Approximation of structural damping and input excitation force

doi:10.1007/s11709-016-0371-9

Front. Struct. Civ. Eng.

2017, Vol. 11

Issue (2) : 244-254 https://doi.org/10.1007/s11709-016-0371-9

RESEARCH ARTICLE

Approximation of structural damping and input excitation force

Mohammad SALAVATI(

)

Institute of Structural Mechanics, Faculty of Civil Engineering, Bauhaus University Weimar, Weimar 99423, Germany

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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

Corresponding Author(s): Mohammad SALAVATI

Online First Date: 21 February 2017 Issue Date: 19 May 2017

Cite this article:

Mohammad SALAVATI. Approximation of structural damping and input excitation force[J]. Front. Struct. Civ. Eng., 2017, 11(2): 244-254.

URL:

https://academic.hep.com.cn/fsce/EN/10.1007/s11709-016-0371-9
https://academic.hep.com.cn/fsce/EN/Y2017/V11/I2/244

Fig.1 Basic concept of the FRF

(33) $H (ω) = F F T (X) F F T (F (t)),$ (34) $H d − 1 (ω) X d (ω) = F d (ω) .$

Fig.2 Matlab Simulink simple model of Mass-Spring-Damper

Tab.1 Comparison of assumed damping ratios with identifies damping ratios by using proposed method and NeXT-ERA

Fig.3 Comparison of the reference mathematical model response and estimated numerical displacement response for various damping ratios: a)

ξ r = 0.09

ξ r = 0.16

ξ r = 0.32

ξ r = 0.63

Tab.2 Overlap similarity between the reference and estimated responses

Fig.4 Comparisons of reference and identified excitation force for each damping coefficient values such as: (a)C1; (b) C2; (c) C3; (d) C4

Tab.3 Overlap similarity of the identified and reference responses for different value of damping coefficients

Fig.5 Comparisons of reference and identified displacement responses for each damping coefficient values by using (a) C1; (b) C2; (c) C3; (d) C4

Fig.6 FE model of the lumped mass system

Fig.7 Comparisons of reference and estimated excitation force; similarity= 97.9483%

Fig.8 Comparisons of reference and estimated acceleration responses; similarity= 99.9869%; FE damping ratio= 0.6; estimated damping ratio= 0.6

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