Vibration Propagation In Ordered And Disordered Periodic Orthotropic Rib-Stiffened Panels

ABSTRACT:Periodically multi-span orthotropic rib-stiffened panels are used widely in many fields, such as civil engineering, aerospace engineering and mechanical manufacturing. In periodic structures, the propagation of vibration exhibits passbands and stopbands. The vibration will not decay in passbands, while the amplitude and energy of vibration will decay in stopbands. In fact, the disorder inevitably exists in periodic structures. In disordered periodic structures, the disorder will enhance vibration localization phenomenon, passbands in former periodic structures will become stopbands.In this paper, the propagation of vibration in ordered and disordered periodic orthotropic rib-stiffened panels which contain single-leaf panels and double-leaf panels is studied basing on thin plate theory and the transfer matrix method. The localization factor of the system is calculated. The effects of many factors, such as the orthotropic material parameter, the rotation and translation rigidity of the rib, the disorder degree of span-length and rib, on the vibration localization are analyzed. The study show that:1) In general, the vibration localization in single-leaf periodic orthotropic panels is more fierce than it in double-leaf periodic orthotropic panels.2) The bending rigidities of the panel in the two main direction of elasticity Dx,Dy and the torsional rigidity Dk will affect the propagation of vibration in the structure. For the relative bending rigidity Dyx=Dy/Dx, When Dyx< 1, with the decrease of Dyx the width of stopband in low frequencies decreases, but the change is very small. When Dyx> 1, with the increase of Dyx, the width of stopband in low frequencies increases, the width of the passband decreases, the vibration localization enhances. For the relative torsional rigidity Dkx= Dk/Dx, with the increase of Dkx, the width of stopband in low frequencies increases, the width of passband decreases, especially in the structure of Dx 1,the effect is very obvious.3) The rotation rigidity and the translation rigidity of the rib have a great influence on the vibration propagation of the structure. With the increase of translation rigidity, the vibration localization enhances firstly, then decays to a fixed state. With the increase of rotation rigidity, the vibration localization in low frequencies of double-leaf panels hardly changes, but the vibration localization in low frequencies of single-leaf panels enhances firstly, then decays to a fixed state. The results coincide with the mono-coupled case when the translation rigidity in multi-coupled system becomes infinite. 4) The disorder of span-length has an obvious effect on the propagation of vibration in the periodic structure, while the disorder of rib hardly has. With the increase of the disorder degree of span-length, the former passbands become stopbands, and the vibration localization in these stopbands enhance. So in real design, we should pay more attention to the disorder of span-length than the disorder of rib.5) We can control the propagation of vibration in special frequencies by adjusting the bending and torsional rigidity of the orthotropic panel or the rotation and translation rigidity of the rib. Meanwhile, we can also change the propagation of vibration by designing appropriate span-length disorder to reduce the vibration in the structure.