Approximation of structural damping and input excitation force

Abstract

Structural dynamic characteristics are the most significant parameters that play a decisive role in structural damage assessment. The more sensitive parameter to the damage is the damping behavior of the structure. The complexity of structural damping mechanisms has made this parameter to be one of the ongoing research topics. Despite all the difficulties in the modeling of damping, there are some approaches like as linear and nonlinear models which are described as the energy dissipation throughout viscous, material or structural hysteretic and frictional damping mechanisms. In the presence of a mathematical model of the damping mechanisms, it is possible to estimate the damping ratio from the theoretical comparison of the damped and un-damped systems. On the other hand, solving the inverse problem of the input force estimation and its distribution to each SDOFs, from the measured structural responses plays an important role in structural identification process. In this paper model-based damping approximation method and a model-less structural input estimation are considered. The effectiveness of proposed methods has been carried out through analytical and numerical simulation of the lumped mass system and the results are compared with reference data. Consequently, high convergence of the comparison results illustrates the satisfactory of proposed approximation methods.

Keywords

structural modal parameters / damping identification method / input excitation force identification / Inverse problem

References

[1] Nanthakumar S S ,  Lahmer T ,  Zhuang X ,  Zic G, Rabczuk  T. Detection of material interfaces using a regularized level set method in piezoelectric structures. Inverse Problems in Science and Engineering, 2016, 24(1): 153–176

[2] Nanthakumar S S ,  Valizadeh N ,  Park H S ,  Rabczuk T . Surface effects on shape and topology optimization of nanostructures. Computational Mechanics, 2015, 56(1): 97–112

[3] Nanthakumar S S ,  Lahmer T ,  Rabczuk T . Detection of multiple flaws in piezoelectric structures using XFEM and level sets. Computer Methods in Applied Mechanics and Engineering, 2014, 275: 98–112

[4] Nanthakumar S S ,  Lahmer T ,  Rabczuk T . Detection of flaws in piezoelectric structures using extended FEM. International Journal for Numerical Methods in Engineering, 2013, 96(6): 373–389

[48] RabczukT, EiblJ, StempniewskiL . Simulation of high velocity concrete fragmentation using SPH/MLSPH. International Journal for Numerical Methods in Engineering, 2003, 56(10): 1421–1444

[49] RabczukT, Belytschko T. A three dimensional large deformation meshfree method for arbitrary evolving cracks. Computer Methods in Applied Mechanics and Engineering, 2007, 196(29–30): 2777–2799

[50] RabczukT, ZiG, BordasS, Nguyen-Xuan H. A simple and robust three-dimensional cracking-particle method without enrichment. Computer Methods in Applied Mechanics and Engineering, 2010, 199(37–40): 2437–2455

[51] RabczukT, Belytschko T. Cracking particles: a simplied meshfree method for arbitrary evolving cracks. International Journal for Numerical Methods in Engineering, 2004, 61(13): 2316–2343

[52] ZiG, Rabczuk T, WallW A . Extended meshfree methods without branch enrichment for cohesive cracks. Computational Mechanics, 2007, 40(2): 367–382

[53] RabczukT, BordasS, ZiG. A three-dimensional meshfree method for continuous multiple crack initiation, nucleation and propagation in statics and dynamics. Computational Mechanics, 2007, 40(3): 473–495

[54] RabczukT, ZiG, BordasS, Nguyen-Xuan H. A geometrically non-linear three dimensional cohesive crack method for reinforced concrete structures. Engineering Fracture Mechanics, 2008, 75(16): 4740–4758

[55] RabczukT, BordasS, ZiG. On three-dimensional modelling of crack growth using partition of unity methods. Computers & Structures, 2010, 88(23–24): 1391–1411

[56] RabczukT, ZiG. A meshfree method based on the local partition of unity for cohesive cracks. Computational Mechanics, 2007, 39(6): 743–760

[57] RabczukT., EiblJ.: Numerical analysis of prestressed concrete beams using a coupled element free Galerkin/nite element method, International Journal of Solids andStructures, 2004, 41 (3- 4), 1061–1080

[58] RabczukT, Akkermann J, EiblJ . A numerical model for reinforced concrete structures. International Journal of Solids and Structures, 2005, 42(5–6): 1327–1354

[59] RabczukT, Belytschko T. Application of particle methods to static fracture of reinforced concrete structures. International Journal of Fracture, 2006, 137(1–4): 19–49

