Analytical modeling and impedance characterization of thermomechanically-coupled nonlinear structural dynamics

[+] Author and Article Information
Benjamin A. Goodpaster

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

Ryan L Harne

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

1Corresponding author.

ASME 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 post-buckled beam and the energetic snap-through vibration that are otherwise hidden by studying displacement amplitudes alone.

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