Nonlinear radial breathing vibrations of CFRP laminated cylindrical shell with non-normal boundary conditions subjected to axial pressure and radial line load at two ends

Abstract

The cylindrical shell structure is an important kind of the primary structures in many engineering community. Under axial excitation and radial line load, the nonlinear radial breathing vibrations of a carbon fiber reinforced polymer (CFRP) laminated cylindrical shell with different temperature is investigated in this paper. Based on von Karman type nonlinear geometric relationship, the first-order shear deformation shell theory is applied to model the kinematics of deformations, and Hamilton’s principle is used to drive the differential governing equations. Galerkin method is utilized to obtain the nonlinear ordinary differential governing equations along the radial displacement of the system under the non-normal boundary conditions that one generatrix of the cylindrical shell is clamped and both ends of the shell are free. The bifurcation diagrams, maximum Lyapunov exponent diagrams, phase portraits, the time history diagrams, three-dimensional phase portraits and poincare maps are obtained by using the fourth-order Runge-Kutta algorithm. The influences of the radial line load, the axial excitation as well as the ratio of length to thickness on the nonlinear radial breath vibrations characteristics of the CFRP laminated cylindrical shell are studied in detail by numerical calculations. The results show that the radial line load, axial excitation and ratio of length to thickness can be used to control the nonlinear dynamic motions.