Nonlinear forced vibration and resonance analysis of rotating stiffened FGM truncated conical shells in a thermal environment

In this paper, a semi-analytical method is presented for nonlinear vibration analysis of rotating stiffened truncated conical shells with functionally graded materials (FGM) in the thermal environment subjected to harmonic excitation. Considering Coriolis acceleration and the centrifugal force, the governing equations of stiffened rotating FGM truncated conical shells are extracted utilizing the classical shell theory regarding the nonlinear von Karman relationships and the smeared stiffeners technique. The partial differential equations are discretized to a set of ordinary nonlinear equations by employing Galerkin's approach. The condensation method is utilized to reduce the equations of motion into the transverse direction. For analyzing the nonlinear resonance behavior, we use the multiple scales method. According to this approach, the primary resonance of the nonlinear vibration of the stiffened rotating FGM truncated conical shells is examined. Besides, linear free vibration of the stiffened rotating shell is analyzed to investigate the natural circular frequency. Numerical results are studied to investigate the influence of shell rotating speed on the frequency response curve. Also, the effects of force amplitude, volume-fraction index, temperature changes, and different vertex angles on the frequency response curve are examined for various rotating speeds.