumferential ribs. The functionally graded materials invented by Japanese material scientists in 1984 (Koizumi, 1993) are a class of composites made from a mixture of cera- mics and metals. The metal-rich side is placed in regions where mechanical properties, such as toughness, need to be high, while the ceramic-rich side, which has low thermal conductivity and can withstand high tempera- tures, is placed in regions of large temperature gradi- ents; this provides a gradual compositional variation from ceramic to metal. The mechanical properties of these microscopically inhomogeneous materials vary Indian Institute of Technology Roorkee, India Corresponding author: Rahul Saini, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand 247667, India. Emails: rahulsainiiit@gmail.com; rsaini@ma.iitr.ac.in Received: 18 March 2019; accepted: 26 August 2019 Journal of Vibration and Control ! The Author(s) 2019 Article reuse guidelines: sagepub.com/journals-permissions DOI: 10.1177/1077546319876389 journals.sagepub.com/home/jvc – 73 87 20 , Vol. 26(1–2) 20