Vibration Localization In Periodic Multi-span Beams

There are many practical applications of periodic structure in civil architectures, aero planes and bridge structures engineering. Periodic structures exhibit pass bands and stop bands. Disorder causes vibration localization phenomenon in structures. Localization destroys the mode regularities of periodic structure. Some substructures' response amplitude will become very large under force, thus it will cause energy accumulation or furthermore cause fatigue rupture. So it's very important to analysis vibration localization phenomenon in disordered periodic structures since it can provide theoretical bases for the vibration control and vibration reduction design of important substructures.In this paper, the vibration localization phenomenon in periodic multi-span beam is studied. Firstly, we discuss the vibration localization phenomenon in Euler Bernoulli beam. Consider the effects of the disorder introducing from span length, rigidity, non-dimension spring stiffness for the localization factors in two cases of mono-coupled and bi-coupled. Also research the combined effects of disorder and structure damping on the dynamics of the multi-span beams and compare their influences when considering damping. Secondly, we discuss the vibration localization phenomenon in Timoshenko beams. Research the same phenomenon and compare with Euler Bernoulli beam. In the end, we discuss the vibration localization phenomenon in truss beams. These results show that: (1) There exist passbands and stopbands in periodic multi-span beam. The vibration localization phenomenon occurs, and the vibration localization is enhanced with the disorder increasing. The disorder of span-length influence for localization phenomenon is larger than rigidity. (2) The rigidity of supporting for periodic multi-span beams has large influence for the width of bands. The vibration localization is enhanced with the rigidity of supporting increasing. Vibration localization in periodic multi-span beams is more sensitive to the translation rigidity than to the rotation rigidity. When the translation rigidity tends to infinite, the bi-coupled system becomes to mono-coupled. (3) The result of Timoshenko beams tends to Euler beams with height-to-span ratio increasing. (4) The vibration localization phenomenon occurs when truss beams' longitudinal bars or battens exists disorder.