Vibration Localization In Ordered And Disordered Periodic Double-Leaf Stiffened Panels

Double-leaf periodically stiffened multi-span panels are used widely in aeroplanes, civil architectures and bridge structures. In order to enhance axial anti-stable and transverse rigidity of the plate structure, stiffeners are often employed. If the stiffeners are placed equally and other parts are identical, the structure is periodic. The propagation of vibration and wave in periodic structures exhibits passbands and stopbands. However, disorder always occurs in real double-leaf periodically stiffened multi-span panels. The disorder may cause large effect on vibration of periodic structures. Eventhough the vibration or wave lies in passbands of the ideal periodic structures, the vibration localization phenomena still exist.In this paper, the vibration localization of double-leaf periodically stiffened multi-span panels is studied. The stiffeners are simply replaced by translational and rotational springs. The double-leaf periodically stiffened multi-span panels which are coupled through single rotation or both rotation and transverse displacements are considered respectively. By employing the method of transfer matrix, 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 passbands and stopbands. When the span-length is disordered, the vibration localization phenomenon occurs, and the vibration localization is enhanced with the disorder increasing. (2) When the double-leaf periodically stiffened multi-span panels are coupled only through rotation, the vibration localization first decreases, then increases and finally tends to the situation of the single-leaf panel with the rotation rigidity of the stiffeners increasing. For some particular values of the rotation rigidity, the vibration localization in low frequencies is very weak, and the low-frequency vibration can travel through the whole double-leaf panel. (3) When the double-leaf periodically stiffened multi-span panels are coupled through both rotation and transverse displacements, as the rotation rigidity of the stiffeners increases, the vibration localization first decreases, then increases to a fixed state with less change in the regions of the passbands and stopbands. The increase of the translation rigidity of the stiffeners enhances the vibration localization in low frequencies, but has less influence on the vibration localization in high frequencies. For the case of infinite translation rigidity, the whole frequency zone becomes a stopband. (4) Vibration localization in the double-leaf periodically stiffened multi-span panels is more sensitive to the translation rigidity than to the rotation rigidity.