1/3 Subharmonic resonance of a nonlinear composite laminated cylindrical shell in subsonic air flow

Abstract

The 1/3 subharmonic resonance of a composite laminated circular cylindrical shell with clamped boundary conditions at both ends in subsonic air flow under radial harmonic excitation is investigated. The equation of motion of the composite cylindrical shell is derived from the Donnell’s nonlinear shell theory and the Galerkin’s method is adopted to transform the equation of motion of the shell into a nonlinear ordinary differential equation. The 1/3 subharmonic resonance of the shell is analyzed by using the method of multiple scales and the sufficient and necessary conditions for the stability of the steady-states of the 1/3 subharmonic resonance is obtained by solving the eigenvalue problem of the linearized equations. The influences of the subsonic air flow on the 1/3 subharmonic resonance of the shell are discussed for different modes and the effects of the ply angles are analyzed for the fundamental mode. The numerical results of the threshold curves and the amplitude–frequency relations of the 1/3 subharmonic resonance are illustrated. From the results it can be seen that the existence region for the 1/3 subharmonic resonance is reduced and the amplitude of the subharmonic resonance is dropped with the flow velocity increasing. The composite shell with 45° ply angle exhibits better dynamic characteristic than that with other ply angles. The interval of the frequency ratio for the instability of the steady-state of the subharmonic resonance is broader when the ply angle is chosen as 45° than that of other ply angles for given amplitude of the external excitation.