Free and forced vibration analysis of multi-stepped circular cylindrical shells with arbitrary boundary conditions by the method of reverberation-ray matrix

A semi-analytical procedure for free and forced vibration analysis of multi-stepped circular cylindrical shell with arbitrary boundary conditions is developed with the employment of the method of reverberation-ray matrix. Based on the Flügge thin shell theory, the equations of motion of the circular cylindrical shell are introduced and exact solutions of the traveling wave form along the axial direction and the standing wave form along the circumferential direction are obtained for each segment of uniform shell. With such a unidirectional traveling wave form solution, the method of reverberation-ray matrix is adopted to calculate natural frequencies and steady-state responses of the multi-stepped circular cylindrical shell. Comparisons of the present results with those previously published in literature and those obtained by the finite element method prove that the method of reverberation-ray matrix is applicable and of high precision for free and forced vibration analysis of the multi-stepped circular cylindrical shell. Effects of elastic support stiffness and the number of steps on natural frequencies are investigated.