Authors: Schweizer, Ben
Strauß, Frank
Heuveline, Vincent
Title: Existence and approximation results for shape optimization problems in rotordynamics
Language (ISO): en
Abstract: We consider a shape optimization problem in rotordynamics where the mass of a rotor is minimized subject to constraints on the natural frequencies. Our analysis is based on a class of rotors described by a Rayleigh beam model including effects of rotary inertia and gyroscopic moments. The solution of the equation of motion leads to a generalized eigenvalue problem. The governing operators are non-symmetric due to the gyroscopic terms. We prove the existence of solutions for the optimization problem by using the theory of compact operators. For the numerical treatment of the problem a finite element discretization based on a variational formulation is considered. Applying results on spectral approximation of linear operators we prove that the solution of the discretized optimization problem converges towards the solution of the continuous problem if the discretization parameter tends to zero. Finally, a priori estimates for the convergence order of the eigenvalues are presented and illustrated by a numerical example.
Issue Date: 2008-02-15
Provenance: Springer
Citation: Heuveline, V., Strauss, F., Schweizer, B.: Existence and approximation results for shape optimization problems in rotordynamics. In: Numer. Math. 109 (2008), 311-332. DOI: 10.1007/s00211-008-0138-x
Appears in Collections:Schweizer, Ben Prof. Dr.

Files in This Item:
File Description SizeFormat 
rotor_preprint.pdf184.63 kBAdobe PDFView/Open

This item is protected by original copyright

All resources in the repository are protected by copyright.