The casing was simplified using a simply supported end and a fixed supported end cylindrical shell based on geometric characteristics of thin-walled structures of aero-engine casing. The dynamic equations were established and solved by multi-scale method

and the stability of zero solution and non-zero solution of casing dynamic equations under the radial harmonic excitation was studied. Then the transient process of system mode from single-mode motion to composite mode motion and the transfer of energy between the modes were studied; in addition

the vibration characteristic of casing under radial harmonic excitation was also numerically simulated. Results show that periodic motion

periodic doubling motion and chaotic motion appear alternately with the increase of radial harmonic excitation.