Large Amplitude Free Vibration Analysis of Functionally Graded Annular Plates

Abstract

The geometrically non-linear axisymmetric free vibration of functionally graded annular plate (FGAP) having both edges clamped is analyzed in this paper. The material properties of the constituents are assumed to be temperature-independent and the effective properties of FGAP are graded in thickness direction according to a simple power law function in terms of the volume fractions. Based on the classical Plate theory and von Karman type non-linear strain-displacement relationships, the nonlinear governing equations of motion are derived using Hamilton’s principle. The problem is solved by a numerical iterative procedure in order to obtain more accurate results for vibration amplitudes up to twice the plate thickness. The numerical results are given for the first two axisymmetric non-linear mode shapes, for a wide range of vibration amplitudes and they are presented either in a tabular or in a graphical form, to show the significant effects that the large vibration amplitudes and the variation in material properties have on the non-linear frequencies and the associated bending stresses of the FGAP.

Nonlinear free and forced vibration analysis of FG‐CNTRC annular sector plates

“…A few studies have been carried out on the nonlinear vibration analysis of annular plates [42][43][44][45][46][47]. Using a sector p-element, Houmat [46] studied the nonlinear free vibration of laminated sector plates based on the FSDT.…”