Research Papers

Absorption of Resonant Vibrations in Tuned Nonlinear Jointed Structures

[+] Author and Article Information
Malte Krack

Institute of Aircraft Propulsion Systems,
University of Stuttgart,
Stuttgart 70569, Germany
e-mail: malte.krack@ila.uni-stuttgart.de

Lawrence A. Bergman

Department of Aerospace Engineering,
University of Illinois at Urbana-Champaign,
Urbana, IL 61801
e-mail: lbergman@illinois.edu

Alexander F. Vakakis

Department of Mechanical
Science and Engineering,
University of Illinois at Urbana-Champaign,
Urbana, IL 61801
e-mail: avakakis@illinois.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 July 30, 2015; final manuscript received October 29, 2015; published online December 8, 2015. Assoc. Editor: Michael Leamy.

J. Vib. Acoust 138(2), 021001 (Dec 08, 2015) (8 pages) Paper No: VIB-15-1294; doi: 10.1115/1.4032000 History: Received July 30, 2015; Revised October 29, 2015

A novel concept for the passive mitigation of forced, resonant vibrations is presented. The key to this concept is an absorption phenomenon which relies on the energy conversion from low to high frequencies by means of nonlinearity. The vibration energy of a resonantly driven substructure is transferred to an internally resonant substructure within the system. Compared with the well-known linear tuned vibration absorber (LTVA), the main advantage of the proposed concept is that no separate absorber is required, but instead the existing modal structure is properly tuned and inherent nonlinearities are utilized. Just like the former concept, however, the proposed concept is limited to a narrow frequency bandwidth, which represents its main drawback of the approach. The concept is exemplified for a system of two beams connected via a nonlinear joint with a soft, unilateral-elastic characteristic. It is demonstrated that when the system is appropriately tuned, its vibration level is reduced by 60–80%, i.e., by a factor of 2.5–5. Moreover, it is shown how the efficacy and robustness of the concept can be optimized.

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Fig. 1

Three different concepts for tuned vibration absorption: (a) conventional LTVA, (b) NTVA [9], and (c) proposed tuned vibration absorption within the structure using inherent nonlinear effects

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Fig. 2

Investigated model: (a) two beams connected via a unilateral joint and (b) preloaded unilateral-elastic contact model; E1 = 6 × 106 = E2, ρ1 = 2500 = ρ2, l1 = 1.0 = l2, b1 = 0.02 = b2, h1 = 0.02, and h2 = 2h1(1 + Δ)

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Fig. 3

Steady-state response of the first bending modes in the tuned case with Δ = 0.18 (solid lines) and the detuned case with Δ = 0.5 (dashed lines): (a) normalized modal amplitude q1* of the left beam and (b) normalized modal amplitude q2* of the right beam; amplitudes are normalized by the maximum response of the first harmonic of q1 in the detuned case; N0 = 1.05, pexc = 1.0

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Fig. 4

Spectrum of the nonlinear, unilateral contact force fu for a harmonic input displacement uc=ûc cos Ωt with a large amplitude ûc→∞

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Fig. 5

Dynamic receptance of the left beam's first bending mode for different values of the reduced excitation level: (a) Δ = 0.18 and (b) Δ = 0.32

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Fig. 6

Dependence of the response level on the tuning parameter Δ

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Fig. 7

Sensitivity of the tuning characteristic with respect to the ratio pexc/N0 between the excitation level and the joint preload

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Fig. 8

Sensitivity of the tuning characteristic with respect to the overall damping level Dall

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Fig. 9

Sensitivity of the tuning characteristic with respect to the damping D2 of the right beam's first bending mode, while all other modes have a fixed damping ratio Dk = 1% ∀k ≠ 2

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Fig. 10

Sensitivity of the tuning characteristic with respect to the contact angle αc introducing frictional character to the joint behavior; μ = 0.3, kt = kn, and pexc/N0 = 9.5

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Fig. 11

Sensitivity of the tuning characteristic with respect to additional linear-elastic character of the joint behavior




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