A Modal‐Based Substructure Method Applied to Nonlinear Rotordynamic Systems

Abstract

The discretisation of rotordynamic systems usually results in a high number of coordinates, so the computation of the solution of the equations of motion is very time consuming. An efficient semianalytic time-integration method combined with a substructure technique is given, which accounts for nonsymmetric matrices and local nonlinearities. The partitioning of the equation of motion into two substructures is performed. Symmetric and linear background systems are defined for each substructure. The excitation of the substructure comes from the given excitation force, the nonlinear restoring force, the induced force due to the gyroscopic and circulatory effects of the substructure under consideration and the coupling force of the substructures. The high effort for the analysis with complex numbers, which is necessary for nonsymmetric systems, is omitted. The solution is computed by means of an integral formulation. A suitable approximation for the unknown coordinates, which are involved in the coupling forces, has to be introduced and the integration results in Green's functions of the considered substructures. Modal analysis is performed for each linear and symmetric background system of the substructure. Modal reduction can be easily incorporated and the solution is calculated iteratively. The numerical behaviour of the algorithm is discussed and compared to other approximate methods of nonlinear structural dynamics for a benchmark problem and a representative example.

Berechnung von Schwingungen beim Aufwickeln eines Stahlbandes in einem Steckelwalzwerk

“…In [9] ist eine Anwendung für dynamische Systeme mit zeitlich veränderli-chen Parametern dargestellt, und in [10] wird ein nichtlineares System mit zeitlich veränderlicher Masse behandelt. Eine Erweiterung auf dynamische Systeme unter Berück-sichtigung der Substrukturtechnik ist in [11] dargestellt und gestattet eine effiziente Berechnung für größere Systeme. In [12] …”

An efficient method for structural coupling of mechanical systems by using frequency response functions

“…They compared the modes and the frequency response functions (FRFs) for three bladed assembly and real test data. Holl, 2009, presented a semianalytic time integration method combined with a substructure technique for rotordynamic systems. He used two substructures of the equation of motion defining symmetric and linear systems for each substructure.…”