Hybrid Methods And Optimization Design For The Mid-frequency Vibration Of Built-up Structures And Vibro-acoustic Systems

Built-up structures and vibro-acoustic systems refer to systems composed of multiple components with significantly different dynamic characteristics,which are widely used in large vehicles such as carrier rockets,aircraft,trains and ships.Vehicles may be subjected to a wide range of excitation frequencies during their operation.In order to improve the safety,comfort and stability of the system it is essential to study the dynamic behavior of the built-up structure or vibro-acoustic system when optimizing the design.As we all know,Finite Element Method(FEM)and Statistical Energy Analysis(SEA)have been widely used for the low-and high-frequency vibration analysis of built-up structures and vibro-acoustic systems,respectively.However,due to the remarkable difference in dynamic properties between the different components of the built-up structure or vibro-acoustic system,the different components may be subjected to deformations with significantly different wavelengths as the excitation frequency increases:some components are subjected to short wavelength deformation and have a high modal density,while other components are subjected to long wavelength deformation and have a low modal density,which means that the built-up structure or vibro-acoustic system typically exhibits mid-frequency vibration behavior.The mid-frequency vibration analysis of a built-up structure or vibro-acoustic system faces two difficulties.First,many degrees of freedom(DOFs)are required to obtain detailed deformation,which leads to a sharp increase in computing cost.Second,the response may be very sensitive to the uncertainties of the system,which can result in meaningless deterministic analysis.Both of those difficulties arise from the decreasing wavelength of the deformation and become increasingly severe as the frequency increases.Hence,neither the FE method nor SEA can describe the motion of built-up structures and vibro-acoustic systems well.In this context,the hybrid FE-SEA method,which combines FE and SEA for predicting the ensemble average response,may be the best analysis scheme.However,this method still has some disadvantages such as low computational efficiency and inaccurate description of specific problems.In this dissertation,two more effective hybrid methods are developed according to the principles of the hybrid FE-SEA method.Moreover,the size and topology optimization of built-up structures and vibro-acoustic systems are studied by using these improved methods.The details can be summarized as:1)A new hybrid method is developed for the mid-frequency vibration of vibro-acoustic systems.The Boundary Element(BE)method is used to describe the motion of a deterministic acoustic cavity.By enforcing the continuity conditions of displacement and velocity at the coupling interface,the dynamic coupling between the deterministic acoustic cavity and the statistical structure described by SEA is established.Then,a hybrid BE-SEA method for the mid-frequency vibration of vibro-acoustic systems is proposed.Post-processing provides formulations for calculating the sound pressure at points inside the acoustic cavity.Due to the nature of the BE method for acoustics,the proposed method not only has few degrees of freedom,but also automatically satisfies the Sommerfeld radiation condition at infinity for exterior acoustics problems.2)The hybrid FE-SEA method developed for mid-frequency vibration of built-up structures needs to compute the total dynamic flexibility matrix at every frequency,which is very time consuming.An improved hybrid FE-SEA method is developed to overcome this problem.In the present method,first,dynamic condensation is introduced to reduce the order of the deterministic FE component,which results in significant reduction of the total dynamic stiffness matrix.Then,noting that the dynamic stiffness matrix of the deterministic component is established by using the FE method,a fast inverse algorithm is employed to calculate the dynamic flexibility matrix of the slave degrees of freedom of the deterministic component generated in the condensation process.These two steps avoid the direct inverse computation of a large matrix at each frequency point of interest,resulting in significant time saving.3)The sizing optimization on the mid-frequency vibration of the built-up structures is studied based on the hybrid FE-SEA method.In the optimization model,the size parameters of the deterministic and statistical subsystems are taken as design variables.The energy of the system under a specific frequency,or the frequency-aggregated energy of the system in a given frequency band,is taken as the objective function to be minimized.In this context,an efficient direct differentiation method for sensitivity analysis is derived.Then the optimization problem is solved by using a gradient-based mathematical programming algorithm.4)The topology optimization of a sound absorbing layer for the mid-frequency vibration of vibro-acoustic systems is studied by using the above improved hybrid methods.Based on the SIMP approach an artificial sound absorbing material model is suggested and the relative densities of the sound absorbing material are taken as design variables.The sound pressure level at a specified point in the acoustic cavity is to be minimized by distributing a given amount of sound absorbing material.An efficient direct differentiation scheme for the response sensitivity analysis is proposed.