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Chaos & Complex Systems Seminar
Nonlinear normal modes for analysis of geometrically nonlinear structures
Date: Tuesday, September 19th
Time: 12:05 pm - 1:00 pm
Place: 4274 Chamberlin (refreshments will be served)
Speaker: Matthew Allen, UW Department of Mechanical Engineering
Abstract: Geometric nonlinearity is an important consideration when designing many structures, for example the skin panels for future hypersonic cruise vehicles where intense pressures and aerodynamic heating can cause the panels to vibrate in and out of buckled states. Highly flexible joined-wing aircraft, which are being sought for station keeping at high altitude, can also exhibit nonlinear dynamic phenomena. It may also be possible to add a nonlinear element to an otherwise linear structure in order to reduce vibration levels and increase its life, leading to quieter automobiles or more durable spacecraft. All of these applications are challenging because numerical response predictions are expensive and these nonlinear systems exhibit a large range of phenomena, each of which may require a specialized analysis technique. This work shows that tremendous insight can be gained into the dynamics of these types of nonlinear structures using undamped nonlinear modal analysis.

This presentation highlights advances in modeling for geometrically nonlinear structures and discusses how nonlinear modes can be used in analysis, design and testing. While academics have used simplified Galerkin/Ritz models for years to qualitatively study the geometrically nonlinear response of plates and beams, those methods often do not scale to industrial practice where the geometry is far more complicated and many degrees of freedom must be considered. The work focuses on structures that are modeled in commercial finite element software and uses a non-intrusive approach in which a series of static loads are applied to the structure and a nonlinear Reduced Order Model (ROM) is fit to the load-displacement behavior. Nonlinear modes prove to be effective in discerning whether the reduced basis contains the fidelity needed to capture the dynamics of interest and in assuring that the loads are large enough to allow the ROM to be accurately computed. Nonlinear modes are also found to be intimately connected to the response of the structure to random loading, such as the pressure fields experienced by many aircraft. These concepts are demonstrated by applying them to a variety of finite element models, showing that the nonlinear modes provide tremendous insight into the dynamics of the structure.
Host: Clint Sprott
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