[60] RabczukT, EiblJ. Modeling dynamic failure of concrete with meshfree particle methods. International Journal of Impact Engineering, 2006, 32(11): 1878–1897

[5] Juang J N, Pappa  R S. Eigen-system realization algorithm for modal parameter identification and model reduction. Journal of Guidance, Control, and Dynamics, 1985, 8(5): 620–627

[6] Mohanty P, Rixen  D J. Identifying mode shapes and modal frequencies by operational modal analysis in the presence of harmonic excitation. Experimental Mechanics, 2005, 45(3): 213–220

[7] Moaveni B, Barbosa  A, Conte J P ,  Hemez F M . Uncertainty analysis of modal parameters obtained from three system identification methods. In: Proceedings of the 25th International Modal Analysis Conference (IMAC-XXV). Orlando, USA, 2007

[8] Amani M G, Riera  J, Curadelli O . Identification of changes in the stiffness and damping matrices of linear structures through ambient vibrations. Structural Control and Health Monitoring, 2007, 14(8): 1155–1169

[9] Yang Y B, Chen  Y J. A new direct method for updating structural models based on measured modal data. Engineering Structures, 2009, 31(1): 32–42

[10] Fan W, Qiao  P Z. Vibration-based damage identification methods: a review and comparative study. Structural Health Monitoring, 2011, 10(1): 83–111

[11] Ozcelik  O, Salavati   M. Variability of modal parameter estimations using two different output-only system identification methods. Journal of Testing and Evaluation, 2013, 41(6): 20120361

[12] Doebling SW, Farrar  Ch, Prime MB ,  Shevitz DW . Damage identification and health monitoring of structural and mechanical systems from changes in their vibration characteristics: A Literature Review. Los Alamos National Laboratory Report. LA-13070-MS. UC900, 1996

[13] Salawu O S. Detection of structural damage through changes in frequency: A review. Engineering Structures, 1997, 19(9): 718–723

[14] Modena C, Sonda  D, Zonta D . Damage localization in reinforced concrete structures by using damping measurements, damage assessment of structures. In: Proceedings of the international conference on damage assessment of structures, DAMAS 99, 1999, 132–141

[15] Kawiecki G.Modal damping measurements for damage detection. In: European COST F3 conference on system identification and structural health monitoring. Madrid, Spain, 2000, 651–658

[16] Zonta D, Modena  C, Bursi OS . Analysis of dispersive phenomena in damaged structures. In: European COST F3 conference on system identification and structural health monitoring. Madrid, Spain, 2000, 801–810

[17] Zou Y, Tong  L, Steven G P . Vibration-based model-dependent damage (delamination) identification and health monitoring for composite structures–a review. Journal of Sound and Vibration, 2000, 230(2): 357–378

[18] Curadelli R O ,  Riera J D ,  Ambrosini D ,  Amani M G . Damage detection by means of structural damping identification. Engineering Structures, 2008, 30(12): 3497–3504

[19] Gomaa F R, Nasser  A A, Ahmed Sh   O. Sensitivity of Modal Parameters to Detect Damage through Theoretical and Experimental Correlation. International Journal of Current Engineering and Technology, 2014, 4(1): 172–181

[20] Wang M L, Kreitinger  T J. Kreitinger, Identification of force from response data of a nonlinear system. Soil Dynamics and Earthquake Engineering, 1994, 13(4): 267–280

[21] Ma C K, Lin  D C. Input forces estimation of a cantilever beam. Inverse Problems in Engineering, 2000, 8(6): 511–528

[22] Steltzner A D, Kammer D C.Input Force Estimation Using an Inverse Structural Filter. IMAC XVII, 1999

[23] Ma C K, Chang  J M, Lin  D C. Input forces estimation of beam structures by an inverse method. Journal of Sound and Vibration, 2003, 259(2): 387–407

[24] Ekke J. Oosterhuis, Wouter   B. Eidhof, Peter   J.M. van der  Hoogt, de Boer  A. Force prediction via the inverse FRF using experimental and numerical data from demonstrator with tunable nonlinearities. In: Proceedings of the 13th international congress on sound and vibration. Vienna, Austria, 2006

[25] Hisham. A. Al-Khazali. Calculations of frequency response functions (FRF) using computer smart office software and nyquist plot under gyroscopic effect rotation. International Journal of Computer Science and Information Technology & Security, 2011, 1(2): 90–97

