130
SINGLE DEGREE OF FREEDOM STRUCTURES
Define the following three nondimensional parameters which will aid in investigating this last resuit relating the one-third subharmonic response amplitude
to the excitation frequency eu = 3u>s.
Q, = — ;
W®
'
128 fci
J
k
ti —
e.
Po
(5.96)
Here, the frequency parameter
is of order unity and the stiffness parameter
Ka is arbitrarily small (of order e). When these nondimensional parameters are
used with équation (5.95), the resuit is
(5.97)
Q® - (1 + 32Ks^)q4 +
- Ks = 0
Figure 5.11 Effect of nonlinear stiffness on the amplitude and frequency of the
one-third subharmonic response.
It is observed that the last équation is cubic in
and quadratic in Aa and
- tor a fixer! value of
the amplitude-frequency behavior can be deduced.