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

Abstract

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.

Electrical power management and optimization with nonlinear energy harvesting structures

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Nonlinear Mechanics of Beams With Partial Piezoelectric Layers

“…Due to internal modal energy transfer, four saddle-node (SD) bifurcations appear in the primary resonance region. Additionally, it is seen that the system displays three torus (TR) bifurcations with quasiperiodic motion between TR 1 and TR 2 as well as between TR 3 and SD 3 . The details of the quasiperiodic motion at Ω p /ω 1 =1.06 is shown in Fig.…”

Thermal coupling model of a traveling flexible printing electronical membrane subjected to nonlinear electrostatical force

“…Kazemi et al 13 used finite elements to obtain the effects of temperature, material length parameters, boundary conditions and aspect ratio on the nonlinear behavior of a microplate. By predicting discrete dynamic bifurcation, Goodpaster and Harne 14 explored whether the coupling between the thermal domain and the mechanical domain would significantly affect the structural dynamics and clarified the closeness between the distributed parameter structure and the bifurcation. Kumar and Panda 15 utilized the von Karman theory to establish the nonlinear frequency response analysis of a functionally graded plate running under the surface of a heated base plate.…”