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Transient forced vibration of rotationally periodic structures
Author(s) -
Fricker A. J.,
Potter S.
Publication year - 1981
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620170703
Subject(s) - vibration , substructure , finite element method , equations of motion , mathematics , mathematical analysis , transient (computer programming) , modal analysis , harmonic , degrees of freedom (physics and chemistry) , fourier series , work (physics) , modal , virtual work , harmonics , motion (physics) , classical mechanics , physics , computer science , structural engineering , engineering , acoustics , chemistry , quantum mechanics , voltage , polymer chemistry , thermodynamics , operating system
The calculation of the response of rotationally periodic structures to transient forces and prescribed motions is considered. The work extends the work previously described by Thomas 1 in which only the free and harmonic forced vibration problems were considered. It is assumed that the finite element method is to be used, so that the equation of motion of the structure contains a finite number of degrees‐of‐freedom whose responses are governed by mass, stiffness and damping matrices. It is shown that an exact solution to the equation of motion of the idealized full structure can be obtained by solving the equation of motion of a single substructure for a number of different spatial Fourier harmonics of force (and hence response). A modal method of solving this equation is described. a brief description of the implementation of the method in a suite of computer programs, and the application of the programs to a practical problems, is also given.