Theory and experiment studies on frequency response of conical shells with bolt boundary

The present study proposes a semi-analytical method for solving the frequency response of conical shells with bolt boundaries. The non-uniform artificial spring technology is employed to simulate the bolt loosening or noloosening boundary conditions, which is closer to the real bolt contact situation. Donnell's shell theory as well as the displacement assumption of Chebyshev polynomials are employed in theoretical modeling, and the governing equation is obtained by the Lagrange equation. The rationality of the established model is confirmed through comparisons with existing literature and modal tests, revealing that the maximum errors of theoretical results compared to literature and experiment are 0.82 % and 3.9 %, respectively. From both theoretical and experimental aspects, the frequency response of conical shells with bolt loosening boundary conditions are explored. Subsequently, the combined effects of cone sizes and loosening degrees on frequency responses of bolted conical shells are analyzed. Results demonstrate that bolt loosening significantly reduces the fundamental frequency while this attenuation diminishes with increasing mode order. The increase in the bolt loosening degree results in the attenuation of the formant value, confirming an increase in the modal damping ratio. The influence of cone angle on frequency response is directly tied to the bolt loosening degree. The established model proves dependable for predicting the vibration characteristics of bolted conical shells under varying loosening degrees, offering valuable insights for the design and operational phases of thin-walled conical shell structures.