Mode Localization in Transverse Vibration of Variable-density Simply Supported Beam

Hodges firstly discovered the phenomenon of mode localization in structural dynamics. This phenomenon mainly takes place in periodic structures such as cyclic symmetrical structures, continuous beams and large space structures. When happening, this phenomenon converges most vibrating energy into the local of structures, then leads to the failure of structures. In fact, this phenomenon has brought some detriments into the reality, especially in aeronautics and astronautics. The research objects in study are currently limited in simply structures like spring-mass systems and continuous beams. The axial and torsional vibration of variable-density bars have been studied by O. O. Bendiksen. Based on the Floquet solution, here, vibration of variable-density simply supported beam is solved by Fourier Series Method. Nature frequencies and modes are obtained. The characteristics of nature frequencies group and mode localization are observed. The application of continue fraction improves calculation presision.