Modal Analysis for Nonlinear Dynamics: Quasi-Static Perspectives for Dissipative Dynamics by Dr. Nidish Balaji, June 2022

Modal Analysis for Nonlinear Dynamics: Quasi-Static Perspectives for Dissipative Dynamics

Dr. Nidish Balaji

Rice University, Houston, Texas, USA

June 14, 2022

Abstract:

The talk is designed to be a tutorial introduction to the general area of Quasi-Static Nonlinear Modal Analysis (QSNMA), which involves the employment of Quasi-Static (QS) computational approaches for the near-resonant characterization of nonlinear systems. It will start with a brief historical overview of the concept of Nonlinear Modal Analysis (NMA), followed by a discussion of which concepts from linear dynamics naturally generalize to the nonlinear case and which do not. Undamped and damped (decaying) periodic motion concepts will be highlighted in order to serve as a backdrop for the remainder of the talk. The single nonlinear mode theory will be invoked as a general motivation. Next, the Quasi-Static Modal Analysis (QSMA) approach will be introduced using undamped linear dynamics as a point of departure. Its distinctiveness will be brought out through a discussion of merits and demerits in comparison to periodic motion concepts. As a successor in spirit, the Rayleigh Quotient-based Nonlinear Modal Analysis (RQNMA) approach will be presented from a constrained work stationarity standpoint. The resulting formulation will be discussed in relation to both QSMA and the periodic motion concepts. This will be followed by outlines of two broad areas of ongoing research in QSNMA: (1) The additional considerations necessary for the study of dissipative dynamics; and (2) the effect of the co-existence of multiple modes on the modal characteristics. Both of these will be presented with an intention to generate debate and discussion. The talk will finally conclude with a summary of the key gaps identified in the area of quasi-static nonlinear modal analysis in comparison with other computational approaches in the literature.

Biography:

Dr. Nidish Balaji received his Ph.D. from Rice University in 2021 under the guidance of Prof. Matthew Brake. His dissertation research focused on Tribomechadynamics – the efficient and accurate modeling of the physics and nonlinear dynamics of a jointed structure. Since graduating, Dr. Balaji has been a postdoc under both Prof. Brake and Prof. Chris Jermaine, with a research focus on using data driven methods to enhance digital image correlation measurements. Later this year, Dr. Balaji will start a new postdoc position at the University of Stuttgart as a Humboldt Research Fellow under the mentorship of Prof. Malte Krack.

Slides