[26] Foss  G, Niezrecki   C. Special topics in structural dynamics volume 6. In: Proceeding of the 32nd IMAC. A conference and exposition of structural dynamics, 2014

[27] Unavane  T V ,  Panse  Dr. M. S . New method for online frequency response function estimation using circular queue. International Journal for research in emerging science and technology, 2015, 2(6): 134–137

[28] Rayleigh L. Theory of Sound (two volumes). New York: Dover Publications, 1897

[29] Lee J H, Kim  J. Direct identification of damping parameters from FRF and its application to compressor engineering. In: Proceedings of International Compressor Conference at Purdue University. 2000, 869–876

[30] Yamaguchi H, Adhikari  R. Energy-Based evaluation of modal damping in structural cables with and without damping treatment. Journal of Sound and Vibration, 1995, 181(1): 71–83

[31] Xu B, Wu  Z, Chen G ,  Yokoyama K . Direct identification of structural parameters from dynamic responses with neural networks. Engineering Applications of Artificial Intelligence, 2004, 17(8): 931–943

[32] Slavic J, Simonovski  I, Boltezar M . damping identification using a continuous wavelet transform: application to real data. Journal of Sound and Vibration, 2003, 262(2): 291–307

[33] Min C, Park  H, Park S ,  PARK  H ,  PARK  S . Direct identification of non-proportional modal damping matrix for lumped mass system using modal parameters. Journal of Mechanical Science and Technology, 2012, 26(4): 993–1002

[34] Arora V. Direct structural damping identification method using complex FRFs. Journal of Sound and Vibration, 2015, 339: 304–323

[35] Pan Y, Wang  Y. Iterative method for exponential damping identification. Computer-Aided Civil and Infrastructure Engineering, 2015, 30(3): 229–243

[36] Kimball A.Vibration Damping, Including the Case of Solid Damping, Trans. ASME, APM51–52, 1929

[37] Thomson W T. Theory of Vibration with Applications. Prentice-Hall, Englewood Cliffs, NJ, 1972

[38] Lazan B J. Damping of Materials and Members in Structural Mechanics. Oxford: Pergamom Press, 1968

[39] Frizzarin M, Feng  M Q, Franchetti  P, Soyoz S ,  Modena C . Damage detection based on damping analysis of ambient vibration data. Structural Control and Health Monitoring, 2010, 17: 368-385

[40] Montalvão D ,  Silva J M M . An alternative method to the identification of the modal damping factor based on the dissipated energy. Mechanical Systems and Signal Processing, 2015, 54–55: 108–123

[41] O’Callahan J ,  Piergentili F . Force estimation using operational data. In: International Modal Analysis Conference 1996. Dearborn, USA, 1996

[42] Hong L L, Hwang  W L. Empirical formula for fundamental vibration periods of reinforced concrete buildings in Taiwan. Earthquake Engineering & Structural Dynamics, 2000, 29(3): 327–337

[43] Ma C K, Chang  J M, Lin  D C. Input forces estimation of beam structures by an inverse method. Journal of Sound and Vibration, 2003, 259(2): 387–407

[44] Suwała G, Jankowski  Ł. A model-less method for added mass identification. Diffusion and Defect Data, Solid State Data. Part B, Solid State Phenomena, 2009, 147–149: 570–575

[45] Khoo S Y, Ismail  Z, Kong K K ,  Ong Z C ,  Noroozi S ,  Chong W T ,  Rahman A G A . Impact force identification with pseudo-inverse method on a light weight structure for under-determined, even-determined and over-determined cases. International Journal of Impact Engineering, 2014, 63: 52–62

[46] Rajkumar  S, Dewan  A, Bhagat Sujatha   C, Narayanan S . Comparison of various techniques used for estimation of input force and computation of frequency response function (FRF) from measured response data. In: the 22nd International Congress on Sound and Vibration- ICSV22. Florence, Italy, 12–16, July, 2015

[47] Chopra A K. Dynamics of structures. 3rd ed. Prentice-Hall, Upper Saddle River (NJ), 2007

Acknowledgements

The author gratefully acknowledges the Institute of Structural Mechanics, Civil Engineering Faculty of Bauhaus University Weimar in Germany.

RIGHTS & PERMISSIONS

2016 Higher Education Press and Springer-Verlag Berlin Heidelberg