  Asymptotic behaviour of eigenvalues and eigenfunctions of a stiff problem is
described in the case of the fourth-order ordinary differential operator.
Considering the stiffness coefficient that depends on a small parameter epsilon
and vanishes as epsilon tends to zero on a subinterval, we prove the existence
of low and high frequency resonance vibrations. The low frequency vibrations
admit the power series expansions on epsilon but this method is not applicable
to the description of high frequency vibrations. However, the nonclassical
asymptotics on epsilon of the high frequency vibrations were constructed using
the WKB method.
