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Research Papers

An Experimental Characterization of the Impedance and Spectral Content of Multistable Structural Responses During Dynamic Bifurcations

[+] Author and Article Information
Benjamin A. Goodpaster

Department of Mechanical and
Aerospace Engineering,
The Ohio State University,
Columbus, OH 43210

Ryan L. Harne

Department of Mechanical and
Aerospace Engineering,
The Ohio State University,
Columbus, OH 43210
e-mail: harne.3@osu.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 August 16, 2017; final manuscript received February 13, 2018; published online April 20, 2018. Assoc. Editor: Miao Yu.

J. Vib. Acoust 140(5), 051009 (Apr 20, 2018) (8 pages) Paper No: VIB-17-1368; doi: 10.1115/1.4039533 History: Received August 16, 2017; Revised February 13, 2018

The ability to predict multistable structural dynamics challenges the development of future high-performance air vehicles that will be subjected to extreme multiphysics loads. To aid in the establishment of methodologies that characterize the response states of harmonically excited multistable structures, a catalog of empirical and practical evidence is necessary. Recent research has suggested that evolving aspects of mechanical impedance metrics may be correlated with measurable quantities, although their relation to bifurcations of the dynamic response remains incompletely understood. Motivated to begin establishing such knowledge base, this research seeks to construct a library of experimental evidence from which to draw generalized insights on the impedance- and spectral-changing trends of multistable structures undergoing severe nonlinear response due to harmonic loading. A connection between vanishing real and imaginary components of impedance and dynamic bifurcations is uncovered. In the process, a technique to forecast dynamic bifurcations is articulated, which utilizes mechanical impedance measurements in real-time to monitor the susceptibility of postbuckled structural components to undergo dynamic bifurcations. An examination of higher-order harmonics of the dynamic responses further illuminates the nearness to bifurcations and may help classify the precise response regime. Thus, by correlating the real-time impedance and spectral response with analytical predictions, a future tool may be established for condition monitoring and diagnosis.

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Figures

Grahic Jump Location
Fig. 1

Schematic of experimental platform employed in this research. Beam numbering denotes relative nearness to shaker.

Grahic Jump Location
Fig. 2

Frequency sweep conducted at an excitation amplitude of 2.84 m/s2. (a) Velocity amplitude response of all three beams with respect to excitation frequency. (b) and (c) Impedance measures for beams 1–3 with increasing and decreasing excitation frequency, respectively. Dashed lines with circular endpoints indicate transitions between distinct low-amplitude dynamic regimes. Light (dark) gray lines indicate increasing (decreasing) excitation frequency during bifurcation transitions.

Grahic Jump Location
Fig. 5

Frequency sweep conducted at an excitation amplitude of 6.63 m/s2. (a) Velocity amplitude response of all three beams with respect to excitation frequency. (b) and (c) Impedance measures for beams 1–3 with increasing and decreasing excitation frequency, respectively. Dashed lines with circular endpoints indicate dynamic bifurcations. Light (dark) gray lines indicate increasing (decreasing) excitation frequency during bifurcation transitions.

Grahic Jump Location
Fig. 4

(a)–(c) Short time Fourier transform of beam accelerations across the duration of the frequency sweep for beams 1–3, where the fundamental frequency responses are shown in Fig. 3. Arrows above each plot indicate locations of dynamic bifurcations. The excitation frequency is denoted via light dashed lines.

Grahic Jump Location
Fig. 3

Time series comparison (a) before and (b) after the dynamic bifurcation occurring at approximately 20.25 Hz with increasing excitation frequency

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Fig. 9

(a-c) Frequency content of dynamic response across the duration of the experimental excitation amplitude sweep for beams 1–3. Arrows above each plot indicate dynamic bifurcations. The lowest order harmonic for all beams is 11 Hz, coincident with excitation frequency.

Grahic Jump Location
Fig. 8

Experimental amplitude sweep conducted at an excitation frequency of 11 Hz. (a) Velocity amplitude response of all three beams with respect to excitation amplitude. (b) Impedance measures for beams 1 (right) and 2 (left). Dashed lines with circular endpoints indicate dynamic bifurcations. Light (dark) gray markers indicate increasing (decreasing) excitation amplitude during bifurcation transitions.

Grahic Jump Location
Fig. 7

(a)–(c) Frequency content of dynamic response across the duration of the experimental frequency sweep for beams 1–3. Arrows above each plot indicate intrawell dynamic bifurcations, while regions of snap-through and aperiodic response are denoted by dashed and dotted boxes, respectively. The excitation frequency is denoted via dashed lines.

Grahic Jump Location
Fig. 6

Time series comparison (a) before and (b) after the transition from high-amplitude snap-through response to low amplitude intrawell response occurring at approximately 15 Hz

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