Application Of Wave Based Method For Coupled Structural-acoustic Analysis

The requirement for noise control has been increasingly strict with the development of people’s quality of lives.In practical engineering,many issues concerning noise prediction and noise control can be simplified as problems of coupling between elastic structures and acoustic cavities,namely structural-acoustic coupling.For example,the driver’s cab and the aircraft cabin.The structural-acoustic coupling problems are the base for the research of noise control.Therefore,it is of great significance to find an analytical approach which is of high efficiency and reliability.A new approach – WBM(Wave Based Method),and the hybrid FE(Finite Element Method)-WBM have been adopted in this paper to discuss the problems of structural bending vibrations and structural-acoustic coupling.First of all,the wave based method which is based on the Mindlin plate theory,is applied to the analysis of flat plate bending vibrations.Taking the rectangular plate as an example,a model for plate bending vibrations based on the wave based method is constructed in the software Matlab,and numerical evaluation is performed.In order to validate the effectiveness of the wave based method,several finite element models with different element sizes are built in software Optistruct and simulation analysis is performed.Then compare the normal displacement color plots and displacement-frequency response curves at response points between finite element model and WBM model.And the results demonstrate that within a certain range,with the decreasing of the element sizes,the finite element models are becoming increasingly finer and the simulation results fit the WBM evaluation results better.And finally,error analysis and convergence analysis are performed.Therefore,the validity and the high convergence rate of the WBM applied in the plate bending vibrations have been proved through comparing with finite element analysis.Secondly,based on the WBM used in the flat plate bending vibrations,the WBM is expanded to the analysis of coupled structural-acoustic systems.In the first place,the WBM for 3D acoustic analysis has been induced.The equations for plate bending and acoustic pressure are established respectively through weighted residual formulation,by applying acoustic pressure continuity condition and normal velocity continuity condition at the coupling boundaries.And the equations are finally assembled into the system equation,solving which the weighting coefficients for structural and acoustic wave functions can be attained.Substituting the weighting coefficients into the expansions for structural displacement and acoustic pressure,the dynamic parameters of plate displacement and cavity pressure can be obtained.Taking a simple 3D structural-acoustic system consisting of a rectangular plate and a cuboid cavity as an example,the WBM is successfully applied in the coupled system by programming in Matlab and performing numerical evaluation.Then,several finite element models with different element sizes are built in software Optistruct and simulation calculations are performed.The results of simulation are compared with that of the numerical evaluation,which shows that with the decreasing of the element sizes,the simulation results fit the WBM evaluation results better even using a few wave functions.Under this circumstance,the WBM applied in the structural-acoustic system is verified to be reliable and of high convergence rate.Finally,in consideration of the complexity of structural-acoustic system in practice and to combine the computational efficiency of WBM and the model flexibility of FEM,a new hybrid FE-WBM approach is proposed,which containing three coupled sections namely FE-FE-WBM.In the new FE-WBM approach,the structure is analyzed by finite element method,and the acoustic cavity is analyzed by hybrid FE-WBM method with small part of it analyzed by finite element method while the rest majority of the cavity analyzed by wave based method.The equations for plate bending and acoustic pressure are established respectively by applying acoustic pressure continuity condition and normal velocity continuity condition at the coupling boundaries,through weighted residual approach.System matrix is obtained by assembling plate bending equation and cavity pressure equation.The nodal displacement for structure,nodal pressure for FE acoustic cavity and weighting coefficients for acoustic wave functions are figured out by solving the system matrix.And in this case,plate displacement and cavity pressure can be worked out.At last,by constructing a car-like finite element model in the software Optistruct and comparing simulation results with numerical evaluation results by programming in Matlab,the feasibility of the newly-proposed hybrid FE-WBM approach is validated.