Available online at www.sciencedirect.com Finite Elements in Analysis and Design 40 (2004) 935–952 www.elsevier.com/locate/nel Reduction of nite element equations for a rotor model on non-isotropic spring support in a rotating frame A. Nandi Department of Mechanical Engineering, Jadavpur University, Calcutta 700 032, India Received 18 January 2003; accepted 28 May 2003 Abstract A simple method of reduction is presented for nite element model of non-axisymmetric rotors on non- isotropic spring support in a rotating frame. The frame is rotating about the undeformed centreline of the bearings with a speed equal to the shaft spin speed. In this frame the stiness matrix, mass matrix and Coriolis matrix for the non-axisymmetric rotor (rotor with rectangular cross-section, cracked rotor, etc.) is independent of time but the support forces become periodic function of time. Therefore, in a rotating frame, it becomes necessary to deal with a large set of linear ordinary dierential equations with periodic coecients at support degrees of freedom, which requires substantial computational eort. To eectively handle this large system it needs to be reduced keeping the essential information almost intact. ? 2003 Elsevier B.V. All rights reserved. 1. Introduction Finite element technique has become a popular tool in rotordynamic analysis. Nelson and McVaugh [1] were among the rst researchers to suggest a Rayleigh shaft element and rigid disc element for modelling of rotating shaft-disc system supported on bearings. Then several shaft ele- ments were developed to introduce shear deformation eect [2]. Tapered shafts were modelled using conical shaft elements [3–5]. Stephenson and Rouch [6] proposed axisymmetric solid elements. Three-dimensional solid elements were also proposed to model shafts with complicated geometry [7,8]. As the nite element models became more and more complicated the number of degrees of freedom involved also increased. Therefore, it became necessary to use reduction techniques. Several techniques evolved based on Guyan reduction and modal transformation. Kane and Torby [9] proposed an extended modal reduction method for reducing nite element equations obtained from a rotor model. The equations were formed in state space and the vibration E-mail address: arghyan@yahoo.com (A. Nandi). 0168-874X/$-see front matter ? 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0168-874X(03)00121-5