TY - GEN

T1 - On the extension of global vibration modes with Ritz-vectors needed for local effects

AU - Sherif, Karim

AU - Witteveen, Wolfgang

AU - Irschik, Hans

AU - Holl, Helmut

AU - Mayrhofer, Karl

N1 - Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2011

Y1 - 2011

N2 - In Ritz-vector based model reduction techniques, the problem-oriented combination of different kind of Ritz-vectors may significantly influence the quality of the reduction base. It is common to combine global vibration modes with Ritz-vectors, which are necessary to characterize local effects. Even if the global vibration modes and the local Ritz-vectors may be separately orthogonal with respect to the mass and stiffness matrix, the combined reduced system is usually not decoupled. By using common decoupling strategies the separation of the two mode groups is lost. In this contribution, we will present a transformation procedure in order to obtain a combined and decoupled mode base, which is still separable into global vibration modes and Ritz-vectors due to local effects. Due to the clear separation of the two kinds of modes it is possible to give a frequency limit for the relevance of the inertia effects of the second mode group. In case the inertia effects of the second mode group may be neglected, the dimension of the differential equation of motion can be reduced once more again. At our theoretical considerations, an example is presented for the sake of illustration.

AB - In Ritz-vector based model reduction techniques, the problem-oriented combination of different kind of Ritz-vectors may significantly influence the quality of the reduction base. It is common to combine global vibration modes with Ritz-vectors, which are necessary to characterize local effects. Even if the global vibration modes and the local Ritz-vectors may be separately orthogonal with respect to the mass and stiffness matrix, the combined reduced system is usually not decoupled. By using common decoupling strategies the separation of the two mode groups is lost. In this contribution, we will present a transformation procedure in order to obtain a combined and decoupled mode base, which is still separable into global vibration modes and Ritz-vectors due to local effects. Due to the clear separation of the two kinds of modes it is possible to give a frequency limit for the relevance of the inertia effects of the second mode group. In case the inertia effects of the second mode group may be neglected, the dimension of the differential equation of motion can be reduced once more again. At our theoretical considerations, an example is presented for the sake of illustration.

UR - http://www.scopus.com/inward/record.url?scp=79958085693&partnerID=8YFLogxK

U2 - 10.1007/978-1-4419-9305-2_4

DO - 10.1007/978-1-4419-9305-2_4

M3 - Conference contribution

SN - 9781441993045

T3 - Conference Proceedings of the Society for Experimental Mechanics Series

SP - 37

EP - 46

BT - Linking Models and Experiments - Proceedings of the 29th IMAC, a Conference on Structural Dynamics, 2011

PB - Springer New York LLC

T2 - IMAX XXIX

Y2 - 31 January 2011 through 3 February 2011

ER -