Research On Time-dependent Force Reconstruction Approach From Acoustic Measurements

Accurate acquisition of forces plays an important role in the research of structural optimization design,health monitoring,vibration and noise control,and so on.The force acting on a structure is often difficult to be measured directly by the force transducer,for example,the location of the force is unknown in advance.In this case,it is often more appropriate to reconstruct the force indirectly based on the measured response.The response can be vibration response,such as acceleration,velocity or displacement,or acoustic response,such as pressure or particle velocity.In some circumstances,acoustic measurement has some advantages than vibration measurement,such as time-dependent force reconstruction using response data at multiple measurement points as inputs.On the one hand,acoustic measurement is a non-contact measurement way,which avoids the influence of additional mass on structural vibration when the contact vibration sensors measure multiple point responses.On the other hand,compared with non-contact laser vibration measuring equipment,acoustic measuring equipment is more economical and convenient to form an array to measure the sound field simultaneously.In view of this,the time-dependent force reconstruction approach from acoustic measurements is studied in this dissertation.The research objects of force reconstruction involved in this dissertation are divided into two types: thin plate and arbitrarily shaped structure.Three force reconstruction approaches are proposed for the reconstruction of time-dependent forces acting on a thin plate structure with the planar shape.At First,an indirect reconstruction approach of timedependent forces acting on a thin plate based on real-time nearfield acoustic holography(RT-NAH)is proposed.It first uses RT-NAH technique to reconstruct the vibration responses on the surface of the plate based on measured pressures,and then the equation of motion of the plate is used to calculate the forces based on the reconstructed vibration responses as the inputs.Secondly,a direct reconstruction approach of time-dependent forces acting on a thin plate based on RT-NAH is proposed.Through the derived impulse response function relating the force spectrum to the particle velocity spectrum or pressure spectrum,the forces can then be reconstructed directly in a one-step inversion process from the measured particle velocities or pressures.Thirdly,a reconstruction approach of time-dependent forces acting on a thin plate based on time-domain plane wave superposition method is proposed,which eliminates the limitation caused by the array measurement point layout in the above approaches.For an arbitrarily shaped structure,based on the governing equation between the force and sound,the impulse response function obtained by the impact test method,and a regularization method with the mixed norm term,a reconstruction approach of time-dependent forces acting on an arbitrarily shaped structure from acoustic measurements is proposed.The detailed research contents of this dissertation are shown as follows:An indirect reconstruction approach of time-dependent forces acting on a thin plate based on RT-NAH is proposed.It consists of two steps: reconstruction of vibration responses based on RT-NAH and calculation of the time-dependent forces acting on a thin plate.Firstly,a microphone array is used to measure the sound pressures in the near field of the thin plate.And then,the measured sound pressures are taken as the inputs of the RT-NAH to reconstruct the vibration responses,including the vibration acceleration,velocity,and displacement,on the surface of the plate.The equation of motion of the plate can then be processed to calculate the time-dependent forces with all these reconstructed vibration responses as the inputs.In the process of vibration displacement reconstruction by RT-NAH technique,the impulse response function relating the vibration displacement spectrum to the pressure spectrum is derived for the first time.Results of numerical simulations as well as experiments demonstrate that the proposed approach can identify the locations of the forces accurately and reconstruct the time-histories of the forces effectively.A direct reconstruction approach of time-dependent forces acting on a thin plate based on RT-NAH is proposed.The impulse response function between the force spectrum and vibration velocity spectrum on the surface of the plate is deduced based on the equation of motion of the plate,and the impulse response function between the vibration velocity spectrum on the plate surface and particle velocity spectrum on the hologram plane is utilized to establish the impulse response function relating the force spectrum to the particle velocity spectrum in the wavenumber-time domain.Based on this,the force reconstruction is directly carried out with the particle velocities measured on the hologram plane as the inputs.Similarly,the impulse response function between the force spectrum and pressure spectrum is also established in the wavenumber-time domain based on the impulse response function between the vibration velocity spectrum or vibration acceleration spectrum and pressure spectrum on the hologram plane,and the measured pressures are used as the inputs to reconstruct the forces directly.Both results of numerical simulations and experiment demonstrate the feasibility and effectiveness of the timedependent force reconstruction approach.On the one hand,the proposed approach can reconstruct the time-dependent forces acting on a thin plate from particle velocity measurements.On the other hand,for the reconstruction of time-dependent forces acting on a thin plate from pressure measurements,the proposed approach can obtain a similar reconstruction accuracy compared with the indirect reconstruction approach of timedependent forces acting on a thin plate based on RT-NAH,but its reconstruction process can be performed more simply.A reconstruction approach of time-dependent forces acting on a thin plate based on time-domain plane wave superposition method is proposed.By directly discretizing the integral of two-dimensional Fourier transform,the limitation of the array measurement point layout in the above approaches is eliminated,and the time-dependent forces reconstruction of thin plate based on the arbitrary array layout is realized.It includes two parts: the direct reconstruction method of time-dependent forces acting on a thin plate based on force-sound impulse response and the indirect reconstruction method of timedependent forces acting on a thin plate based on vibration-sound impulse response.Results of simulations and experiments verify the feasibility and effectiveness of the proposed approach,which further expands the scope of application of the previous two approaches in the aspect of array layout.A reconstruction approach of time-dependent forces acting on an arbitrarily shaped structure from acoustic measurements is proposed.Based on the governing equation between the force and sound in the spatial and temporal domains and the impulse response function obtained by the impact test method,the time-dependent forces on the surface of a vibrating structure can be reconstructed with the pressures measured in the near field of the structure as inputs,and the shape of the vibrating structure can be arbitrary,that is to say,it is not limited to a plane.In the reconstruction process,a regularization method with the mixed norm term is introduced to resolve the ill-posed problem,which is able to take advantage of the prior knowledge of space and time characteristics of the forces to improve the reconstruction effect.The numerical simulations of reconstructing the timedependent forces acting on a plate and the experiments of reconstructing the impact forces acting on a plate,a semi-cylindrical shell and an elliptically-shaped structure are carried out to demonstrate the effectiveness of the proposed approach for reconstructing the forces in the space-time domain.In this dissertation,the time-dependent forces reconstruction approaches for thin plate and arbitrarily shaped structure are studied.It provides a non-contact and real-time measurement way to identify the locations of forces and reconstruct their time-histories,thereby helping to further diagnose the mechanical cause of the radiated noise and providing a reference for noise control.