Vibration Characteristics Of Built-up Structures Based On The Energy Boundary Element Analysis

A large number of vibration problems in most of the equipment will have a great impact.It may reduce the precision and service life,and even lead to safety accidents.The existing methods of vibration analysis are mainly based on the traditional finite element method and the energy method.Compared with the traditional finite element method and the Statistical Energy Analysis(SEA),the Energy Finite Element Method(EFEM)is more advantageous and effective in frequency.In order to improve the calculation efficiency and precision of the original method,this thesis synthesizes the Finite Element Method(FEM),Boundary Element Method(BEM)and EFEM to form Energy Boundary Element Analysis(EBEA)to investigate the vibration characteristics of build-up structures.This method could provide theoretical guidance for the sound and vibration prediction and structural design of large build-up structures such as high-speed train carriages and ships.This thesis is subsidized by the National Natural Science Foundation,"Hybrid Energy Flow Method for Prediction of Broadband Vibration and Acoustics in Extra Large Structures Such As High-Speed Train Carriages"(No.51675306).The main research contents of this thesis are as follows:The energy equation of one-dimensional rod,shaft,beam structure and two-dimensional plate structure are studied.For one-dimensional structure,the energy density and energy flow relation of the structure are deduced by the displacement solution under harmonic excitation,and the approximate energy equation is obtained.For two-dimensional plate structure,the energy equation of two-dimensional plate structure is obtained by analyzing the energy density and intensity of different wave types.After comparing the energy density equations of one-dimensional and two-dimensional structures,it is found that both are similar to the heat conduction equations.The BEM is combined with the EFEM to on the basis of the energy equation.The Free Space Green function is solved;and the partial integral is transferred to the differential operator.The idea of the BEM is combined with the EFEM to form the EBEA.One-dimensional structure is used to solve the energy density of the rod,shaft and beam and the accuracy of the result is reliable compared with the EFEM.It is found that the solution process of EBEA is simpler and more direct in the case of guaranteeing high precision.Based on the one-dimensional coupled structure,the energy transfer characteristics of the coupled structures are analyzed.The energy transfer coefficient is solved,and the influence of the coupled angle and cross-sectional area on the energy transfer coefficients of the one-dimensional coupled structure is analyzed.The process can provides a theoretical basis for simplifying the energy transfer coefficient of the build-up frame structure.The EBEA is applied to the build-up frame structure.Through analyzing the energy flow density and intensity of the build-up frame structure,the vibration transmission path of the structure is visualized,and the method is successfully applied to the build-up frame structure.The method is extended from one-dimension structure to the two-dimensional structure,and the results of the EFEM and the EBEA are compared to verify the correctness of the method.The influence of the parameters(coupling angle,plate's thickness and excitation frequency)on the energy transfer coefficient is analyzed from the energy transfer coefficient of the coupled plate structure.The EBEA is applied to the energy density and intensity of the coupled plate structure,the shape of n-shaped structure and the shape of ?-shaped structure.The energy flow path is analyzed by comparing the energy intensity diagram,so that the energy flow can provide theoretical support for the analysis of vibration characteristics of large machine.