Study On Computation Method Of Acoustic Radiation Based On Frequency Averaged Quadratic Pressure

The random phenomenon of radiated noise caused by random vibration is very common in the engineering field.Due to factors such as assembly relationships,manufacturing tolerances,and material defects,there is a difference between the actual state and the design state of the machine under working condition,and this difference increases as the operating frequency increases,and then the machine radiates noise with random characteristics.And the random phenomenon of sound radiation caused by the random load of the structure in the working state is often difficult to avoid because of the influence of the environment and its own factors.For such situations,the problems of random acoustic radiation are rarely considered in the frequency bandwidth.The frequency averaged quadratic pressure method is used to predict the random noise radiated from the structure in the frequency bandwidth.In this paper,the frequency averaged quadratic pressure method is researched.First of all,CEBIEF method(Combined Energy Boundary Integral Equation Formulation)and coupling coefficient method are proposed to deal with the nonuniqueness problem of the frequency averaged quadratic pressure method in full space at the irregular frequencies.Secondly,the frequency averaged quadratic pressure method in half space is established for predicting the random acoustic radiation of structures with random vibration in half space,and CEBIEF method and the coupling method in half space are proposed to solve the nonuniqueness problem at the irregular frequencies.Finally,to predict the acoustic radiation from a thin-body structure with random vibration,the thin-body frequency averaged quadratic pressure method is proposed based on the thin-body Helmholtz boundary integral equation.The acoustic radiation problems of the typical structures such as cylindrical shells and thin plates are analyzed based on frequency averaged quadratic pressure method in free space,frequency averaged quadratic pressure method in half space,and thin-body frequency averaged quadratic pressure method.The numerical examples show that frequency averaged quadratic pressure method can deal with the random acoustic radiation problems of structures with random vibration.And these methods become a possible choice for technicians to deal with this kind of acoustic radiation problems.The main contents of this paper are as follows:(1)The frequency averaged quadratic pressure method based on the frequency averaged Helmholtz boundary integral equation is derived.Based on the basic idea of explicit evaluation,the expressions of singular integrals which are encountered in the frequency averaged Helmholtz boundary integral equation is given.Combining the finite element method and the frequency averaged quadratic pressure method is applied to the random acoustic radiation problem of cylindrical shells under random loadings.The results show that combining the finite element method and the frequency averaged quadratic pressure method can be used to predict the random acoustic radiation from structure under random loadings.(2)In order to solve the nonuniqueness problem of the frequency averaged quadratic pressure method based on the frequency averaged Helmholtz boundary integral equation at the irregular frequencies,CEBIEF is proposed.This method is based on the frequency averaged Helmholtz boundary integral equation,and the internal and surface points of closed surface are selected to establish frequency averaged Helmholtz boundary integral equation for composing overdetermined equations,and by solving the overdetermined equations the unknowns on the surface are determined.And then the acoustic radiation of structures can be calculated with the frequency averaged quadratic pressure method.The numerical examples are implemented,and the results show that CEBIEF method can get the solution conveniently and quickly.However,the number of CEBIEF points increases as the calculating frequency increases,and CEBIEF method may fail.For the general structure,a discriminant function is proposed to determine whether the calculating frequency is the failure frequency and whether CEBIEF method get the unique solution in the case that failure area and the needed number of CEBIEF points are uncertain.(3)The frequency averaged normal derivative Helmholtz boundary integral equation is established,and this equation is applied to determine the boundary condition of the frequency averaged quadratic pressure method.Based on the basic idea of explicit evaluation,the expressions of the hypersingular integrals in the frequency averaged normal derivative Helmholtz boundary integral equation are given.It has been found that this equation,like the frequency-averaged Helmholtz boundary integral equation,can be used to calculate the frequency averaged quadratic pressure,but it also suffers from the problem that the solution is not unique at the irregular frequency,and the irregular frequencies of the two sets of equations are different.(4)CEBIEF method has the advantages of simple programming and convenient use,but in order to robustly solve the nonuniqueness problem at the irregular frequencies,the coupling coefficient method is established.In this method,the surface points of closed surface are selected to establish frequency averaged Helmholtz boundary integral equation and the frequency averaged normal derivative Helmholtz boundary integral equation,and two sets of equations form the new equations by coupling coefficient.By solving the equations the unknowns on the surface are determined.(5)To calculate the acoustic radiation of structures with random vibration in half space,the frequency averaged quadratic pressure method based on frequency averaged Helmholtz boundary integral equation and the frequency averaged normal derivative Helmholtz boundary integral equation in half space are established,respectively.With the proposed CEBIEF method and coupling method in half space,the nonuniqueness problem is solved.The numerical examples show that CEBIEF method and the coupling method in full and half space can be used to calculate the acoustic radiation of structures with random vibration.(6)For predicting the random acoustic radiation of thin-body structures with random vibration,the thin-body frequency averaged quadratic pressure method based on thin-body Helmholtz boundary integral equation is established.By combining finite element method and the thin-body frequency averaged quadratic pressure method,the numerical examples are implemented for thin-body structures under random loadings,and the results show that the thin-body frequency averaged quadratic pressure method can be used to calculate the random acoustic radiation of the thin-body structures with random vibration.