Analysis Of High-Frequency Vibration Response Of Structure Based On Radiative Energy Transfer Method

Beam and plate structures are widely used in aerospace,transportation and other fields,and often inevitably suffer from high-frequency loads,which may lead to struc-tural fatigue failure or even strength failure.The traditional finite element method(FEM)is difficult to analyze the high frequency response due to the high computational cost caused by the small vibration wavelength and the low computational robustness caused by the sensitiveness to the structural uncertainty.At present,the most popular high-frequency algorithms are the statistical energy analysis(SEA),and the energy fi-nite element method(EFEM).However,due to the assumption of diffusion field,SEA can only give the average energy response of the vibrating subsystem.EFEM is valid only for one-dimensional systems.For this reason,the French scholar Le Bot proposed the radiative energy transfer method(RETM)through the specific heat like radiation,which can accurately estimate the energy response of any position in the domain.The purpose of this dissertation is to analyze the high frequency vibration responses of beam and plate based on RETM.The main contents of this dissertation are as follows:(1)Research on statistical characteristics of subsystemsThe statistical characteristics of the subsystems in low frequency and high fre-quency are compared,including wave number,wave propagation velocity,wave group velocity,modal shape,modal number,modal frequency and modal overlap factor.The effective region of SEA in frequency and damping plane is discussed.The results show that the effective region of SEA is very narrow at high frequency,where the damping should be small enough.(2)Response analysis of beam under high frequency vibration based on RETMThe RETM model of a isotropic material(IM)beam is established,and simula-tion results are compared with theoretical solutions.Based on Lagrangian equation and Hamilton principle,we derive the vibration control equations for functionally graded materials(FGM)beam,where the coupling effect of the longitudinal tension and com-pression and the transverse bending is considered.The evanescent wave term was intro-duced for the first time in the RETM model,and the results obtained are more consistent with the theoretical solutions,indicating that the model can be directly applied to the analysis of composite beams.(3)Response analysis of high frequency vibration of plate based on RETMBased on RETM,the response analysis of high-frequency vibration of plates is carried out,including the out-of-plane bending vibration and the in-plane longitudinal and shear vibrations.Theoretical formulae of the plate is deduced,and it is verified that the energy velocity is equal to the group velocity.Through the infinite plate example,the RETM direct field solution is in good agreement with the theoretical far-field so-lution,but EFEM gives wrong results.In the finite plate example,RETM results are in good agreement with the theoretical solutions,while EFEM presents great errors in comparison with the theoretical solutions.