| Summary: | 碩士 === 國立成功大學 === 機械工程研究所 === 81 === This thesis is described for the free vibration of
elastically restrained trapezoidal plate which thickness
is linear variable along one direction and takes an
opposite boundary conditions as special cases, such as
simple support or clamp support etc. In this paper, a semi-
analytical finite strip method which is combined with the
analysis solution and the finite element method is used for
solving the problem. One makes use of the transform
functions to map an arbitrarily shaped plate of the Cartesian
coordinate system into the natural coordinate ξ-η plane, then
divides the plane into some strips. Thus the problem is reduced
to a one-dimension beam of problem. For uniform problem, the
shape function which satisfied the elastically restrained
condition is derived and concisely expressed in terms of
the four normalized fundamental solutions of the beam governing
characteristic differential equation. If the problem is non-
uniform, an approximated method which is developed by Sen-Yung
Lee and Yee-Hsiung Kuo is used in this paper. Finally, the
transverse displacement function is taken into the energy
equations, then stiffness and mass matrices can be got. The
natural frequence is obtained by the generalize Jacobi method.
A feature of the finite strip method is only need few strips
for the results, so the storage can be reduced. Results in this
paper are in excellent agreement with those found in the
literature.
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