Circumferential modal coupling analysis of orthogonally stiffened cylindrical shell coupled with internal rectangular plate using semi-analytical wavenumber-frequency method

Orthogonally stiffened cylindrical shell coupled with internal rectangular plate is widely applied in engineering industries. The significant effects of the internal plate on vibration signatures of the shell have been demonstrated. Little attention has been paid to vibration analysis in the wavenumber-frequency domain. This paper aims to conduct the circumferential modal coupling analysis of the coupled model using the semi-analytical wavenumber-frequency method. The coupled model is disassembled into the stiffened cylindrical shell and rectangular plate. The interface potential between the shell and rectangular plate is derived based on a unified variational modeling procedure, in which the transformation of the coordinate system must be conducted. The displacement fields of the shell are expanded with the Fourier series along the circumferential direction. The vibratory field in wavenumber-frequency space is analytically obtained. The numerical method is utilized to illustrate the convergence and accuracy of the proposed method. The results demonstrate that the internal plate affects modal characteristics and then results in the alterations of the number and the shifts of resonance peaks. The phenomenon can be demonstrated by the circumferential modal contribution of the vibration response. Besides, it should be noted that the dominant circumferential modes for the input energy and vibrational energy are inconsistent owing to the strong shell-plate coupling effect.