Impact Vibration of Strongly Unsymmetrical Beams (Sub-Harmonic Vibrations Including Internal Resonance)

Impact vibration of cantilever beams with collision wall, that is set with almost no clearance, was treated as an example of impact vibration of strongly unsymmetrical system. Vibrations in the wide excitation frequency range from near 1st natural frequency to near 2nd natural frequency were investigated. The followings were made clear from the numerical analysis: (1) Near 2nd natural frequency, the internal resonance between the 1/7-th sub-harmonic vibration of 1st mode and the primary resonance of 2nd mode is occurred. Because the vibration has a feature of the 1/4-th sub-harmonic vibration, vibration amplitudes become large at the excitation frequencies near 1/4, 2/4 and 3/4 times of 2nd natural frequency. (2) The even order sub-harmonic vibrations of 1st mode occur. (3) The amplitude of the vibrations mentioned at (2) becomes large, if its frequency is close to those of the vibrations mentioned at (1) occur. It is supposed that the energy of the primary resonances of 2nd mode flows into the even order sub-harmonic vibrations of 1st mode through the odd order sub-harmonic vibrations of 1st mode.