Topology Optimization And Sensitivity Analysis Of Acoustic Structural Coupled Systems

Highly developed industries in modern cities make people's lives become more comfortable and convenient.However,environmental pollution,especially noise pollution,is one of the most serious problems facing mankind today.As a result,how to effectively reduce noise becomes a problem that needs to be solved urgently.In the research field of vibration noise,the acoustic structural coupled system is an important research object.The enclosed cavities are the most common acoustic structural coupled systems,such as the passenger compartment of a car and the airplane cabin.The acoustic structural coupled systems have two typical features:firstly the acoustic cavity is enclosed by the external structure and secondly the coupling between the sound field and the structure is considered.At present,the deterministic external loads are the most commonly used in the design optimization of the acoustic structural coupled systems.However,stochastic loads are widely existed in the actual engineering.Therefore,topology optimization of the acoustic structural coupled systems excited respectively by harmonic load,stationary random load and non-stationary random load have been researched and the corresponding sensitivity analysis formulas are derived in this dissertation.The main contents of this dissertation are given as follows:1.Topology optimization of the acoustic structural coupled systems under harmonic excitations.The topology optimization and sensitivity analysis of the bi-material structure are investigated for minimizing the sound pressure level of the coupled systems under harmonic excitations.The dynamic equation of the acoustic structural coupled systems is described by using the finite element method.Based on the microstructure-based design domain method,a bi-material structural interpolation model is established,which makes the topological optimization problem become the optimal bi-material(matrix material and inclusion material)distribution problem.The relational expressions between the structural element matrices and the topological design parameters are constructed.The topological design problem of the acoustic structural coupled systems under harmonic excitations is proposed.The volume fraction of inclusion material in each element is regard as a topological design variable.The sound pressure level of the specified reference point is taken as the objective function and the total structural weight is treated as the constraint function.Using the adjoint method,the sensitivity formula of the sound pressure level at the specified reference point with respect to each topological design variable is derived.The relaxed form of optimality criterion method is applied to solve the optimization problem of the acoustic structural coupled systems.Numerical examples confirm the validity of the presented methods.2.Topology optimization and sensitivity analysis of the acoustic structural coupled systems under stationary random excitations.This dissertation focuses on the optimal bi-material topological configuration problem of the coupled systems under stationary random excitations.In the optimization problem,the mean value of the power spectrum densities of sound pressure at the specified reference points in the concerned excitation frequency range is taken as the objective function.The total structural weight is regarded as the constraint function.In order to suppress the intermediate density elements in the optimal design,an improved objective function is presented by introducing a penalty term into the original objective function.The pseudo excitation method and the mode superposition method are used together to solve the random response analysis problem of the coupled systems.After this,based on the pseudo excitation method,the sensitivity formula of the mean value of the power spectrum densities of sound pressure at the specified reference points with respect to each topological design variable is derived by using the adjoint method and the direct method,respectively.In the numerical examples,the influences of the reference point position,structural weight constraint,natural frequency constraint and penalty term on the optimization results are discussed,respectively.3.A method for response analysis of the acoustic structural coupled systems under non-stationary random excitations.This dissertation investigates the random response analysis of the acoustic structural coupled systems under uniformly modulated evolutionary random excitations.The pseudo excitation method is introduced to transfer the random response analysis of the coupled systems under uniformly modulated evolutionary random excitations into the transient response analysis under deterministic excitations.A method integrating the pseudo excitation method and the precise integration method is presented for computing the non-stationary random response of acoustic structural coupled systems.By comparison with the Monte-Carlo method and the Newmark method,the validity and efficiency of the presented methods are verified in the numerical examples.4.Topology optimization and sensitivity analysis of the acoustic structural coupled systems under non-stationary random excitations.We consider the topology optimization and sensitivity analysis of the bi-material structure for reducing the random acoustic response of the coupled systems under uniformly modulated evolutionary random excitations.In the optimization problem,the design objective is minimizing the average power spectrum density of sound pressure at the reference points in the concerned excitation frequency range and time range by configuring the given amount of materials.Based on the pseudo excitation method and the precise integration method,the adjoint method and the direct method for the sensitivity analysis of the objective function with respect to each topological design variable are developed,respectively.Numerical examples demonstrate the validity of the sensitivity analysis method and the feasibility of the optimization method.