| Summary: | 碩士 === 大葉大學 === 機械工程研究所 === 83 === The purposes of the paper are to develop an elastic formula-
tion system of rotary elements and to approach the curve of
rotors' frequencies with respect to angular velocity in the
gyroscopic conservative system. In the study, the analysis of
free vibration with gyroscopic is divided into the following
objects, first, to fomulate the governing equations of the
element using Hamilton's principle, second, to employ the
finite element method with governing equa- tions, we convert
successfully into standard form of eigenvalue problems, third,
to run a FORTRAN program written under the VAX computer to
calculate complex form of eigenvalues. The element used in the
paper is a rotary model based on uni- form 3D beam element
which has two nodes with one reference point and has three
translations and three rotational deformations each one nodes
in the three dimension space system which undergoes a general
rotational motion, so the proper composition can model driving
shaft, rotating beam, crankshaft, and so on. For confirming it'
s feasibility and correctness, we have some cases respectively
to be compared with the finite element program COSMOSM and
papers, that have good results under both stationary and
rotational conditions. In addition, we can skillfully obtain
the matrix form of gover- ning equations for the nodes of the
element through the help of the symbolic computation program,
and convert into the program language form. Its advantages are
to decrease the time spent on writing a program and to avoid
the human errors. The elastic formulation system has haply
finished by the symbolic computation program in conjunction
with finite element method.
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