A Seven-Parameter Spectral/<i>hp</i> Finite Element Model for the Linear Vibration Analysis of Functionally Graded Shells with Nonuniform Thickness

Abstract

This contribution presents a finite element shell model capable of performing linear vibration analyses of shell-type structures made of functionally graded material (FGM). The model is based on the seven-parameter spectral/hp finite element formulation, which allows the analysis ofFG shells of either uniform or nonuniform thickness. Equations of motion are derived using the Hamilton’s principle and the material properties of the constituents are considered to follow a power-law volume distribution through the thickness direction. The verification of the present model is carried out by comparing with numerical results available in the literature, and with numerical simulations performed in a commercial software. To demonstrate the capabilities of the present formulation, the free vibration response of different shell structures, with nonuniform thickness, to the variation of the geometrical parameters (e.g., radius-to-thickness ratio) and the mechanical properties is reported.

Keywords

• functionally graded material
• seven-parameter shell formulation
• finite element model
• natural frequencies
• numerical results
• thickness variation