Attach rotational resonators to a host beam to form a phononic crystal beam. Complex band structure of the phononic beam containing rotational resonators was derived though Transfer Matrix Method based on Euler-Bernoulli beam theory. The results showed that narrow band locally resonant band gaps and wide band Bragg band gaps could be achieved by rotational resonators. The effects of rotational resonator parameters, such as rotational stiffness and moment of inertia on the band gaps were analyzed, and general changing law of the band gaps was obtained. Locally resonant band gap could be broadened by minimizing the moment of inertia when the rotational stiffness remains constant. Excessively large or small rotational stiffness could minimize locally resonant band gap while Bragg band gap could be broadened effectively by increasing rotational stiffness and moment of inertia simultaneously. Finally, band gaps property of the phononic crystal beam were verified though transverse vibration transmission calculation using Spectrum Element Method.
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