| The optimal design of sound-absorbing materials can effectively reduce structural vibration noise,which plays an important role in noise control.The boundary element method(BEM)has become a powerful tool for optimizing design of sound-absorbing materials because of its advantages in external sound field analysis.However,the fundamental solution of the boundary integral equation is usually frequency dependent,resulting in good optimization results at one frequency point not being significant or even worse at other frequency points,i.e.single frequency optimization results are susceptible to frequency.Therefore,it is necessary to carry out a broadband optimization analysis of soundabsorbing materials adhering to the structural surface.However,the coefficient matrix must be reconstructed at each frequency point in the broadband segment,which leads to the low efficiency of broadband optimization for complex structural models.Thereby,it is essential to develop a numerical algorithm for accelerated the broadband optimization analysis of sound-absorbing materials.This paper mainly carries out the accelerated analysis for acoustic broadband optimization,and the acoustic scattering problem of structural surface adhered sound-absorbeing materials is taken as an example to investigate the effects of some important parameters(frequency,frequency range,etc.)on the system response,and to verify the accuracy and efficiency of the algorithm.The specific research content is as follows:(1)Constructing a series expansion of the Green’s function in the boundary integral equation using the series expansion method.The coefficient matrix of the acoustic system equation is frequency dependent,leading to the repeated construction of the coefficient matrix at each frequency in the broadband calculation.The Taylor expansion is used to decouple the integrand function in the BEM into the product of frequency dependence and frequency independence terms,and the series expansion expression of the boundary integral is constructed.As a result,the coefficient matrix only needs to be constructed once for the broadband calculation,improving computational efficiency and reducing storage costs.(2)Constructing the reduced-order model that retain the basic structure and key properties of the original boundary element model appling the adaptive Taylor-based secondorder Arnoldi(AT-SOAR)method.For large-scale complex structural problems,the solution of the system equations is time-consuming.The AT-SOAR method is used to obtain a reduced-order model that retains the basic structure and key characteristics of the original boundary element model,and automatically determines the number of expansion points and order of orthonormal basis,thus finally achieving high accuracy and high efficiency in predicting the system response in the target frequency band.(3)Broadband optimal design of structural surface adhered sound-absorbing materials based on isogeometric boundary element method(IGABEM).An isogeometric method based on the Catmull-Clark subdivision surface is used to discretize the boundary integrals,and the system equation set is established by combining the collocation point method.The isogeometric discretization form of the acoustic boundary integral equation is derived using the Burton-Miller method to overcome the non-uniqueness problem of solution.A set of singularity-free boundary integral equations for the sound field and boundary integral equations for acoustic sensitivity are derived using the Cauchy principal value and the Hadamard finite partial integration method.The impedance boundary condition is established to simulate the acoustic properties according to the Delany-Bazley-Miki empirical model,and the method of moving asymptotes(MMA)is combined to carry out the broadband optimization analysis of the sound-absorbing materials distribution.The AT-SOAR method is used to accelerate the solution of the system response,which offers the feasibility of broadband optimization analysis of complex structural problems. |
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