Nonlinear free vibration analysis of functionally graded plates and shell panels using quasi-3D higher order shear deformation theory

Abstract

This paper presents the nonlinear free vibration behavior and response of functionally graded plates and shell panels under various boundary conditions. The displacement formulation followed uses a sinusoidal non-polynomial quasi-3D higher order shear deformation theory with six variables and, the parabolic transverse stress distribution functions are used to model stresses in the thickness direction. Present formulation employs the Green-Lagrange nonlinear strains along with Sander’s approximation to account for larger flexural response which could be experienced by the structure. An eight noded C⁰ continuous isoparametric finite element is used for numerical implementation of nonlinear finite element solver developed in MATLAB. Developed numerical formulation is employed to study and analyze the nonlinear free vibration response of the spherical, cylindrical and hyperboloid shell panels and the obtained results are seen to be consistent and good agreement with the literature thus establishing the effectiveness and accuracy of the present work.

Keywords:

• Functionally graded plates and shells
• Quasi-3D shear deformation theory
• green-lagrange nonlinear strains
• Sander’s approximation
• nonlinear free vibration analyses

Disclosure statement

No potential conflict of interest was reported by the authors.

Acknowledgements

Authors acknowledge the help and support provided by the Department of Aerospace Engineering, Indian Institute of Technology Kharagpur for conducting and completing this research work.

Additional information

Funding

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.