Nonlinear dynamic response and vibration of spiral stiffened FG toroidal shell segments with variable thickness

Abstract

In this study, the nonlinear vibratory responses and primary resonance (PR) of the spiral stiffened functionally graded (SSFG)-toroidal shell segments (TSSs) are investigated. The shell segments considered are with variable thickness and subjected to external excitations. Both the concave and convex TSSs are investigated in this study. The TSSs considered are reinforced with internal spiral stiffeners and are assumed to be continuously graded along their thickness direction. To model the stiffeners, the smeared stiffeners technique is utilized. Also, the improved Donnell shell theory, von-Kármán nonlinear geometric assumptions, and Galerkin’s method are applied to derive the discretized nonlinear governing equation of SSFG-TSSs with variable thickness. To examine the PR responses, the multiple scales method is utilized. To investigate the nonlinear vibratory behaviors, the 4th order P-T method is used. Although the results of the present research are verified with previous research available in the literature, the response of nonlinear vibration is compared with the 4th order Runge–Kutta (R-K) method as well. The influences of geometrical and material parameters on the natural frequencies, nonlinear vibration, and PR responses of SSFG-TSSs are also studied.

Keywords:

• FG toroidal shell segments
• variable thickness
• spiral stiffeners
• nonlinear vibration and primary resonance
• improved Donnell shell theory
• multiple scales method
• P-T method

Acknowledgments

The authors greatly appreciate the supports of the Natural Sciences and Engineering Research Council of Canada (NSERC), Xiamen University of Technology and the University of Regina to the present research.

Disclosure statement

No potential competing interest was reported by the authors.

Additional information

Funding

This work was supported by Natural Sciences and Engineering Research Council of Canada (NSERC), Xiamen University of Technology and the University of Regina.