Study On The Statistical Characteristics And Radiative Energy Transfer Model Of Structures In High-frequency Vibroacoustics

Anisotropic composite beams and plates as primary structural components have wide applications in mechanical and aerospace engineering because of their excellent corrosion resistance,high strength,and rigidity with low weight,For example,the skin of the large aircraft,the thermal protection structure of high-speed aircraft and the panels of the high-speed train.These structures are often subjected to high-frequency fluctuation excitation caused by turbulent boundary layer during service.Nowadays,high-frequency vibroacoustic problems have attracted wide attentions among engineers and researchers.Since deterministic analysis methods such as the finite element method and boundary element method have the upper limit of frequency in solving vibroacoustic problems with complex composite structures,they are often not suitable for high-frequency vibroacoustic analysis.Therefore,some researchers have proposed a number of energy methods in which the basic analysis variable is the statistical averaged energy,such as the statistical energy analysis(SEA),vibration conductivity approach(VCA),and radiative energy transfer method(RETM).Among them,RETM is proposed by the analogy with radiative heat transfer and belongs to the category of geometrical acoustics.RETM has been moved to be able to estimate the energy response and power flow for systems in two and three dimensions.However,at present,RETM is only suitable for homogeneous isotropic media,which limits its application in the fields related to the vibration of composite materials.Moreover,in practical application,the energy variable cannot be directly applied.Based on the basic theory of RETM,this paper studies the high-frequency vibroacoustic problems with composite structures and the conversion relationship between energy and stress/strain.The main contents include:(1)Reviewing the analysis frameworks of the statistical methods for high-frequency vibroacoustics.Firstly,the basic theory of SEA is reviewed,and the phys-ical meaning of analysis parameters is clarified.Then,the statistical properties of the high-frequency vibration energy fields of beams,plates,and cavities in the damping-frequency plane are studied,including the explanation of three regions of vibrational fields:modal field,diffuse field,and free field.Finally,the application of layered porous media in passive vibration isolation is introduced by using the SEA and transfer matrix method(TMM).(2)Research on high-frequency vibration characteristics of composite beams based on the RETM.Taking composite laminated beam as the research object,the dis-persion relation,wave group velocity,point mobility of infinite system,modal density,and input power are derived by considering Timoshenko beam model,and the RETM model of one-dimensional structure for multiwave propagation system is established.Then,the results of the model are compared with those of the existing Euler-Bernoulli beam model,and it is concluded that there is almost no difference between the two models in the vibrational field dominated by bending,but the difference is significant at the higher frequencies dominated both by shear and bending.Finally,the RETM results are compared with the theoretical solution of the wave propagation approach to verify the correctness of the model proposed in this paper.(3)Research on high-frequency vibration characteristics of two-dimensional anisotropic media based on RETM.Firstly,Fermat's principle is used to prove that the energy ray propagates along a straight line in a homogeneous two-dimensional anisotropic medium,and the equivalence of Fermat's principle and Snell's law at the coupling boundary of the coupled anisotropic media is proved.Then,the explicit expression of the directivity function of radiative energy intensity of point source in two-dimensional(2D)anisotropic media is derived for the first time;Finally,RETM for 2D anisotropic media is established to estimate the high-frequency vibration responses of orthotropic membranes,automobile tires and anisotropic thin plates,and the predicted results are compared with the modal superposition solution or the finite element method(FEM)solution.It is concluded that the RETM model can accurately predict the average energy distribution and energy flow field of high-frequency structural vibration.(4)Establishing high frequency vibration stress/strain integral expression based on RETM.In this dissertation,the dynamic stress/stain of vibrational structure is estimated for the first time based on the RETM.Firstly,it is theoretically proved that the kinetic energy density of beams or thin plate is equal to the potential energy density when the beam or thin plate vibrates at high frequencies.Then the conversion relation-ship between energy density and stress/strain is established according to the expression of elastic potential energy in elastic theory.According to the RETM theory,the mean square value of stress/strain at the observation point is superimposed by the mean square value of stress/strain converted by the energy carried by the energy ray passing through the point,and the integral expression of the mean square value of stress/strain is con-structed.Finally,the accuracy of the model is proved by several examples.