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Mass condensation : A semi‐automatic method for reducing the size of vibration problems
Author(s) -
Ramsden J. N.,
Stoker J. R.
Publication year - 1969
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.1620010403
Subject(s) - vibration , transformation (genetics) , inertia , set (abstract data type) , normal mode , computer science , condensation , reversing , mode (computer interface) , process (computing) , degrees of freedom (physics and chemistry) , matrix (chemical analysis) , transformation matrix , algorithm , structural engineering , mechanical engineering , acoustics , engineering , classical mechanics , physics , materials science , kinematics , programming language , biochemistry , chemistry , operating system , quantum mechanics , composite material , gene , thermodynamics
The paper presents a method for reducing the size of a vibration analysis by generating an inertia matrix referred to a limited set of ‘master’ vibrational freedoms. In designing a computer program to perform this mass condensation process, the emphasis has been on providing a two way interface between structural analysis and vibration analysis programs. The transformation from the full set of degrees of freedom to the master set makes extensive vibration calculations economically feasible giving solutions in terms of the amplitudes of the master freedoms. However, by reversing the transformation after completion of a vibration analysis, it is possible to restore the full set of freedoms, allowing automatic plotting of mode shapes in full detail, and re‐entry to the structural analysis program for the purpose of computing dynamic stresses. A worked example is given. This is a realistic machine tool structure rather than the simple plates or beams which are usually used for illustration purposes. Natural frequencies and mode shapes, calculated with various degrees of condensation, are compared with those obtained by using all possible freedoms. A comparison is also made with an intuitive selection of ‘lumped masses’.