Nonlinear Damping and Forced Response of Laminated Composite Cylindrical Shells with Inherent Material Damping

Abstract

In this paper, the nonlinear damping and forced response behaviors of laminated composite cylindrical shells considering the internal damping of composite materials are investigated. Based on Donnell nonlinear shell theory, the dynamic governing equations of composite cylindrical shells with geometrical nonlinearity are established by using the Hamilton principle, in which the inherent material damping is taken into account by complex modulus method. The dependence of nonlinear damping on vibration amplitude and amplitude–frequency response are analytically obtained by the Galerkin method in conjunction with harmonic balance method. By comparing the results of natural frequency and modal damping with those in the literature, the correctness of the above theoretical analysis is verified. Furthermore, the effects of the circumferential wave number, lamination schemes, vibration amplitude and geometric configuration on the nonlinear damping and forced responses of the composite cylindrical shell with unidirectional, angle-ply and cross-ply laminations are analyzed. The results show that the damping dissipation capacity of the composite cylindrical shell is amplitude-dependent, and the effect of the amplitude on the nonlinear damping characteristics gradually decreases with the increase of the length-to-radius ratio. The ply angle not only affects the value of the resonance peak, but also significantly changes the degree of the soft and hard spring characteristics of the composite cylindrical shell. With the increase of internal material damping, the amplitude-frequency curve of the composite cylindrical shell changes from the coexistence of hard and soft characteristics to the only soft characteristics.