Free Vibration of Functionally Graded Truncated Conical Shells Using the GDQ Method

Abstract

The free vibration analysis of a functionally graded material (FGM) truncated conical shell is presented using the method of generalized differential quadrature (GDQ). Based on Love's first approximation theory, governing equations are derived. The material properties of FGM shells are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. Then, using the GDQ method, the natural frequencies of the shells for various boundary conditions can be obtained. The effects of the materials’ constitution and the shape geometry on the natural frequencies are discussed in detail.

Keywords:

• functionally graded materials (FGMs)
• truncated conical shell
• free vibration
• generalized differential quadrature (GDQ)

Acknowledgments

This work is supported by the National Natural Science Foundation of China (Nos. 11262010, 11272278), the Postdoctoral Science Foundation of China (No. 20110491664), and the Natural Science Foundation of Gansu Province (No. 1112RJZA032). The authors gratefully acknowledge all of the support.