Nonlinear vibration analysis of laminated composite angle-ply cylindrical and conical shells.

• Nonlinear free vibration of laminated composite angle-ply cylindrical and conical shells was studied. • The Ritz method was used for obtaining the ordinary differential equations. • The combination of multiple scales method and modal analysis was used for obtaining the results. This paper presents the combination of multiple scale method and modal analysis in order to investigate nonlinear vibration of laminated composite angle-ply cylindrical and conical shells. The shells are modeled considering the shear deformation and rotary inertia while the geometrical nonlinearity is modeled using von Karman approach. Hamilton principle is used for obtaining the basic equations of the system. These equations are converted to nonlinear ordinary differential equations depending on time variable using Ritz method. The results of this study are validated against the results of open literature and good agreement is observed. The effects of several parameters including the layers' angle, the number of the layers, semi-vertex angle, length, radius and also each layer's thickness on nonlinear frequency ratio, fundamental linear frequency and nonlinear frequency are illustrated in details. [ABSTRACT FROM AUTHOR]