Dynamic response analysis of a cycle symmetry structure to a periodic time domain loading

Abstract

A finite element analysis was performed to assess the dynamic response of a rotating turbopump impeller (cyclic symmetric) to a periodic time domain triangular pressure pulse loading induced on the impeller by the rotation of the impeller past stationary diffuser vanes. A summary of the cyclic symmetry methodology and cycl ic symmetry boundary conditions used to reduce the model to a manageable size (40,000 degrees of freedom vs. 120,000 degrees of freedom for the full model) is given. Two new analysis algorithms that were applied for the modal dynamic response analysis are detailed. The f i r s t a lgori thm involves appending vectors to the eigenvector set which (with the retained eigenvectors) will completely represent the spatial portion of the dynamic loading. The second algorithm is a time domain response method (as opposed to the frequency domain) for the solution to an arbitrary periodic time domain loading. The Modal Truncation vectors with the time domain solution method results in a complete representation of the applied dynamic loading in both the spatial and time domains for the dynamic response analysis. An analysis was performed on a cyclic symmetric structure, turbopump impeller, for the periodic time domain dynamic response due to a time domain periodic pressure pulse loading. The cyclic symmetry was N=6. That is to say the structure can be described by a 116 segment and sequentially clocking this about an axis to form the complete structure. A modal response analysis was required for all of the cyclic symmetry models because of the spatial form of the dynamic loading. Special vectors, MT (Modal Truncation) vectors, were appended to the modal set to accurately capture the spatial portion of the loading and the solution of the periodic modal response was completely evaluated in the time domain rather than transforming into and back from the frequency domain. The first section of this paper describes the model and the analysis performed (cyclic symmetry models and loads, eigenvalue results and time domain results). The second section describes the methodology used in the complete representation of the spatial part of the applied dynamic loads. The periodic time domain modal solution methodology is described in the third section and two example problems of this method are g i v e n . U. Cvclic S?rmmetrv Model DescrlFlon h a . . . lv&