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Research Papers

Nonlinear System Identification Technique for a Base-Excited Structure Based on Modal Space Formulation

[+] Author and Article Information
Sushil Doranga, Christine Q. Wu

Department of Mechanical Engineering,
University of Manitoba,
Winnipeg, MB R3T 5V6, Canada

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received July 16, 2015; final manuscript received July 27, 2016; published online August 22, 2016. Assoc. Editor: Bogdan I. Epureanu.

J. Comput. Nonlinear Dynam 11(6), 061016 (Aug 22, 2016) (16 pages) Paper No: CND-15-1220; doi: 10.1115/1.4034394 History: Received July 16, 2015; Revised July 27, 2016

Most of the nonlinear system identification techniques described in the existing literature required force and response information at all excitation degrees-of-freedom (DOFs). For cases, where the excitation comes from base motion, those methods cannot be applied as it is not feasible to obtain the measurements of motion at all DOFs from an experiment. The objective of this research is to develop the methodology for the nonlinear system identification of continuous, multimode, and lightly damped systems, where the excitation comes from the moving base. For this purpose, the closed-form expression for the equivalent force also known as the pseudo force from the measured data for the base-excited structure is developed. A hybrid model space is developed to find out the nonlinear restoring force at the nonlinear DOFs. Once the nonlinear restoring force is obtained, the nonlinear parameters are extracted using “multilinear least square regression” in a modal space. A modal space is chosen to express the direct and cross-coupling nonlinearities. Using a cantilever beam as an example, the proposed methodology is demonstrated, where the experimental setup, testing procedure, data acquisition, and data processing are presented. The example shows that the method proposed here is systematic and constructive for nonlinear parameter identification for base-excited structure.

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Figures

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Fig. 1

Nonlinear system identification flow chart

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Fig. 2

Five DOF lumped parameter model

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Fig. 3

Reconstructed force vector at low base acceleration

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Fig. 4

Reconstructed force vector at high base acceleration

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Fig. 5

Measured and fitted mode 1 nonlinear restoring force

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Fig. 6

Modal force and response at each mode resulting from the base acceleration of 4 m/s2

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Fig. 7

Measure and fitted modal restoring force (mode 2 excitation)

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Fig. 8

Restoring force surface obtained from least square regression for mode 2 with direct stiffness term: ((a) RFS and (b) stiffness projection)

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Fig. 9

Measured and fitted modal restoring force (mode 3 excitation)

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Fig. 10

Measured and fitted modal restoring force (mode 4 excitation)

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Fig. 11

Measured and fitted modal restoring force (mode 5 excitation)

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Fig. 12

Experimental setup for vibration testing

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Fig. 13

(a) Low level response data of the beam and (b) high level response data of the beam

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Fig. 14

Absolute value of the low level pseudo-excitation force projected at the measured degree-of-freedom

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Fig. 15

Pseudo-excited projected force at the measured degrees-of-freedom

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Fig. 16

Modal displacement at first mode

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Fig. 17

Modal displacement at second mode

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Fig. 18

Modal displacement at third mode

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Fig. 19

Measured and identified restoring force in 3D surface

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Fig. 20

Modal restoring force as a function of displacement

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Fig. 21

Validation of identified parameters using different excitations

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Fig. 22

Measured modal restoring force (mode 2)

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Fig. 23

Measured and fitted modal restoring force (mode 2)

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Fig. 24

Force displacement plane

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Fig. 25

Comparison of measured and simulated modal response (base excitation 1 mm)

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