Optimal Design Of Acoustic And Vibro-acoustic Topology Based On Fast Multi-pole Boundary Element

Reducing the sound emission of machines,systems,and structures has become a key component of an engineer's work.To achieve a good noise control,several treat-ments can be utilized,including topology design,damping layer and absorbing material layer,and finally consists in acoustic topology optimization.This dissertation forces on the acoustic topology optimization using the boundary element method(BEM)because this numerical technique offers several advantages in predicting exterior sound field.Based on the noise prediction,two optimization models are established to reduce the sound radiation or the noise level at specified regions.The main contents include four parts as follows:Sound radiation and scattering analysis based on the acoustic BEM.The Bur-ton and Miller formulation is selected to overcome the non-uniqueness problem arising in exterior acoustic problems when using a single boundary integral equation.The hy-persingular integrals arising from Burton and Miller approach is evaluated using the Cauchy principle integral and Hadamard finite-part integrals.However,the conven-tional BEM still suffers from the large computational cost due to its fully populated coefficient matrix,and thus is difficult to be directly applied to large-scale problems.In this work,we utilize the fast multipole method(FMM)with the assistance of iterative solver to achieve a fast boundary element analysis,forming the fast multipole boundary element method(FMBEM).With the FMBEM,problems with hundreds of thousand or even millions unknowns can be easily solved on normal desktop PC.Furthermore,we also implement the acceleration of adjoint analysis different from sound analysis by modifying the existing FMM.The adjoint analysis is not common in sound analysis,but contributes a lot to the topology optimization.Hence,the acceleration to adjoint analysis improves the computational efficiency for topology optimization.Structural-acoustic analysis based on FEM-BEM.A structural-acoustic anal-ysis model is established based on the coupled finite element method and boundary element method(FEM-BEM).The structural vibration is analyzed by the FEM,and acoustic domain is analyzed by the BEM.Strong interaction between the structural and acoustic domain is considered,and finally leads to a two-way coupling scheme.To solve this coupled system,the Schur complement is employed to eliminate the unknowns of structural component to obtain the sound pressures.Then the structural response results are computed by a backward step of sound pressure into the coupled system.For large-scale boundary element(BE)component,the FMM is also used leading to an efficient coupled method,i.e.,the FEM-FMBEM.This method allows the vibration analysis of large-scale and fluid-loaded structures.With the response results from structural-acoustic analysis,the non-negative intensity(NNI)can be derived from radiation mode analysis.Since NNI omits the near-field cancellation effects in sound intensity,it has been proven to be an efficient visualization of surface contributions to sound power and could identify radiating hot spots.This quantity seems to be helpful in radiation control.Topology optimization for structural-acoustic system.An efficient topology optimization procedure with density-based approaches for exterior acoustic-structure interaction problems is established.This optimization model optimize the material dis-tribution to minimize the radiated sound power.The adjoint variable method(AVM)formulations are derived for sensitivity analysis of arbitrary objective function,and the feedback coupling between the structural and acoustic domains are taken into consid-eration in the sensitivity analysis.In addition to the application of FMM in the acoustic BEM response analysis,the FMM is now updated to adapt to the arising different mul-tiplications in the AVM equations.These accelerations save considerable computing time and memory.With the gradient information,the optimization problem is solved by the method of moving asymptotes(MMA).Distribution optimization of porous material over structural surfaces.An ap-proach to optimize the distribution of porous material over structural surfaces is devel-oped by topology optimization.Different from the coupled system,the structural com-ponent in this part is simplified to porous material layer,and can be modeled by local impedance boundary conditions.To simulating the absorbing property,acoustic absorp-tion characteristics over surface are numerically computed using the Delany-Bazley-Miki empirical model and rigid-backing assumption.Based on the solid isotropic ma-terial with penalization(SIMP)method,the optimization is performed by setting the artificial element densities of porous material as the design variables,minimizing the sound pressure or the dissipated sound power as the design objective.As a key treat-ment,we also develop a fast sensitivity analysis approach based on the AVM and FMM.According to the gradient information,the MMA is used for solving the optimization problem to find the optimal solution.Based on the acoustic BEM and FEM-BEM,two optimization models are devel-oped to optimize the distribution of structural material or porous material.By using these two optimization models,the sound radiation or noise level at some specified regions can be reduced,and finally yields an efficient noise control.