NSF Award
2307538
This work focuses on the prediction, suppression, and optimization of elastic instability in three engineering settings: (i) bridge decks, (ii) piezo-electric energy harvesters, and (iii) aircraft and projectile paneling. In these settings, airflow may lead to the onset of flutter instability, giving rise to pervasive oscillatory behaviors in the structure. We perform a comprehensive analysis of this phenomenon through the examination of particular partial differential equation models of flexible plates. Although the relevant models are based on applications, these plate equations are quite recent. The research work will determine if, when, and how thin structures are destabilized by ambient airflows. Accordingly, improvements can be made in the implementation and understanding of large deflection modeling in engineering and will improve predictive capabilities for the purposes of developing technologies, such as next-generation projectile paneling and piezo-elastic energy harvesters. Understanding these nonlinear dynamics translates into the ability to design new devices efficiently and effectively. This research may impact additional application areas, including biological control of human tissue. This award also provides research opportunities for undergraduate and graduate students, and postdoctoral scholars. <br/><br/>We address three plate configurations in a unified manner through a focus on nonlinear plate modeling and the (in)stability of associated evolutionary partial differential equations. We determine and execute related computational methods and numerical studies. The physical configurations require mixed and higher boundary conditions for 4th-order PDEs on spatial domains with corners. In each configuration, we analyze the qualitative properties of PDE solutions, which requires an understanding of the dynamics as a function of system parameters and geometry. Via the self-destabilization framework, we investigate limit cycle oscillations (and global attractors) for the dynamical systems generated by these plate systems. Qualitative studies allow us to reflect on our modeling choices, and this work: (i) improves plate modeling to yield better predictions; (ii) develops a rigorous theory for novel models; (iii) addresses a gap in the literature concerning unstable nonlinear plates with mixed boundary conditions; (iv) represents a synergy of modeling, theory, and computation.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
