Energy Finite Element Method And Its Application To Automobile Body

Energy Finite Element Analysis(EFEA),which employs the energy density as the primary variation of energy equation,is a numerical method to analyze the problem of vibration and vibro-acoustic in the structures at middle and high frequencies.In this method,the energy transfer equation is a relationship in terms of time-and space-averaged energy variables.This energy flow method can solve not only the problem of crowed modes at middle and high frequencies for the Finite Element Analysis(FEA),but also the problem of lost information of spatial variation within each subsystem at middle and high frequencies for Stantistical Energy Analysis(SEA).Considering the deficiencies of traditional analysis methods,we need to develop a new alternative approach to solve the problem of vibration and vibro-acoustic in the structures at middle and high frequencies along with the rapid development of high performance,lightweight and intelligentization on the automobile and aeronautical products.In this thesis,the differential governing equations in terms of energy density for slender rods,Euler-Bernoulli beams and thin plates are derived from classical displacement equations.The relationship between energy flow and energy density to solve the problem of discontinuous nodal values of energy density at the joints is obtained by using the energy flow equilibrium equation in the coupled structures.This thesis focuses on the main tasks as follows:(1)The research of the vibration problem in the rod and coupled structures excited by harmonic point excitations.The tasks include developing the energy finite element equation for the rod structures,deriving the relationship between energy flow and energy density in the coupled structures,and discussing the distribution of energy density of the free-climped simple rod and two coupled rods.(2)An analysis of the problem of the vibrating Euler-Bernoulli beam and coupled structures excited by harmonic excitations.A relationship between space-averaged energy density and intensity is established.This relationship is used to develop the differential equation of vibrating beam.The EFEA equation is applied to the predictions of the free-climped beam,two coupled beams and three coupled beams.(3)The research of the vibrating problem in the thin plate and coupled structures.The main tasks are the development of energy finite element equation for the vibrating thin plate,the transform between the physical system and natural system,an analysis of energy transfer efficients in the coupled structures.The distribution of energy density of the simple thin plate with flexural wave,L-type thin plate and 150-degree thin plate with flexural,longitudinal and shear waves are discussed.(4)An analysis of the vibration problem in the automobile body composed by thin plates.The geometric model of automobile body and energy finite element model are developed.The boundary conditions of EFEA model are defined.The distribution of energy density in the automobile body excited by the engine excitation or wheel excitation are analyzed.The innovation points in the thesis are: 1)the derivation of energy transfer coefficients of flexural,longitudinal and shear waves in the joint of two coupled plates,which is used to solve the problem of wave type conversion,2)the establishment of energy finite element model for finite coupled plates,and the development of the relationship between energy density and energy flow for three wave types in the joint,which is used to deal with the problem of discontinuous energy density in the coupled structures,3)applying the energy finite element theory of the finite coupled plates into the automobile body.This thesis focuses on the development of vibrating rods,beams,plates and coupled structures.The energy finite element equation is applied to the prediction of energy density in the automobile body which is subjected to the excitation.The results of energy density are significant for the designers or researchers.