On radially symmetric vibrations of functionally graded non-uniform circular plate including non-linear temperature rise

Abstract

In this study, the free axisymmetric vibrations of functionally graded circular plate of linearly varying thickness controlled by a taper parameter in radial direction and non-linear temperature rise along the thickness have been investigated on the basis of classical plate theory. The plate material is graded in transverse direction and its mechanical properties are temperature-dependent. The temperature over the top and bottom surfaces is assumed to be uniformly distributed. Hamilton's principle has been used to derive the governing equations for thermo-elastic equilibrium and axisymmetric motion of such a plate model. The generalized differential quadrature method has been employed to obtain the thermal displacements and characteristic equations, for clamped and simply supported plates. The lowest three roots of these equations have been computed and reported as the values of frequency parameter for the first three modes of vibration. Effect of thickness parameter, volume fraction index and temperature difference has been analyzed on the vibration characteristics of the plate. A study with temperature-independent material properties has also been performed. Results have been compared with the published work.