A complex eigenvector is a result of nonproportional damping present in a structural system. However, it is difficult to identify the accurate damping matrix considering the modal sparsity and coordinate sparsity. A nonproportional viscous damping parameter identification is formulated as an unconstrained optimization problem in the present study. The damping coefficient of each element is considered as the design variable for the optimization problem. The objective function is defined using the incomplete complex eigenvectors, which are generated because of the presence of external damping devices in the structure. This objective function is then minimized using standard particle swarm optimization to identify the damping coefficient of the damping matrix. The accuracy and efficiency of the particle swarm optimization are investigated by solving a few numerical problems with simulated measured data. The proposed method works well with the incomplete measured modal data. The current methodology performs satisfactorily with and without noisy data. A comparison study is performed with the existing gradient-based method, and the results show that the proposed method performs better than the existing gradient-based method for the present problem with and without noisy measurement data.
AdhikariS (2006) Damping modelling using generalized proportional damping. Journal of Sound and Vibration293(1–2): 156–170. DOI: 10.1016/j.jsv.2005.09.034.
3.
AdhikariSWoodhouseJ (2001) Identification of damping: part 1, viscous damping. Journal of Sound and Vibration243(1): 43–61. DOI: 10.1006/jsvi.2000.3391.
4.
AroraV (2011) Comparative study of finite element model updating methods. Journal of Vibration and Control17(13): 2023–2039. DOI: 10.1177/1077546310395967.
5.
AroraV (2014) Structural damping identification method using normal FRFs. International Journal of Solids and Structures51(1): 133–143. DOI: 10.1016/j.ijsolstr.2013.09.017.
6.
BhattacharjeeANandaB (2018) Damping study of composites using wavelet analysis. Journal of Vibration and Control24(21): 5141–5151. DOI: 10.1177/1077546317745256.
7.
CaugheyTK (1960) Classical normal modes in damped linear dynamic systems. Journal of Applied Mechanics27: 583–588. DOI: 10.1115/1.3627262.
8.
CaugheyTKO’KellyMEJ (1965) Classical normal modes in damped linear dynamic systems. Journal of Applied Mechanics32(6): 583–588.
9.
CoelhoLDSKrohlingRA (2006) Nonlinear system identification based on B-spline neural network and modified particle swarm optimization. In: IEEE international conference on neural networks - conference proceedings, 16–21 July 2006, pp. 3748–3753. Vancouver, Canada: IEEE. DOI: 10.1109/ijcnn.2006.247392.
10.
DimouCKKoumousisV (2009) Reliability-based optimal design of truss structures using particle swarm optimization. Journal of Computing in Civil Engineering23(2): 99–109.
11.
ElegbedeC (2005) Structural reliability assessment based on particles swarm optimization. Structural Safety27(2): 171–186. DOI: 10.1016/j.strusafe.2004.10.003.
12.
FouriePCGroenwoldAA (2002) The particle swarm optimization algorithm in size and shape optimization. Structural and Multidisciplinary Optimization23(4): 259–267. DOI: 10.1007/s00158-002-0188-0.
13.
FriswellMIInmanDJPilkeyDF (1998) Direct updating of damping and stiffness matrices. AIAA Journal36(3): 491–493. DOI: 10.2514/2.396.
14.
FritzenC-P (1986) Identification of mass, damping, and stiffness matrices of mechanical systems. Journal of Vibration and Acoustics108(1): 9–16. DOI: 10.1115/1.3269310.
15.
GrecoRMaranoGC (2015) Identification of parameters of Maxwell and Kelvin-Voigt generalized models for fluid viscous dampers. Journal of Vibration and Control21(2): 260–274. DOI: 10.1177/1077546313487937.
16.
IbrahimSR (1983) Dynamic modeling of structures from measured complex modes. AIAA Journal21(6): 898–901. DOI: 10.2514/3.8168.
KennedyJEberhartR (1995) Particle swarm optimization. In: Proceedings of ICNN'95 - international conference on neural networks, 27 November–1 December 1995, pp. 1942–1948, Vol. 4. Perth, Australia: IEEE. DOI: 10.1109/ICNN.1995.488968.
19.
LancasterPPrellsU (2005) Inverse problems for damped vibrating systems. Journal of Sound and Vibration283: 891–914. DOI: 10.1016/j.jsv.2004.05.003.
20.
LeeJ-HKimJ (2001) Development and validation of a new experimental method to identify damping matrices of a dynamic system. Journal of Sound and Vibration246(3): 505–524. DOI: 10.1006/jsvi.2001.3670.
21.
MinasCInmanDJ (1991) Identification of a nonproportional damping matrix from incomplete modal information. Journal of Vibration and Acoustics113(2): 219–224. DOI: 10.1115/1.2930172.
22.
MohanSCMaitiDKMaityD (2013) Structural damage assessment using FRF employing particle swarm optimization. Applied Mathematics and Computation219(2): 10387–10400. DOI: 10.1016/j.amc.2013.04.016.
23.
MondalSChakrabortyS (2016) An inverse approach for the determination of viscous damping model of fibre reinforced plastic beams using finite element model updating. The International Journal of Acoustics and Vibration21(1): 93–102. DOI: 10.20855/ijav.2016.21.1399.
24.
MondalSChakrabortyS (2018) Identification of non-proportional viscous damping matrix of beams by finite element model updating. Journal of Vibration and Control24(11): 2134–2148. DOI: 10.1177/1077546316678528.
25.
NandaBMaityDMaitiDK (2012) Vibration based tructural damage detection technique using particle swarm optimization with incremental swarm size. International Journal of Aeronautical and Space Sciences13(3): 323–331. DOI: 10.5139/IJASS.2012.13.3.323.
26.
NandaBMaityDMaitiDK (2014) Modal parameter based inverse approach for structural joint damage assessment using unified particle swarm optimization. Applied Mathematics and Computation242: 407–422. DOI: 10.1016/j.amc.2014.05.115.
27.
PhaniASWoodhouseJ (2007) Viscous damping identification in linear vibration. Journal of Sound and Vibration303(3–5): 475–500. DOI: 10.1016/j.jsv.2006.12.031.
PradhanSModakSV (2012) A method for damping matrix identification using frequency response data. Mechanical Systems and Signal Processing33: 69–82. DOI: 10.1016/j.ymssp.2012.07.002.
30.
RayleighL (1877) Theory of Sound (Two Volumes). New York, USA: Dover Publications.
31.
SaadaMMArafaMHNassefAO (2013) Finite element model updating approach to damage identification in beams using particle swarm optimization. Engineering Optimization45(6): 677–696. DOI: 10.1080/0305215X.2012.704026.
32.
SuLMeiS-QPanY-H, et al. (2019) Experimental identification of exponential damping for reinforced concrete cantilever beams. Engineering Structures186: 161–169. DOI: 10.1016/j.engstruct.2019.02.015.
33.
VeeramuthuvelPShankarKSairajanK (2017) Application of RBF neural network in prediction of particle damping arameters from experimental data. Journal of Vibration and Control23(6): 909–929. DOI: 10.1177/1077546315587147.
34.
VellarLSOntiveros-PérezSPMiguelLFF, et al. (2019) Robust optimum design of multiple tuned mass dampers for vibration control in buildings subjected to seismic excitation. Shock and Vibration2019(1): 1–9. DOI: 10.1155/2019/9273714.
35.
WoodhouseJ (1998) Linear damping models for structural vibration. Journal of Sound and Vibration215(3): 547–569. DOI: 10.1006/jsvi.1998.1709.
