Research Papers

Fluidic Flexible Matrix Composite Vibration Absorber for a Cantilever Beam

[+] Author and Article Information
Bin Zhu

Department of Mechanical and
Nuclear Engineering,
The Pennsylvania State University,
University Park, PA 16802
e-mail: bxz134@gmail.com

Christopher D. Rahn

Department of Mechanical and
Nuclear Engineering,
The Pennsylvania State University,
150A Hammond Building,
University Park, PA 16802
e-mail: cdrahn@psu.edu

Charles E. Bakis

Department of Engineering
Science and Mechanics,
The Pennsylvania State University,
University Park, PA 16802
e-mail: cbakis@psu.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 March 21, 2014; final manuscript received October 25, 2014; published online December 3, 2014. Assoc. Editor: Jiong Tang.

J. Vib. Acoust 137(2), 021005 (Apr 01, 2015) (11 pages) Paper No: VIB-14-1089; doi: 10.1115/1.4029002 History: Received March 21, 2014; Revised October 25, 2014; Online December 03, 2014

Fluidic flexible matrix composite (F2MC) tubes with resonant fluidic circuits can absorb vibration at a specific frequency when bonded to flexible structures. The transverse structural vibration applies cyclic axial strain to the F2MC tubes. The anisotropic elastic properties of the composite tube amplify the axial strain to produce large internal volume change. The volume change forces fluid through a flow port and into an external accumulator. The fluid inertance in the flow port (inertia track) and the stiffness of the accumulator are analogous to the vibration absorbing mass and stiffness in a conventional tuned vibration absorber. An analytical model of an F2MC-integrated cantilever beam is developed based on Euler–Bernoulli beam theory and Lekhnitskii's solution for anisotropic layered tubes. The collocated tip force to tip displacement analytical transfer function of the coupled system is derived. Experimental testing is conducted on a laboratory-scale F2MC beam structure that uses miniature tubes and fluidic components. The resonant peak becomes an absorber notch in the frequency response function (FRF) if the inertia track length is properly tuned. Tuning the fluid bulk modulus and total flow resistance in the theoretical model produces results that match the experiment well, predicting a magnitude reduction of 35 dB at the first resonance using an F2MC absorber. Based on the experimentally validated model, analysis results show that the cantilever beam vibration can be reduced by more than 99% with optimally designed tube attachment points and flow port geometry.

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Fig. 2

Schematic diagram of the F2MC-integrated cantilever beam model: side view with tube and beam shown separated for clarity (top) and assemble cross section view (bottom)

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Fig. 1

Schematic diagram of an F2MC vibration absorber attached to a cantilever beam

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Fig. 3

Schematic diagram of the FMC composite shell with axial and pressure loading

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Fig. 4

FMC tubes used in the experimental study with a US penny for scale (left) and an illustration of the wall cross section (right)

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Fig. 5

Experimental F2MC beam prototype

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Fig. 6

Experimental setup for testing of the F2MC beam system

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Fig. 7

Experimental and theoretical FRFs for an F2MC beam without fluid (ov) and with fluid and the inertia track closed (cv) or open with different inertia track lengths of (1) hp = 3 m, (2) hp = 4 m, and (3) hp = 5 m for (a) first and second modes and (b) a zoom-in view of first mode

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Fig. 8

Theoretical FRF of F2MC-beams with fluid bulk modulus varied from 20 MPa to 2 GPa

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Fig. 9

Theoretical vibration attenuation for F2MC absorbers with parameters from Tables 1 and 2. Filled circles indicate designs with >15 dB attenuation.

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Fig. 10

F2MC tube attachment point locations with >15 dB first and second mode attenuation: (a) histogram of left (x1) and right (x2) attachment points for first mode; (b) histogram of left (x1) and right (x2) attachment points for second mode; (c) normalized first mode displacement (solid line) and slope (dashed with x) distributions; and (d) normalized second mode displacement (solid line) and slope (dashed with x) distributions

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Fig. 11

Distributions of (a) hp, (b) rp, and (c) Iw with > 15 dB vibration attenuation in the first (dark/thick bar) and second (light/thin bar) modes

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Fig. 12

Theoretical FRFs: bare beam (solid), F2MC-beam with hp = 5.9 m, rp = 0.5 mm, x1 = 0, x2 = 150 mm (dashed), and F2MC-beam with hp = 1.1 m, rp = 0.8 mm, x1 = 90 mm, x2 = 240 mm (dashed-dotted)




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