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Research Papers

Optimal Force Inputs for Environmental Vibration Testing of Full Scale Slender Aerospace Vehicles

[+] Author and Article Information
D. Ramkrishna

DRDL,
Hyderabad 500058, India
e-mail: rkdinavahi@rediffmail.com

Ashok Joshi

Professor
Department of Aerospace Engineering,
IIT Powai,
Mumbai 400076, India
e-mail: ashokj@aero.iitb.ac.in

P. M. Mujumdar

Professor
Department of Aerospace Engineering,
IIT Powai,
Mumbai 400076, India
e-mail: mujumdar@aero.iitb.ac.in

Y. Krishna

DRDL,
Hyderabad 500058, India
e-mail: dr.ykrishna@gmail.com

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received July 9, 2014; final manuscript received April 4, 2015; published online June 2, 2015. Assoc. Editor: Paul C.-P. Chao.

J. Vib. Acoust 137(5), 051009 (Oct 01, 2015) (11 pages) Paper No: VIB-14-1249; doi: 10.1115/1.4030359 History: Received July 09, 2014; Revised April 04, 2015; Online June 02, 2015

A hypothesis is presented in this paper for evaluating the root mean square (RMS) errors in acceleration for determining the optimal locations of the exciters during the vibration testing of slender flexible structures, e.g., missiles, rockets, and space vehicles. Simulation studies are carried out on a realistic slender nonuniform beam in a free–free conditions to characterize the error estimations in the desired and achieved acceleration spectra at different locations of the structure. The optimal locations of the exciters are obtained using a real-coded genetic algorithm (RCGA) with minimal required force levels and the corresponding RMS error estimates. It has been observed that RMS force levels are a minimum when the exciter and control sensor locations are noncollocated. This study also provides a methodology in deriving the optimum force levels required for the environmental vibration testing of the full vehicle structure. The RMS error levels are found to be a minimum at the control sensor locations.

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References

Figures

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Fig. 1

(a) Normalized EI and mass distribution of flexible structure along the length, (b) acceleration FRF at x/L = 0.00 of the structure with exciter at x/L = 0.53 showing rigid and flex modes, and (c) first four normalized mode shapes of the nonuniform beam

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Fig. 2

Flow chart for unconstrained optimization using RCGA

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Fig. 3

Surface plot showing the variation of required RMS force per unit desired acceleration level for single exciter and single control sensor

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Fig. 4

(a) Variation of the minimum required RMS force levels and the corresponding exciter location with generation number and (b) optimal location of exciter for each control sensor location for the minimum required RMS force levels (number of exciter = 1, number of control sensor = 1)

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Fig. 5

(a) Surface plot and (b) contour plot showing the variation of normalized RMS error (dB) at the optimal locations of the exciter for single exciter and single control sensor

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Fig. 6

(a) Required force spectrum at x/L = 1.00 to achieve desired spectrum at x/L = 0.00 and (b) comparison of desired and achieved acceleration PSD at x/L = 0.00 with alarm (± 3 dB) and abort (±6 dB) limits

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Fig. 7

Surface plot showing the variation of required RMS force per unit desired acceleration level at (a) exciter 1, (b) exciter 2, and (c) locations of exciters in two exciters and single control sensor configuration

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Fig. 8

Optimal locations of exciters for each control sensor location for the minimum required RMS force levels (number of exciters = 2, number of control sensor = 1)

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Fig. 9

(a) Surface plot and (b) contour plot showing the variation of normalized error (dB) at the optimal locations of the exciter for two exciters and single control sensor

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Fig. 10

Surface plot showing the variation of required RMS force per unit desired acceleration level at (a) exciter 1, (b) exciter 2, (c) exciter 3, and (d) locations of exciters in three exciters and single control sensor configuration

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Fig. 11

Optimal locations of exciters for each control sensor location for the minimum required RMS force levels (number of exciters = 3, number of control sensor = 1)

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Fig. 12

(a) Surface plot and (b) contour plot showing the variation of normalized error (dB) at the optimal locations of the exciter for three exciters and single control sensor

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Fig. 13

Schematic of the test setup for modal testing of the beam

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Fig. 14

Comparison of the required experimental force spectra obtained at different locations of the exciter on the beam (number of exciters = 1, number of control sensor = 1)

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Fig. 15

Comparison of the required experimental force spectra obtained at different locations of the exciter on the beam (number of exciters = 2, number of control sensor = 1)

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