Abstract: A simple third order mathematical relation formulated
by perturbation technique determines that the small change in the depth of rectangular
cross-section from H to other conditions remaining the
same, causes a corresponding change in torsional frequency The relation between them is
approximately a linear one and the
constant of proportionality can be determined from the known parameters. The
higher-order representations of relations show a non-linear trend
as expected. The perturbation method used in this paper eliminates the need of
working out repeated lengthy algorithms for solving such problems of complicated
geometry. Additionally, the relations obtained by perturbation technique provide
engineers with mathematical estimates prior to costly full-length prototype
design test.
