Session: VIB-01/MSNDC-08-03

Paper Number: 148413

148413 - Group-Theoretic Selection Rule Predicting Mode Participation in Vibration of Symmetric, Time-Varying Systems 

Many systems with repeated substructures are characterized by their nominal symmetry in space and time-varying system parameters that may break this spatial symmetry. The presence of time-varying components within the system matrices leads to distinct symmetry-related properties in system dynamics, differing from those in systems with the nominal spatial symmetry. In this work, the selection rule in group theory is used to provide a framework for analyzing symmetry-related properties of general symmetric, time-varying systems. This method analyzes the properties of a symmetric, time-varying system by determining the coupling among the symmetry species of the reponse, external force, and the time-varying components of system matrices. The method is applicable to systems characterized by nominal spatial cyclic symmetry and other symmetry types. Employing this approach, a mode participation rule is established for time-varying systems with cyclic symmetry as their nominal symmetry in space. This rule enables predictions about which mode types can be excited, based on the phase index components of the external forces and the phase differences in time-varying parameters across substructures. The rule generalizes the mode participation rules and the resonance occurrence/suppression rules in planetary gears, as noted in previous studies, and explains the dynamic properties of bladed disks under engine-order excitations. Importantly, the derivation and application of such rules in any symmetric, time-varying systems do not necessitate solving eigenvalue problems or differential equations. These rules provide engineers with valuable guidance in designing systems aimed at reducing vibrations. 

Presenting Author: Bin Dong Southern Illinois University

Presenting Author Biography: Dr. Bin Dong is an assistant professor in the School of Mechanical, Aerospace, and Materials Engineering at Southern Illinois University-Carbondale. His research focused on the vibrations of symmetric mechanical systems. His research interest is in the symmetry-based vibration analyses using mathematical tools, such as the circulant matrix theory and group theory, and developing numerical methods to efficiently solving eigensolutions of structures composed of coupled symmetric substructures. He is also interested the application of deep learning to the dynamic analysis of mechanical systems with nonlinearities and time-varying system parameters. Prior to his career at Southern Illinois University, he worked as a postdoctoral researcher under the mentorship of Dr. Robert G. Parker at the University of Utah. He obtained his bachelor’s degree from Dalian University of Technology in 2013 and his PhD degree from Virginia Tech in 2019

Authors:

Bin Dong Southern Illinois University