# Three-Dimensional Rotordynamic Finite-Element Formulations

 dc.contributor Aalto-yliopisto fi dc.contributor Aalto University en dc.contributor.author Lantto, Erkki dc.date.accessioned 2020-09-29T09:00:08Z dc.date.available 2020-09-29T09:00:08Z dc.date.issued 2020 dc.identifier.isbn 978-952-64-0034-1 (electronic) dc.identifier.isbn 978-952-64-0033-4 (printed) dc.identifier.issn 1799-490X (electronic) dc.identifier.issn 1799-4896 (printed) dc.identifier.issn 1799-4896 (ISSN-L) dc.identifier.uri https://aaltodoc.aalto.fi/handle/123456789/46754 dc.description.abstract Work presents detailed derivations of various three-dimensional rotordynamic formulations. The equation of motion is derived by two approaches; using Lagrange's equation and using Galerkin's method. It is shown that these approaches give the same equation of motion. Thorough treatment of the relevant kinematics is presented. Nonlinear strain and stress measures are adopted to create formulation, which is valid for large displacements and material rotations, but for small strain levels. Therefore, the resulting equation of motion is nonlinear. This nonlinear equation of motion is linearized yielding a model, which is valid for large equilibrium displacements and small deviations around the equilibrium. In addition, a linearized model, which assumes constant equilibrium displacements, is presented. After the form of the energy expressions and equation of motion are obtained in a generic case, the work presents the implementation details associated with solid element model, cyclic symmetric model and axisymmetric model and how different types of submodels can be combined. In addition, publication presents modal reduction utilizing the symmetry properties present in the axisymmetric model, cyclic model and combined model consisting of axisymmetric and cyclic sub-models. Work contains four simple example cases, which present comparisons to literature and explorethe model validity ranges of different approaches. en dc.format.extent 200 dc.format.mimetype application/pdf en dc.language.iso en en dc.publisher Aalto University en dc.publisher Aalto-yliopisto fi dc.relation.ispartofseries Aalto University publication series SCIENCE + TECHNOLOGY en dc.relation.ispartofseries 5/2020 dc.subject.other Mechanical engineering en dc.title Three-Dimensional Rotordynamic Finite-Element Formulations en dc.type D4 Julkaistu kehittämis- tai tutkimusraportti tai -selvitys fi dc.contributor.school Sähkötekniikan korkeakoulu fi dc.contributor.school School of Electrical Engineering en dc.contributor.department Sähkötekniikan ja automaation laitos fi dc.contributor.department Department of Electrical Engineering and Automation en dc.subject.keyword Rotordynamics en dc.subject.keyword Finite elements en dc.identifier.urn URN:ISBN:978-952-64-0034-1 dc.type.dcmitype text en dc.contributor.lab Computational Electromechanics en local.aalto.formfolder 2020_09_29_klo_11_35
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