Galerkin projections for state-dependent delay differential equations with applications to drilling

Nandakumar Krishnan, Marian Wiercigroch

Research output: Contribution to journalArticle

22 Citations (Scopus)

Abstract

A Galerkin projection scheme to obtain low dimensional approximations of delay differential equations (DDEs) involving state-dependent delays is developed. The current scheme is an extension of a similar, recently proposed scheme for DDEs with constant delays in the publication by P. Wahi, A. Chatterjee 2005. The resulting ordinary differential equations (ODEs) from the Galerkin scheme are easier to integrate using commercial ODE solvers, and are amenable to stability and bifurcation analysis using standard techniques. First, the application of the formulation is demonstrated through a scalar delay differential equation, and the performance of the formulation is assessed. Next, the scheme is applied to a two degrees-of-freedom model describing the coupled axial and torsional vibrations of oil well drill-strings. In both cases, the Galerkin approximations show an excellent agreements with the direct numerical simulations of the original systems.
Original languageEnglish
Pages (from-to)1705-1722
Number of pages18
JournalApplied Mathematical Modelling
Volume37
Issue number4
DOIs
Publication statusPublished - 15 Feb 2013

Fingerprint

State-dependent Delay
Drilling
Delay Differential Equations
Galerkin
Differential equations
Projection
Ordinary differential equations
Oil well drills
Drill strings
Direct numerical simulation
Ordinary differential equation
Torsional Vibration
Formulation
Galerkin Approximation
Bifurcation Analysis
Stability Analysis
Strings
Degree of freedom
Integrate
Scalar

Keywords

  • Galerkin projection
  • state dependent delay
  • drill-strings
  • stability

Cite this

Galerkin projections for state-dependent delay differential equations with applications to drilling. / Krishnan, Nandakumar; Wiercigroch, Marian.

In: Applied Mathematical Modelling, Vol. 37, No. 4, 15.02.2013, p. 1705-1722.

Research output: Contribution to journalArticle

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