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.

• Periodical: Advanced Materials Research (Volumes 971-973)
• Pages: 548-564
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.971-973.548
• Online since: June 2014
• Authors: Boutahar Lhoucine*, Khalid El Bikri, Benamar Rhali
• Keywords: Annular Plate, Functionally Graded Material (FGM), Non-Linear Vibration

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