Three-dimensional elastic exact solution for free vibration of composite cylindrical shells considering ply angle

In order to obtain the exact free vibration solution of laminated cylindrical shell with arbitrary ply angle,the transfer matrix of transverse displacement and stress was established by combining the layer-wise theory with state space method on the basis of three-dimensional elastic theory,the axial and circumferential displacement components were approximated using double helical pattern modes and the free vibration analytic formula of laminated cylindrical shell with arbitrary ply angle under simply supported boundary was derived.The exact form of the free vibration equation was obtained.The validity of the present theoretical method was verified by being compared with the theoretical model from the literature and the finite element methods.The results show that when the considered frequencies are less than two times the ring frequency,the calculation precision for natural frequency of thin shells is less than 1% and that of the thick shells is less than 2%.For the thick shells,the shell can be divided into multi layers along the thickness direction,which can effectively improve the calculation precision.The influence of layer angle on the natural frequency was analyzed based on present method,the results shows that when the circumferential mode is low,the natural frequency is parabolic with the increasing of the layer angle and when the circumferential mode is high,the natural frequency increases monotonically with the increasing of the layer angle.The present method is also suitable for homogeneous isotropic shells and orthotropic cylindrical shells.