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Research Papers

Adaptation of Energy Dissipation in a Mechanical Metastable Module Excited Near Resonance

[+] Author and Article Information
N. Kidambi, K. W. Wang

Department of Mechanical Engineering,
University of Michigan,
Ann Arbor, MI 48109-2125

R. L. Harne

Department of Mechanical Engineering,
University of Michigan,
Ann Arbor, MI 48109-2125
e-mail: rharne@umich.edu

1Corresponding author.

2Current affiliation: Department of Mechanical and Aerospace Engineering, The Ohio State University, Columbus, OH 43210; e-mail: harne.3@osu.edu.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received February 18, 2015; final manuscript received June 26, 2015; published online October 8, 2015. Assoc. Editor: Paul C.-P. Chao.

J. Vib. Acoust 138(1), 011001 (Oct 08, 2015) (9 pages) Paper No: VIB-15-1061; doi: 10.1115/1.4031411 History: Received February 18, 2015; Revised June 26, 2015

Recent studies have demonstrated that the energetic vibrations of strategically designed negative stiffness inclusions may lead to large and adaptable damping in structural/material systems. Many researchers examine these features using models of bistable elements. From the viewpoint of system integration, bistable, negative stiffness elements often interface with positive stiffness elastic members. Under such conditions, the structural/material system may exhibit coexisting metastable states. In other words, the macroscopic displacement/strain remains fixed while the reaction force may vary due to internal change, similar to a phase transition. This coexistence of metastable states is not manifested in an individual (stand-alone) bistable element. Although the static and low frequency linear dynamics of structural/material systems possessing coexisting metastable states have been explored, much remains to be understood regarding the dynamics and energy dissipation characteristics of such systems when excited near resonance, where nonlinear dynamics are more easily activated and damping design is of greater importance. Thus, to effectively elucidate the enhanced versatility of damping properties afforded by exploiting negative stiffness inclusions in structural/material systems, this research investigates a mechanical module which leverages a coexistence of metastable states: an archetypal building block for system assembly. The studies employ analytical, numerical, and experimental findings to probe how near-resonant excitation can trigger multiple dynamic states, each resulting in distinct energy dissipation features. It is shown that, for lightly damped metastable mechanical modules, the effective energy dissipation may be varied across orders of magnitude via tailoring design and excitation parameters.

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Figures

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Fig. 1

(a) Inset: Schematic of the mechanical module that integrates bistable and liner springs in series. Reaction force, F, of mechanical module acted upon by a global end displacement, Z, for three linear spring stiffnesses KL. (b) For sufficiently small linear spring stiffness, the system exhibits coexisting metastable states evidenced by more than one reaction force for one end displacement.

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Fig. 2

Experimental metastable module and experimentation components. The configuration used throughout experimentation is such that the two stable equilibria of the bistable constituent are at θ =  ±10deg.

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Fig. 3

Schematic of the experimental metastable module

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Fig. 4

Schematic of the transformed model formulation of the metastable module

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Fig. 5

(a) Experimentally measured angular rotation amplitude of the rigid arms and (b) analytical predictions of the displacement amplitude as the excitation frequency is varied. In (a), three data points are provided as reference to results shown in Fig. 6.

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Fig. 6

(a) Experimental and (b) simulated hysteresis loops (solid curve) of a snap-through response at 12.5 Hz excitation, and an intrawell response at 22 Hz excitation with 0 mm offset. Symbols in the legend of (a) correspond to the respective conditions from Fig. 5(a).

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Fig. 7

(a) Experimental and (b) simulated hysteresis loops (solid curves) of snap-through response at 0 mm offset at different excitation frequencies

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Fig. 8

(a) Experimental and (b) analytical results of the influence of excitation amplitude on the internal dynamics of the metastable module when excited at constant frequency

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Fig. 9

Experimental hysteresis loops (solid curves) at D = 0 mm offset, 17 Hz excitation frequency, and (a) 200 μm, (b) 300 μm, and (c) 450 μm excitation amplitude. Response type and area enclosed by each loop are indicated.

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Fig. 10

(a) Experimental and (b) analytical results showing the internal dynamics of the metastable module as excitation frequency is varied, while the excitation amplitude and offset remain fixed

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Fig. 11

(a) Experimental and (b) analytical results showing the internal dynamics of the metastable module as excitation frequency is varied, while the excitation amplitude and offset remain fixed. A greater offset is used than that employed for the results shown in Fig. 10.

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Fig. 12

(a) Experimental hysteresis loops (solid curves) for snap-through responses at 14 Hz excitation. Excitation offset and area enclosed by each loop are indicated.

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Fig. 13

(a) Experimental hysteresis loops (solid curves) at 16 Hz excitation and D = 0.7 mm offset. Response type and area enclosed by each loop are indicated.

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