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Research Papers

Analytical Modeling and Impedance Characterization of the Nonlinear Dynamics of Thermomechanically Coupled Structures

[+] 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 Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received March 30, 2018; final manuscript received May 3, 2018; published online June 4, 2018. Assoc. Editor: Ahmet S. Yigit.

J. Appl. Mech 85(8), 081010 (Jun 04, 2018) (9 pages) Paper No: JAM-18-1182; doi: 10.1115/1.4040243 History: Received March 30, 2018; Revised May 03, 2018

In many applications, coupling between thermal and mechanical domains can significantly influence structural dynamics. Analytical approaches to study such problems have previously used assumptions such as a proscribed temperature distribution or one-way coupling to enable assessments. In contrast, time-stepping numerical simulations have captured more detailed aspects of multiphysics interactions at the expense of high computational demands and lack of insight of the underlying physics. To provide a new tool that closes the knowledge gap and broadens potential for analytical techniques, this research formulates and analytically solves a thermomechanical beam model considering a combination of thermal and mechanical excitations that result in extreme nonlinear behaviors. Validated by experimental evidence, the analytical framework facilitates the prediction of the nonlinear dynamics of multi-degree-of-freedom structures exhibiting two-way thermomechanical coupling. The analysis enables the investigation of mechanical and thermomechanical impedance metrics as a means to forecast future nonlinear dynamic behaviors such as extreme bifurcations. For the first time, characteristics of mechanical impedance previously reported to predict the onset of dynamic bifurcations in discrete systems are translated to illuminate the nearness of distributed parameter structures to bifurcations. In addition, fundamental connections are discovered in the thermomechanical evaluations between nonlinear low amplitude dynamics of the postbuckled beam and the energetic snap-through vibration that are otherwise hidden by studying displacement amplitudes alone.

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Figures

Grahic Jump Location
Fig. 1

Experimental system: (a) photograph and (b) schematic

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Fig. 2

(a)–(c) Experimental displacement amplitude, mechanical impedance, and thermomechanical impedance. (d)–(f) Analytical displacement amplitude, mechanical impedance, and thermomechanical impedance. Stars denote the location of a vertical tangency bifurcation in the lower amplitude intrawell regime. Base acceleration is 0.1 m/s2.

Grahic Jump Location
Fig. 3

(a)–(c) Experimental displacement amplitude, mechanical impedance, and thermomechanical impedance. (d)–(f) Analytical displacement amplitude, mechanical impedance, and thermomechanical impedance. Stars denote the location of a vertical tangency bifurcation in the lower amplitude intrawell regime. Base acceleration is 1.0 m/s2.

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Fig. 4

Analytical displacement amplitude with varying maximum transverse temperature rise. Beam subjected to constant base acceleration of 1.0 m/s2 at 16 Hz.

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Fig. 5

(a) Potential energy of the unforced thermomechanical beam. Transition from monostable to bistable occurs at ΔTcr. (b) curvature of potential energy well with respect to transverse displacement, separated by mechanical and thermal components.

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Fig. 6

(a) Mechanical and (b) thermomechanical impedances for increasing ΔT. Base acceleration is constant at 1.0 m/s2 and 16 Hz. Triangle, circle, and star markers correspond to the same markers in Fig. 4.

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