Design Optimization Of Mid-Frequency Vibro-Acoustic Systems Based On A Statistical Modal Energy Distribution Analysis

Industrial equipment will generate varying degrees of noise during operation.Strong noise not only causes structural damage but also affects people's daily life.Therefore,vibration suppression and noise reduction are significant in practical engineering.Due to the complexity of exterior excitation and structural configuration,noise has different forms of expressions in varying frequency ranges.The frequency spectrum in low-frequency ranges is distinctly distributed and exhibits a homogenized tendency in high-frequency ranges whereas shows a mixture characteristic of the above two features in mid-frequency ranges.On the other hand,referring to the research on low-and high-frequency noise predictions,sophisticated numerical methods include finite element method(FEM),boundary element method(BEM),and statistical energy analysis(SEA).However,the noise analysis and optimization in mid-frequency ranges need to be studied in depth.As a newly proposed method,statistical modal energy distribution analysis(SmEdA)is based on the power balance between different modes of the coupled subsystems that combines deterministic and statistical techniques,and can expediently predict the mid-frequency vibro-acoustic response.On the other hand,vibrating noise has a close relationship with the structural sizes,material properties,shape characteristics and topology distributions.Considering these factors comprehensively and designing vibro-acoustic systems with lower noise level appear to be particularly important.This dissertation devotes to develop new optimization models and sensitivity analysis techniques for mid-frequency vibro-acoustic systems in the framework of SmEdA.Via optimizing the structural sizes,structural and acoustic damping layouts,the noise level of mid-frequency systems is significantly reduced.The main content and results are obtained as follows:1.Size optimization of mid-frequency vibro-acoustic systems.An optimization model for minimizing the total acoustic energy of the vibro-acoustic system under broad-band random excitation is established via a SmEdA and a moving-asymptotes solving procedure is presented.In the optimization model,the structural thicknesses at different areas are designated as design variables and the structural material consumption is the constraint condition.Considering the situation that many modal derivatives need to be calculated in the sensitivity analysis process,a semi-analytical sensitivity equation about the total acoustic energy with respect to the structural thickness is emphatically deduced.Therein,a coefficient condensation technique is proposed to avoid the dimensional inconformity of SmEdA coefficient matrices during the difference operation due to the variation of the number of modes per band with the perturbation of structural sizes.Numerical examples demonstrate the effectiveness of the proposed optimization procedure.2.An improvement of the sensitivity accuracy in size optimization by using a mixed sensitivity analysis technique integrating the analytical method with complex variable method(CVM).The aforementioned semi-analytical sensitivity method has a dependence on perturbation steps,which would adversely affect the optimization solution.To address this issue,a novel complex variable method is introduced to calculate the modal sensitivities and then a modified semi-analytical sensitivity analysis technique is developed.Numerical examples are given to validate that the sensitivities obtained by the modified semi-analytical sensitivity analysis technique are more accurate and stable than those by using traditional semi-analytical method(SAM)and overall finite difference method(OFD).Owning to the modified semi-analytical sensitivity analysis method,the optimization procedure is then applied to more complex vibro-acoustic problem,i.e.sound transmission optimization,which belongs to a multilevel-subsystem coupling,and then good effectiveness is gained.3.Local acoustic optimization of mid-frequency vibro-acoustic systems.The energy resolution of classical statistical energy analysis is limited within the subsystem energy,and the local response of designated domains inside the acoustic cavity is difficult to predict.In practical engineering,noise reduction of certain interesting positions or domains inside the acoustic cavity also deserves to be studied.SmEdA is based on the power balance of modal energies and can accurately localize the acoustic energies in designated local domains by using the corresponding modal coordinates,i.e.energy density distribution estimation.Here,the acoustic energy in designated local domains serves as the objective function.By optimizing the thickness distribution of the structural subsystem,the acoustic energy in local domains of the cavity is reduced.Optimization results indicate that size optimization is useful for reducing the local acoustic response and the proposed optimization procedure has directive significance on the improvement of the local acoustic environment in automobile design.4.Layout optimization of viscoelastic damping material in mid-frequency vibro-acoustic systems.Viscoelastic materials that are attached onto the structural surface are effective for reducing vibratory response in vibro-acoustic systems.How to arrange limited amount of material to key positions remains a significant problem in mid-frequency vibro-acoustic systems.Considering the frequency dependence of the viscoelastic material and the relatively smooth feature of the material parameter curves,the corresponding damping parameters are averaged in each frequency band of interest.Based on the methodology of topology optimization,the relative densities of the viscoelastic material are selected as design variables.By optimizing the viscoelastic layouts on the surface of the structural subsystem,the total energy of the acoustic subsystem is reduced to the lowest value.In order to avoid the gray region problem,a volume-preserving Heaviside function is employed to penalize the design variables to crisp 0/1 values without breaking the material volume constraint.The significant reduction of the acoustic energy demonstrates the effectiveness of the layout optimization procedure and optimal results show that the modal coupling factors and acoustic modal energies tend to be more uniform after optimization.5.Layout optimization of porous sound-absorbing material in mid-frequency vibro-acoustic systems.Porous sound-absorbing materials which are applied in the internal cavity can effectively attenuate acoustic waves.The considered optimization problem is minimizing the total energy of the internal acoustic cavity within the prescribed frequency range by reasonably positioning the porous material patches under a given volume constraint where the relative densities of the porous material are designated as design variables.Due to its simplicity and efficiency in numerical and optimization applications,an empirical material formulation,Delany-Bazley model,is implemented for the prediction of the acoustic behavior of the porous material with frequency including the complex density,propagation speed and bulk modulus.By means of a Modal Strain and Kinetic Energy method(MSKE),the modal damping loss factors which are associated with the energy attenuation between different modes of the coupled subsystems are estimated.Because the magnitudes of the acoustic FEM matrices are much lower than those of the structural FEM matrices,the precision of the forward difference method fail and the central difference method gains stable results only in certain perturbation steps at the expense of a double computation.Then,the modified semi-analytical sensitivity analysis technique is used again to estimate the sensitivities of the total acoustic energy with respect to the layout variables.Numerical examples show a significant reduction of acoustic energy and the numbers of acoustic modes tend to decrease after optimization.