Technical Brief

Extracting Mode Shapes for Beams Through a Passing Auxiliary Mass

[+] Author and Article Information
Yao Zhang

School of Civil and Environmental Engineering,
Nanyang Technological University,
50 Nanyang Avenue, Singapore 639798
e-mail: zhangyao@ntu.edu.sg

Hai-Sheng Zhao

School of Civil and Environmental Engineering,
Nanyang Technological University,
50 Nanyang Avenue, Singapore 639798
e-mail: hzhao006@e.ntu.edu.sg

Seng-Tjhen Lie

School of Civil and Environmental Engineering,
Nanyang Technological University,
50 Nanyang Avenue, Singapore 639798
e-mail: cstlie@ntu.edu.sg

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 16, 2018; final manuscript received April 12, 2019; published online June 5, 2019. Assoc. Editor: Mohammed Daqaq.

J. Vib. Acoust 141(5), 054501 (Jun 05, 2019) (5 pages) Paper No: VIB-18-1302; doi: 10.1115/1.4043542 History: Received July 16, 2018; Accepted April 12, 2019

This paper shows an approach to evaluate mode shapes for beams through using a passing auxiliary mass. The coupled system of an auxiliary mass passing over a beam is time-dependent, and the corresponding instantaneous frequencies (IFs) are equivalent to the mode shapes. Hence, reconstruction of the mode shapes is easy to be achieved through estimating the IFs. A simple algorithm based on ridge detection is proposed to reconstruct the mode shapes. This method is effective if the beam is light or the lumped mass is heavy. It is convenient since it requires an accelerometer mounted on the passing auxiliary mass rather than a serious of sensors mounted on the structure itself. It is also more practical because it is usually difficult to install external exciter. A lab-scale experimental validation shows that the new technique is capable of identifying the first three mode shapes accurately.

Copyright © 2019 by ASME
Topics: Mode shapes
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Fig. 1

Coupled system of a passing auxiliary mass and a beam

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Fig. 2

Illustration of the proposed IF estimation method: (a) step 1, (b) step 2, and (c) step 3

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Fig. 3

Experimental setup

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Fig. 4

Vertical acceleration: (a) mv = 0.5 kg, v = 50 mm/s, (b) mv = 0.5 kg, v = 100 mm/s, (c) mv = 1 kg, v = 50 mm/s, and (d) mv = 1 kg, v = 100 mm/s

Grahic Jump Location
Fig. 5

Time-frequency analysis of vertical acceleration: (a) mv = 0.5 kg, v = 5 cm/s, (b) mv = 0.5 kg, v = 10 cm/s, (c) mv = 1 kg, v = 5 cm/s, and (d) mv = 1 kg, v = 10 cm/s

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Fig. 6

Extracted: (a) first-, (b) second-, and (c) third-mode shapes



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