Vibration localization in stiffened plates

The study of vibration localization in disordered engineering structures, especially the application of the vibration localization phenomena as a means of passive vibration control of structures, has become increasingly important in structural dynamics. In this thesis, mode and forced vibration localization of rectangular plates stiffened in one direction and in two orthogonal directions is investigated. The application of the theory of vibration localization in vibration control by judiciously introducing disorders in the stiffeners is presented.; For one-dimensional stiffened plates, vibration mode localization in plates with randomly misplaced stiffeners is studied. Both Kantorovich's method and finite strip method are applied to set up the transfer matrices of stiffened plates. Localization factors, which characterize the average rates of growth or decay of amplitudes of deflection, are determined by the method of transfer matrix. It is observed that the masses, the stiffnesses, and the positions of the stiffeners have a significant effect on the passbands and the localization factors. It is found that the larger the disorder in the stiffeners, the larger the degree of localization in the vibration modes.; For two-dimensional stiffened plates, i.e., plates stiffened in two orthogonal directions, Kantorovich's method and compound strip method are applied to study the vibration mode localization of plates with intermediate simple supports and with rib-stiffeners, respectively. Galerkin's method is employed to investigate the forced vibration localization of stiffened plates. It is found that small disorders of the stiffeners have significant effect on the vibration localization behaviour of the entire plates.; By deliberately introducing disorders into a two-dimensional stiffened plate, it is possible to control the vibration in part of the stiffened plate. The forced vibration response in some panels of the stiffened plates may be significantly smaller than that of the panel directly excited by changing the stiffnesses or the positions of some of the stiffeners. However, for excitation frequency higher than the first natural frequency of the plate, it is difficult, if not impossible, to improve vibration control for all panels of the plate with only a few stiffeners.; As an application example of the theory of vibration localization, a building floor under excitation is studied to illustrate that, by judiciously introducing disorders in the stiffeners, the forced vibration response of some panels of the building floor may be controlled.; The major contributions of this thesis are that, for the fist time, vibration localization in plates stiffened in two orthogonal directions is studied, and it is demonstrated that by purposely introducing disorders in a periodic structure, the localization phenomena can be used as a damping mechanism to control vibration in engineering structures.