Analysis Of Vibration Propagation In Ordered And Disordered Periodically Stiffened Double-Leaf Panels

Periodically stiffened double-leaf multi-span panels are used widely in many fields, such as civil engineering, bridge structures and aero planes, because stiffeners can enhance transverse rigidity and the capacity of anti-destabilization of plates. The propagation of vibration in periodic structures exhibits pass bands and stop bands. Disorder causes vibration localization which destroys the mode regularities of periodic structures and results in energy storage or fatigue rupture because of the large amplitudes of responses. Therefore it's very important to study vibration localization phenomenon in disordered periodic structures. The investigation can provide theoretical basis for the vibration control and vibration reduction design for important substructures.In this paper, the propagation of vibration in periodically stiffened double-leaf multi-span panels with or without inner-span stiffeners is studied by thin plate theory. By employing the transfer matrix method, the localization factor of the system is calculated. The effects of the disorder degree of span-length, the rotation and translation rigidity of the stiffeners on the vibration localization are analyzed. The results show that:1) The propagation of vibration in periodic double-leaf panels exhibits pass bands and stop bands. When the span-length is disordered, the vibration localization phenomenon occurs, and the vibration localization is enhanced by the increasing disorder.2) When the periodically stiffened double-leaf multi-span panels are coupled through both rotation and transverse displacements, with increases of the rotation rigidity of the stiffeners, the vibration localization increases a little in low frequencies and decreases a little in high frequencies, and then tends to be a fixed state. With the increase of the translation rigidity of the stiffeners, the vibration localization first decreases, then increases to a fixed state. The results coincide with the mono-coupled case when the translation rigidity in multi-coupled system becomes infinite. Additionally, vibration localization is more sensitive to the translation rigidity than to the rotation rigidity.3) The translation rigidity and rotation rigidity of the stiffeners of the inner-span stiffeners have large effects on the vibration in middle frequencies, as the rigidity of the stiffeners increases, both the width of stop bands and the vibration localization increase. Therefore the structures vibrate in middle frequencies can be controlled by designing or adjusting rigidity of the inner-span stiffeners.4) The span-length has large effects on the vibration localization in the periodically stiffened double-leaf multi-span panels. As the span-length increases, the width of stop bands in low frequencies decreases, the quantities of the pass bands increase; while in high frequencies the width of pass bands decreases and the quantities of the stop bands increase. The disorder degree of span-length also has large effect on the propagation of vibration at the frequencies except the first stop bands. Consequently vibration control can be carried out by choosing appropriate span-length or span-length disorder.