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Research Papers

# Effective Placement of a Cantilever Resonator on Flexible Primary Structure for Vibration Control Applications—Part 2: Model Updating and Experimental Validation

[+] Author and Article Information
Troy Lundstrom

Department of Mechanical and
Industrial Engineering,
Piezoactive Systems Laboratory,
Northeastern University,
Boston, MA 02115
e-mail: lundstrom.t@husky.neu.edu

Professor
Fellow ASME
Department of Mechanical and
Industrial Engineering,
Piezoactive Systems Laboratory,
Northeastern University,
Boston, MA 02115
e-mail: n.jalili@northeastern.edu

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received February 15, 2017; final manuscript received February 16, 2018; published online April 17, 2018. Assoc. Editor: Mohammed Daqaq.

J. Vib. Acoust 140(5), 051004 (Apr 17, 2018) (14 pages) Paper No: VIB-17-1067; doi: 10.1115/1.4039532 History: Received February 15, 2017; Revised February 16, 2018

## Abstract

In this Part 2 of a two-part series, the experimental verification and comparison of this work are presented. In this paper, the effect of beam-type resonator position on flexible dynamics is determined experimentally. The system is excited using band-limited white noise via electrodynamic shaker, and the data are collected with several transducers and a high-speed camera for each actuator beam mounting location; the first four mode shapes and natural frequencies are determined, and a finite element model (FEM) is developed and updated using these data. An additional set of data is collected using a linear sine chirp forcing function and the updated/experimental frequency response functions (FRFs) and time responses for the base and actuator beam tips are found to correlate. Plots of experimentally determined percent modal strain energy versus attachment position for the first four modes is presented, and a final study is also performed showing the fractional root-mean-square (RMS) strain energy in the actuator with respect to the total system. A final set of data is collected in which the actuator beam is moved up the base beam, the piezoelectric patch of the actuator beam is energized with white noise, and the tip response of the base beam is measured; an RMS base beam velocity versus mount position plot was developed. From this work, it is determined that the most practical/optimal position for the secondary beam to serve as both a sensor and actuator to control base beam tip response over a wide frequency band is in the nondimensionalized range: $0.4≤e<0.6$.

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Topics: Actuators

## References

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## Figures

Fig. 1

(a) Physical two-beam system, (b) schematic diagram of two-beam system, and (c) FEM

Fig. 2

The experimental setup of the two-beam system with detailed view of actuator beam and piezoelectric patch

Fig. 3

Signal routing diagram for EMA setup

Fig. 4

High-speed video images for different mount positions with measurement point labels (tracking point clusters shown in lA=0.0244 m)

Fig. 5

PZT excitation experimental setup

Fig. 6

Effect of actuator mount location on first four experimental mode shapes

Fig. 7

Effect of actuator mount location on first four experimental natural frequencies

Fig. 8

Comparison between experimental and theoretical base beam/actuator beam tip responses

Fig. 9

Effect of actuator mount locations on base and actuator beam FRFs

Fig. 10

(a) Original (THR.)/updated (EXP.) fractional modal strain energy for first four mode shapes; original/updated nondimensionalized frequency comparison for (b) modes 1 and 2 and (c) modes 3 and 4 (legend applies to all plots)

Fig. 11

(a) Theoretical fractional RMS strain energy versus e and ld/lb for modes 1–4 showing location of the cross-sectional cut and (b) comparison between experimental fractional kinetic/strain and theoretical fractional RMS strain energies for modes 1–4

Fig. 12

Base beam tip velocity autopower spectra for (a) 80–1000 Hz band and (b) side views of autopower spectra for modes 1–4

Fig. 13

(a) Normalized RMS modal tip velocity comparison of first four modes for theoretical “theory” and experimental “exp” models and (b) normalized RMS tip velocity comparison using different mode compositions for theoretical “theory” and experimental “exp” models'

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