Nonlinear free flexural vibration of thin circular cylindrical shells

Introduction T HE early development on the topic of nonlinear vibrations of isotropic circular cylindrical shells is well documented by Evensen. In 1976, Raju and Rao presented a finite-element solution, and Evensen commented that the authors had ignored the physics of the problem that thin shells bend more readily than they stretch. Subsequently, Prathap pointed out some inconsistencies in the mathematical analysis carried out by Evensen and also in the physical behavior of the three-term model of Dowell and Ventres. The comments made in Ref. 4 led to reinvestigation of the earlier problem in the present study. The axisymmetric part of the assumed deflected shape plays an important role in the nonlinear behavior of the shell, and so two appropriate threeterm mode shapes for the transverse displacement are chosen. The modal equations obtained by the Galerkin method are solved by the fourth-order Runge-Kutta method to obtain the amplitude-frequency relationship. The numerical results based on the present study and on the analysis of Evensen are compared with the existing experimental values.