Modal Characteristics Of Thin-Walled Cylindrical Shells And Control Of Passive-Active Vibration Isolation Systems

In order to deal with the vibration problem about machinery installed in a cylinder, classical thin shell theories were used to investigate the modal characteristics of a thin-walled circular cylindrical shell. Utilizing the modal superposition method, mobility expressions of a thin-walled cylindrical shell structure with both ends shear diaphragms supported were derived. Combined the power flow theory, the mobility method was applied to derive the power flow transfer equations of the overall isolation system. Then, the effects of vibration isolators which mounted with inclined angles and several active control strategies for the isolation performance were discussed. Finally, a cylindrical shell structure with both ends open and freely hanging was carried on the experimental modal analysis. Details are as follows:General vibration differential equations of thin shell structures were established. Based on the different relationships between displacement and strain, differential equations of free vibration of cylindrical shells were derived using three kinds of commonly used thin shell theories, including Donnell-Mushtari theory, Goldenveizer-Novozhilov theory and Flugge-Byrne-Lur’ye theory. For the shear diaphragms boundary condition which was commonly used in the engineering practice, modal characteristic equations were obtained by analytical method. Combined with some numerical examples, the theoretical results were compared to the results given by commercial finite element analysis softwares, in order to determine the accuracy and scope of each shell theory for different length and thickness of circular cylindrical shells.The contribution of non-radial vibration components and responses of sinusoidal and cosine modes were taken into account. The force, moment and coupling mobility functions of a circular cylindrical shell which simultaneously subjected to harmonic point force and moment excitations were derived. It is shown that non-radial vibration components have remarkable effects on the prediction accuracy for modes and mobility frequency spectrum, and the real parts of coupling mobility functions may be negative.The analytical model for a single-stage passive isolation system which consists of complex excitations, multiple elastic mounts and a circular cylindrical shell foundation was established. The coupled vibration transfer equation of the overall system was derived by the substructure mobility approach. The power flow concept was used to assess vibration transfer characteristics and isolation performances as a cost function. Numerical simulation shows that:with consideration of the distributed parameter characteristic of isolators, the system power spectrum decline slower at higher frequencies resulting in an unreliable design of high-frequency vibration isolation. Interestingly, if increasing the inclined angle of isolators appropriately, one can make three rigid modes of the system gathered in a narrow frequency range. Meanwhile, the power transmitted to the shell is less than the vertical-mounted case, which leads to a better isolation performance. One can obtain independent transverse and pitch oscillation by changing inclined angle of isolators into a specific value.The adaptive feedforward hybrid vibration isolation model which consists of power machinery, inclined isolators, and a circular cylindrical shell foundation was established. The coupled vibration transfer equations of the overall system were derived by the mobility matrix technique. In frequency domain analysis, five active control strategies, including minimization of the total power transmitted to the shell foundation, the cancellation of out-of-plane velocities, the cancellation of out-of-plane forces, the cancellation of the power due only to the out-of-plane velocities and forces and the minimization of the sum of squared out-of-plane velocities and weighted square forces had been used to investigate the behavior of overall system. The numerical simulation results show that the output leaky algorithm can receive good active control constraint effects, and can effectively restrain the phenomenon of power circulation. Using the radial velocities cancellation strategy will change the boundary condition of the shell foundation and result in shell modal peaks moving to higher frequencies. Active isolation when using inclined mounts performs more poorly than the case of using vertical mounts.A vibration modal test platform for a flexible cylindrical shell structure was set up. Using hammer excitation method, the modal characteristics of a elastic suspension thin-walled cylindrical shell were studied. The modal parameters obtained from the experiment were compared with finite element analysis results, and the possible reasons of the error and impacts on test accuracy were also discussed.