Abstract
New expressions of equivalent stiffness and equivalent mass are proposed to study the mechanism for the formation of the band gap in cylindrical three-component phononic crystals. The vibration modes are classified into three classes: transverse, longitudinal, and torsional modes. For each mode, the new expressions for the equivalent stiffnesses and equivalent masses of the spring-mass system are deduced, and these can be used to investigate the key factors for the determination of the band gap in the designed three-component phononic crystal. The results indicate that the flat band is a special feature of the designed cylindrical three-component phononic crystal. Equivalent inertia is the key factor for the determination of the flat band and the band gap in this three-component phononic crystal.
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