Details

Autor(en) / Beteiligte

• Nandakumar, K.
• Wiercigroch, Marian

Titel

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

Ist Teil von

• Applied mathematical modelling, 2013-02, Vol.37 (4), p.1705-1722

Ort / Verlag

Elsevier Inc

Erscheinungsjahr

2013

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• 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.