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Research Papers

Experimental Validation of a Nonlinear Model Calibration Method Based on Multiharmonic Frequency Responses

[+] Author and Article Information
Yousheng Chen

Department of Mechanical Engineering,
Linnaeus University,
Växjö SE-35195, Sweden
e-mail: yousheng.chen@lnu.se

Andreas Linderholt

Department of Mechanical Engineering,
Linnaeus University,
Växjö SE-35195, Sweden
e-mail: andreas.linderholt@lnu.se

Thomas J. S. Abrahamsson

Department of Applied Mechanics,
Chalmers University of Technology,
Gothenburg SE-41296, Sweden
e-mail: thomas.abrahamsson@chalmers.se

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received July 14, 2016; final manuscript received December 21, 2016; published online February 1, 2017. Assoc. Editor: Stefano Lenci.

J. Comput. Nonlinear Dynam 12(4), 041014 (Feb 01, 2017) (13 pages) Paper No: CND-16-1334; doi: 10.1115/1.4035670 History: Received July 14, 2016; Revised December 21, 2016

Correlation and calibration using test data are natural ingredients in the process of validating computational models. Model calibration for the important subclass of nonlinear systems which consists of structures dominated by linear behavior with the presence of local nonlinear effects is studied in this work. The experimental validation of a nonlinear model calibration method is conducted using a replica of the École Centrale de Lyon (ECL) nonlinear benchmark test setup. The calibration method is based on the selection of uncertain model parameters and the data that form the calibration metric together with an efficient optimization routine. The parameterization is chosen so that the expected covariances of the parameter estimates are made small. To obtain informative data, the excitation force is designed to be multisinusoidal and the resulting steady-state multiharmonic frequency response data are measured. To shorten the optimization time, plausible starting seed candidates are selected using the Latin hypercube sampling method. The candidate parameter set giving the smallest deviation to the test data is used as a starting point for an iterative search for a calibration solution. The model calibration is conducted by minimizing the deviations between the measured steady-state multiharmonic frequency response data and the analytical counterparts that are calculated using the multiharmonic balance method. The resulting calibrated model's output corresponds well with the measured responses.

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Figures

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Fig. 1

An overview of the model calibration method

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Fig. 2

(a) CAD model of the structure with the accelerometer positions shown by numbers. A—membrane, B—connector, C—beam, D—U-frame, E—misalignment eliminating bearings. (b)(e) Details of the pretension controller mechanism.

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Fig. 3

Examples of experimental FRFs compared with FRFs of the nominal and calibrated FE models of the frame structure. Left: calibration results. Right: validation results.

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Fig. 4

(a) Experimental setup for the frame-beam-connector structure. (b) The FE-model of the frame-beam-connector structure with the corresponding measured DOFs. q¨1,q¨2,…q¨10 are the measured acceleration responses.

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Fig. 5

Examples of experimental FRFs compared with FRFs of the nominal and calibrated FE models of the frame-beam-connector structure. Left: from the calibration results. Right: from the validation results.

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Fig. 6

(a) Experimental test setup for the testing of nonlinear dynamics. (b) The nonlinear model of the test structure, where fNL is the nonlinear force, q is the displacement responses on the cantilever beam and membrane intersection. f(t) is the applied force whereas q¨1,q¨2, and q¨3 are the measured acceleration responses.

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Fig. 7

An example of multiharmonic nonlinear FRFs from the nominal model excited with the load amplitude 3 N at point 1 and the responses calculated for point 1. Solid lines show FRFs of the underlying linear model, whereas the dotted lines show the nonlinear FRFs. (a) The first-order FRFs, (b) the second-order FRFs, and (c) the third-order FRFs.

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Fig. 8

Examples of calibration results are shown for case 1. The amplitude of the fundamental harmonic of the multisinusoidal excitation is 1 N for the first column and 3 N for the second column. The first, second, and third-order nonlinear FRFs are shown in the first, second and third rows, respectively.

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Fig. 9

An example of validation results is shown for the first-order nonlinear FRF from case 1. The amplitude of the fundamental harmonic of the multisinusoidal excitation is 7 N.

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Fig. 10

Examples of calibration results are shown for case 2. The amplitude of the fundamental harmonic of the multisinusoidal excitation is 1 N for the first column and 3 N for the second column. The first, second, and third-order nonlinear FRFs are shown in the first, second and third rows, respectively.

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Fig. 11

An example of validation results is shown for the first-order nonlinear FRF from case 2. The amplitude of the fundamental harmonic of the multisinusoidal excitation is 7 N.

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