Theoretical modeling and vibration characteristics analysis of double cylindrical connected shell structures with laminated materials under bolt loosening conditions

This article aims to investigate the vibration characteristics of a laminated material double-cylindrical bolt-connected shell structure under bolt connection conditions. The focus is on analyzing the impact of bolt loosening, elastic boundary conditions, and structural parameters on vibration behavior. This will provide a theoretical basis for the design and optimization of bolt-connected shell structures in engineering applications. Based on Sander’s theory, a dynamic model of bolted multi-layer composite cylindrical shells is established, utilizing artificial spring technology to simulate the discrete characteristics and elastic boundary conditions of bolt connections. The displacement function is represented by orthogonal polynomials, and the vibration differential equation of the system is derived by combining with Lagrange’s equation. The natural frequencies and modal shapes of the bolted system are solved using the energy method. The accuracy of the system model was verified through comparative analysis of natural characteristics using the finite element software Abaqus. Furthermore, the effects of parameters such as the number of loose bolts, degree of loosening, position of bolt connection surface, aspect ratio, and thickness-to-diameter ratio on vibration characteristics were analyzed. Research indicates that an increase in the number of loose bolts significantly reduces structural rigidity, but once it exceeds a certain threshold, the frequency tends to stabilize. Loose bolts can lead to nonlinear changes in frequency, and higher-order modes are more sensitive to connection stiffness. The frequency of structures with bolt connection surfaces located in the center is higher than that of other structures, and an increase in the aspect ratio and thickness-to-diameter ratio will increase the natural frequency.