Research On Theory And Methods Of Multilayer Periodic Vibration Isolation System Based On Phononic Crystal

It is one of the most urgent problems needing to be solved in the engineering all the time to suppress harmful vibration. Vibration isolation is one of the most extensive applications in the vibration control. Vibration isolation is to take some measures between the vibration source and system, such as placing appropriate vibration isolators to isolate direct transmission of the vibration. Its essential is to add a subsystem between the vibration source and system. From the point of view of energy, vibration isolation is to change the spectral structure of energy excited to the system by vibration source, thereby vibration is suppressed by reducing the energy of band-pass frequency. Since the eighties of the 20th century, the vibration isolation performances of multilayer structure and periodic composite structure based on phononic crystal have gradually become one of the focuses that the domestic and international vibration fields study. Based on of vibration isolation characteristic of multilayer structure and periodic composite structure based on phononic crystal, research and discussion on theory, computation methods and some key technique questions are carried through in this dissertation. The development history and current situation of non-linear vibration isolation, multilayer structure and periodic composite structure based on phononic crystal have been reviewed in the thesis. Some helpful exploration about multilayer structure and periodic composite structure based on phononic crystal in the field of vibration isolation have been carried out by combining theoretical analysis, numerical simulation with vibration isolation experiment.There exists a lot of phenomena containing the quadratic nonlinear stiffness and damping simultaneously in the vibration systems under the actual circumstances. A 2-degree-of-freedom (DOF) nonlinear vibration model of the system is established and the general forms of its vibration equations which govern its dynamics are obtained. The equations are approximately solved by nonlinear normal modes (NLNM) superposition method based on the theory of Shaw invariant manifolds. The solutions using nonlinear normal modes superposition and direct numerical methods are simulated respectively, and the feasibility is validated by comparing the results. The nonlinear force induced by spring and damping of 2-degree-of-freedom nonlinear vibration isolation system is regarded as applied force, then impulse response temporal method of linear vibrating system is applied in the system, the response of nonlinear vibrating system is obtained approximately by convolution integration between unit impulse response of corresponding linear system and equivalent nonlinear force. Therefore, the vibration isolation effect of the system can be analyzed.A 2-DOF nonlinear vibration isolation system with quadratic nonlinear stiffness and damping is studied, spatial approach by which linear and nonlinear frequency response function is estimated is used to parametrically identify the nonlinear vibration model, and nonlinear stiffness coefficient and nonlinear damping coefficient of the model are optimized by least square method.The transmission properties of elastic waves propagating in three-dimension composite structure embedded periodically with spherical inclusions are analyzed by the transfer matrix method. Firstly, the transfer matrix of monolayer structure is deduced by the wave equations, and the transfer matrix of the entire structure is obtained in the case of boundary conditions of displacement and stress continuity between layers. Then, the effective impedance of the structure is analyzed to calculate its reflectivity and transmissivity of vibration isolation.Finally, numerical simulation is carried out and some useful conclusions are obtained. The substructure method is introduced to set up mathematical model of finite periodic composite structure based on phononic crystal, solve its wave equation, and derive its time-average power flows. On the basis of the theory derivation, numerical simulation is carried out by the method, the power flows of the model is obtained, and the performance of vibration isolation of the structure is analyzed.Based on finite element method and central difference method, the vibration isolation performances of finite periodic composite structure based on phononic crystal are studied. The structure is discreted by finite element method and central difference method, and numerical simulation is carried out. The results show that the modal frequencies of the structure will decrease with the increase of the density of the inner scatterers, the effect of vibration isolation will get better with the increase of the diameter of the inner scatterers, and the effective frequency ranges of vibration isolation will get wider with the increase of the diameter of the inner scatterers.In summary, the vibration isolation performances of multilayer structure and periodic composite structure based on phononic crystal are analyzed in detail by theoretical analysis, numerical simulation and experimental study in this dissertation, which has offered some theoretical foundation for practical application. The research results have important theory significance and engineering application value for promoting the multilayer structure and periodic composite structure based on phononic crystal in reducing vibration and lowering noise at low frequency.