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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.

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.

Slender, lightweight structures are demanded to meet efficiency targets or to enhance vehicle system performance characteristics. Yet, when subjected to static stress for load-bearing purposes, the flexible structural members may buckle. Furthermore, additional dynamic excitations may activate adverse snap-through responses in such post-buckled components, which accelerates fatigue and failure. The severe nonlinearity associated with these phenomena challenges traditional forms of analysis and necessitates studious experimental methods for conclusive system characterization and model validation. This research builds upon state-of-the-art analytical and experimental strategies to examine the complex forced, dynamic behaviors of built-up structures that contain one or more post-buckled members. An analytical modeling and solution formulation is reviewed that is uniquely amenable to the study of multistable structures and permits experimentally-observable measures of impedance to be identified. Through theoretical and experimental studies, the efficacy of the impedance measures is evaluated towards their usefulness in identifying the onset of dynamic bifurcations in the multistable structural dynamics. For moderate amplitudes of input energy, the analysis is found to provide qualitatively accurate prediction of the drive point impedance changes observed prior to dynamic bifurcations from low to high amplitude of displacement.

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