Mode Synthesis and Quasi-modal Method

Abstract

Modal analysis consists of superposing eigenmodes ϕ _i , weighted according to the modal coordinates η _i, through all modes. The modal coordinates no longer have the representation of the original physical coordinates. This chapter discusses methods to reduce the order of the system while preserving the physical coordinates as far as possible. One such method is based on Guyan reduction, in which only the “relatively important” nodes are chosen out of numerous nodes in a finely meshed model. The static deflection modes are developed to reduce the system matrices. The reduced system consists of the physical coordinates of the chosen nodes. Mode synthesis is another method. Here the “most important” nodes are treated with the Guyan reduction method, while the other nodes are considered as internal to the system and undergo modal analysis. Mode synthesis gives a model containing both physical and modal coordinates. Since, however, the mass matrix of this model is not diagonal, no equivalent model of the multiple mass system can be derived. The quasi-modal method is a solution that gives a physical model equivalent to the reduced model obtained by mode synthesis. A convenient model providing an appropriate physical meaning is obtained. In addition, a procedure will be presented in which the response of a bearing journal to a force acting on the rotor is created by the mode synthesis model as a plant transfer function.