Abstract: In this paper, we study the relations between the exis-tance uniqueness of interpolation with boundary condition using bivariate quadric splines connected with triangular partition and positions of interpolating points. After proving the existence uniqueness of interpolation problems at center, vertex and partial center, we give the construction methods for these three interpolating functions.

Key words: bending-torsion coupling vibration of rotor system, sub-synchronous resonance, nonlinear dynamics of rotor, combined resonance of bending-torsion coupling vibration