View source for Nonlinear Wave-Based Vibration Approach for Analytical Determination of Periodic Solutions and Stability in Jointed Bars Nov 2024

{{DISPLAYTITLE:Nonlinear Wave-Based Vibration Approach for Analytical Determination of Periodic Solutions and Stability in Jointed Bars, by Michael J. Leamy, Nov. 11, 2024}}
==Nonlinear Wave-Based Vibration Approach for Analytical Determination of Periodic Solutions and Stability in Jointed Bars==

Michael J. Leamy (with M. Brake and N. Balaji) 

Georgia Institute of Technology



November 12, 2024

===Abstract:===
In this work we detail an analytical, wave-based approach for predicting the forced periodic response and solution stability of continuous systems joined by nonlinear coupling. We first describe an asymptotic approach for determining wave scattering at damped, weakly-nonlinear joints and apply it to elastic bars. Scattering of the incident wave leads to reflection and transmission at the incident frequency and higher harmonics. These scattering relationships are then used in a wave-based vibration approach, together with linear scattering relationships for loading and boundary conditions, to determine the periodic response of the continuous systems to forcing. We then determine solution stability using a local linear analysis. The local linear analysis yields parametrically-excited systems whose stability is found using a strained-parameter approach combined with a second wave-based analysis. Both wave-based approaches, for determining periodic response to forcing and for assessing stability, employ exact wave solutions for the structural members and asymptotic analysis of the joints. This results in nearly-exact solutions, of minimal size, valid for all frequencies – this can be contrasted with numerical approaches requiring increasing degrees of freedom (e.g., finer discretizations) with increasing frequency. Comparisons to finite element-harmonic balance solutions document excellent agreement with speedup on the order of 30X. Planned research and extensions will be discussed for jointed frames composed of beam-like members.

 
===Biography:===

Michael J. Leamy joined the George W. Woodruff School of Mechanical Engineering, Georgia Tech, as an Assistant Professor in August, 2007. He was promoted to Associate Professor (2012) and Professor (2018), and was later named a Woodruff Endowed Professor in 2024. He presently serves as the Editor-in-Chief of the ASME Journal of Vibration and Acoustics, and a Specialty Topic Chief Editor for Frontiers in Acoustics. He received his B.S. from Clarkson University (1993), and his M.S., and Ph.D. (1995, 1998) from The University of Michigan, Ann Arbor, all in Mechanical Engineering. Prior to his position at Georgia Tech, Professor Leamy worked as an Assistant Professor at the United States Military Academy (West Point, NY), a Research Scientist at the MITRE Corporation (McLean, VA), a Research Associate at the NASA Langley Research Center (Hampton, VA), and a Postdoctoral Fellow at Israel’s Institute of Technology (Technion). Professor Leamy’s research interests are in emerging and multidisciplinary areas of engineering science, with an emphasis on nonlinear dynamical behavior in structures, materials, and complex systems. Emerging engineering materials of particular interest include acoustic metamaterials, topological insulators, and reciprocity-breaking nonlinear lattices. He has received the Distinguished Achievement Award (1998) from the University of Michigan, a Koret Foundation Fellowship (1998) from the Technion, the Army’s Superior Civilian Service Award (2003), the Lockheed Dean’s Excellence in Teaching Award (2010), and the Lloyd Hamilton Donnell Best Paper Award from Applied Mechanics Reviews (co-recipient, 2016). In addition, he was named a Fellow by ASME (2014), and a Woodruff Faculty Fellow (2017) by the George Woodruff School of Mechanical Engineering. His past and current editorial positions include serving as an Associate Editor for the Journal of Vibration and Acoustics (2011-2017), Applied Mechanics Reviews (2018-2023), Nonlinear Dynamics (2019-2023), and Wave Motion (2017-Present). Professor Leamy’s research program has been supported by the Ford Motor Corporation, General Motors, Honeywell Inc., Ferrari S.p.A., ThyssenKrupp Elevator America, Sandia National Laboratories, the National Science Foundation, the Department of Energy, the Defense Threat Reduction Agency, the Army Research Office, and the Office of Naval Research.




==Video Presentation ==

Video release has been delayed by request of the presenter. 

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[[Category:Seminar_Series]]
[[Category:Finite_Element_Analysis]]
[[Category:Experimental_Techniques]]