An Approach for Reconstructing the Time-Dependent Force Acting on a Thin Plate from Particle Velocity Measurements

doi:10.3901/JME.2022.01.108

Abstract

Abstract: The force acting on a thin plate is reconstructed in the time domain from particle velocity measurements. First, 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 thin plate, and the impulse response function between the vibration velocity spectrum on the plate surface and particle velocity spectrum on the hologram plane is also utilized to establish the transfer relation directly relating the force spectrum to the particle velocity spectrum in the wavenumber-time domain. Based on this, the force spectrum at each wavenumber point is reconstructed with the particle velocity measured on the hologram plane as the input. The time-dependent force on the plate surface is obtained by performing an inverse spatial Fourier transform to its force spectrum. Both results of numerical simulation and experiment demonstrate that the approach of force reconstruction from particle velocity measurements is feasible and effective in identifying the location of the excitation force and reconstructing its time-history. Meanwhile, the similar reconstruction accuracy can be achieved by the proposed approach compared to the existing reconstruction approach based on pressure measurements, but its reconstruction process can be performed more simply. A real-time and non-contact measurement way is provided here to obtain the time-dependent force acting on a plate, and the direct relationship between the force and the radiated noise is determined, which makes it possible to further understand the mechanical cause of the radiated noise.

Key words: force reconstruction, time-dependent force, thin plate, particle velocity measurements

CLC Number:

TB532

HU Long, ZHANG Yongbin, ZHANG Xiaozheng, BI Chuanxing. An Approach for Reconstructing the Time-Dependent Force Acting on a Thin Plate from Particle Velocity Measurements[J]. Journal of Mechanical Engineering, 2022, 58(1): 108-115.

References

[1] SANCHEZ J,BENAROYA H. Review of force reconstruction techniques[J]. Journal of Sound and Vibration,2014,333(14):2999-3018.
[2] PEZERAT C,GUYADER J L. Force analysis technique:reconstruction of force distribution on plates[J]. Acta Acustica united with Acustica,2000,86(2):322-332.
[3] JACQUELIN E,BENNANI A,HAMELIN P. Force reconstruction:analysis and regularization of a deconvolution problem[J]. Journal of Sound and Vibration,2003,265(1):81-107.
[4] 李晓旺,赵海涛,陈吉安. 基于测点优选和改进L曲线法的动载荷识别[J]. 上海交通大学学报,2020,54(6):569-576. LI Xiaowang,ZHAO Haitao,CHEN Jian. Force identification based on measuring point selection and improved L-curve method[J]. Journal of Shanghai Jiao Tong University,2020,54(6):569-576.
[5] QIAO Baijie,CHEN Xuefeng,LUO Xinjie,et al. A novel method for force identification based on the discrete cosine transform[J]. ASME Journal of Vibration and Acoustics,2015,137(5):051012.
[6] JIANG Hao,WU Haijun,YU Liang,et al. Force identiﬁcation based on the reconstruction of distributed response with an optimized sensor placement[J]. Proceedings of the Institution of Mechanical Engineers,Part C:Journal of Mechanical Engineering Science,2019,233(1):108-119.
[7] AUCEJO M,DE SMET O. A multiplicative regularization for force reconstruction[J]. Mechanical Systems and Signal Processing,2017,85:730-745.
[8] 严刚,孙浩. 基于贝叶斯压缩感知的复合材料结构冲击载荷识别研究[J]. 振动工程学报,2018,31(3):483-489. YAN Gang,SUN Hao. Identification of impact force for composite structure using Bayesian compressive sensing[J]. Journal of Vibration Engineering,2018,31(3):483-489.
[9] AUCEJO M,DE SMET O. On a full Bayesian inference for force reconstruction problems[J]. Mechanical Systems and Signal Processing,2018,104:36-59.
[10] 乔百杰,陈雪峰,刘金鑫,等. 机械结构冲击载荷稀疏识别方法研究[J]. 机械工程学报,2019,55(3):81-89. QIAO Baijie,CHEN Xuefeng,LIU Jinxin,et al. Sparse identification of impact force acting on mechanical structures[J]. Journal of Mechanical Engineering,2019,55(3):81-89.
[11] AUCEJO M,DE SMET O,DEU J F. Practical issues on the applicability of Kalman filtering for reconstructing mechanical sources in structural dynamics[J]. Journal of Sound and Vibration,2019,442:45-70.
[12] LOURENS E,REYNDERS E,DE ROECK G,et al. An augmented Kalman filter for force identiﬁcation in structural dynamics[J]. Mechanical Systems and Signal Processing,2012,27:446-460.
[13] 卢立勤,乔百杰,张兴武,等. 共轭梯度最小二乘迭代正则化算法在冲击载荷识别中的应用[J]. 振动与冲击,2016,35(22):176-182. LU Liqin,QIAO Baijie,ZHANG Xingwu,et al. Application of conjugate gradient least squares iteration regularization algorithm in impact load identification[J]. Journal of Vibration and Shock,2016,35(22):176-182.
[14] PEZERAT C,LECLERE Q,TOTARO N,et al. Identification of vibration excitations from acoustic measurements using near field acoustic holography and the force analysis technique[J]. Journal of Sound and Vibration,2009,326(3-5):540-556.
[15] WILLIAMS E G. Fourier acoustics:sound radiation and nearfield acoustical holography[M]. San Diego:Academic Press,1999.
[16] WU S F,ZHOU Pan. Analyzing excitation forces acting on a plate based on measured acoustic pressure[J]. Journal of the Acoustical Society of America,2016,140(1):510-523.
[17] BI Chuan-Xing,HU Long,ZHANG Yong-Bin,et al. Reconstruction of the force applied to a plate in the time domain from sound pressure measurements[J]. ASME Journal of Vibration and Acoustics,2020,142(3):031007.
[18] GRULIER V,PAILLASSEUR S,THOMAS J H,et al. Forward propagation of time evolving acoustic pressure:formulation and investigation of the impulse response in time-wavenumber domain[J]. Journal of the Acoustical Society of America,2009,126(5):2367-2378.
[19] WILLIAMS E G. Regularization methods for near-field acoustical holography[J]. Journal of the Acoustical Society of America,2001,110(4):1976-1988.
[20] HANSEN P C. Analysis of discrete ill-posed problems by means of the L-curve[J]. Siam Review,1992,34(4):561-580.
[21] ROCHEFOUCAULD O L,MELON M,GARCIA A. Time domain holography:Forward projection of simulated and measured sound pressure ﬁelds[J]. Journal of the Acoustical Society of America,2004,116(1):142-153.