Determination of the excitation frequencies of laminated orthotropic non-homogeneous conical shells

•Parametric vibration of non-homogeneous (NH) laminated conical shells is analyzed.•Basic relations and equations are derived using the Donnell-Mushtari shell theory.•Mathieu-type differential equation is obtained by using Galerkin method.•The excitation frequencies are determined using Bolotin's method.

The excitation frequencies of parametric vibration of laminated non-homogeneous orthotropic conical shells (LNHOCSs) under axial load periodically varying with time, are determined using the classical shell theory (CST). The basic equations are found using the Donnell-Mushtari shell theory and reduce to the Mathieu-Hill type differential equation, in which the instability is examined by the Bolotin method. To validate of current results was made a comparison with the previous studies. The effects of stacking sequences, axial load factors, non-homogeneity, as well as the variation of geometric characteristics on the backward and forward excitation frequencies (BFEFs) of conical shells are studied in detail.