Full-field strain estimation of subsystems within time-varying and nonlinear systems using modal expansion

Marius Tarpø*, Tobias Friis, Christos Georgakis, Rune Brincker

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

Virtual sensing allows for the estimation of stress and/or strain response in unmeasured locations of a system. Often, these virtual sensing techniques assume a linear and time-invariant system with proportional damping. In this article, one virtual sensing technique - the modal expansion - is proven applicable for stress/strain estimation of subsystems within time-varying and nonlinear systems with general viscous damping where the time-varying and nonlinear effects act externally on the subsystems. This technique uses the mode shapes of the subsystem to expand the response by a subspace projection. It is proven that the mode shapes of the underlying undamped and linear system form a basis for the response of the time-varying and nonlinear systems with general viscous damping. Therefore, a truncation of the mode shapes results in modal truncation errors that depend on the span of the applied mode shapes. Thus using an appropriate set of undamped and linear mode shapes of the subsystem, the modal expansion allows for estimation of the stress/strain response for “linear” subsystems within time-varying and nonlinear systems with general viscous damping. This concept is proven both numerically and experimentally.

Original languageEnglish
Article number107505
JournalMechanical Systems and Signal Processing
Volume153
Number of pages19
ISSN0888-3270
DOIs
Publication statusPublished - 2021

Keywords

  • Hybrid modal analysis
  • Structural health monitoring
  • Structural modification theory
  • Virtual sensing

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