Order reduction of parametrically excited linear and nonlinear structural systems

Venkatesh Deshmukh, Eric Butcher, S. C. Sinha

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

Order reduction of parametrically excited linear and nonlinear structural systems represented by a set of second order equations is considered. First, the system is converted into a second order system with time invariant linear system matrices and (for nonlinear systems) periodically modulated nonlinearities via the Lyapunov-Floquet transformation. Then a master-slave separation of degrees of freedom is used and a relation between the slave coordinates and the master coordinates is constructed. Two possible order reduction techniques are suggested. In the first approach a constant Guyan-like linear kernel which accounts for both stiffness and inertia is employed with a possible periodically modulated nonlinear part for nonlinear systems. The second method for nonlinear systems reduces to finding a time-periodic nonlinear invariant manifold relation in the modal coordinates. In the process, closed form expressions for "true internal" and "true combination" resonances are obtained for various nonlinearities which are generalizations of those previously reported for time-invariant systems. No limits are placed on the size of the time-periodic terms thus making this method extremely general even for strongly excited systems. A four degree-of-freedom mass- spring-damper system with periodic stiffness and damping as well as two and five degree-of-freedom inverted pendula with periodic follower forces are used as illustrative examples. The nonlinear-based reduced models are compared with linear-based reduced models in the presence and absence of nonlinear resonances.

Original languageEnglish (US)
Pages (from-to)458-468
Number of pages11
JournalJournal of Vibration and Acoustics, Transactions of the ASME
Volume128
Issue number4
DOIs
StatePublished - Aug 2006
Externally publishedYes

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Nonlinear systems
nonlinear systems
degrees of freedom
Stiffness
stiffness
Control nonlinearities
nonlinearity
Degrees of freedom (mechanics)
Linear systems
dampers
linear systems
Damping
inertia
damping
matrices

ASJC Scopus subject areas

  • Mechanical Engineering
  • Mechanics of Materials
  • Computational Mechanics
  • Acoustics and Ultrasonics

Cite this

Order reduction of parametrically excited linear and nonlinear structural systems. / Deshmukh, Venkatesh; Butcher, Eric; Sinha, S. C.

In: Journal of Vibration and Acoustics, Transactions of the ASME, Vol. 128, No. 4, 08.2006, p. 458-468.

Research output: Contribution to journalArticle

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