Free and forced vibrations of composite cylindrical–cylindrical​ shells with partial bolt loosening connections: Theoretical and experimental investigation

In the present study, the free and forced vibrations of composite cylindrical–cylindrical shells with partial bolt loosening connections are investigated both experimentally and theoretically. Initially, a theoretical model is proposed based on the assumption of primary and secondary connection springs with reduced stiffnesses related to different loosening positions of connection bolts. The equation of motion is derived for predicting the fundamental frequencies, mode shapes, and vibration displacement responses on the basis of the Rayleigh–Ritz method, the Jacobian polynomial approach, the modal superposition technique, etc. To ensure the calculation accuracy of the present model, a convergence study is conducted to determine the truncation number. Also, to give a solid validation of the model, some detailed tests, such as the pulse, sweeping-frequency, and resonant excitations, are conducted on a combined shell specimen, which is obtained by assembling two different composite cylindrical shells via twelve M8 bolts, with a torque wrench being adopted to control the torques in the connection bolts to achieve the desired partial bolt loosening effect. By comparing the calculated and tested results, it can be found that the present model is reliable to predict the structural dynamic parameters because the calculation errors of natural frequencies and resonant displacements are less than 7.4 and 11.9 %, respectively. Finally, the impact of critical bolt loosening parameters on vibration characteristics of the combined shells is evaluated, with some important conclusions being highlighted to illustrate the reduction mechanism of dynamic properties as the partial bolt loosening degree and number increase or the loosening pattern becomes more complex.