it will be clear that near the ‘‘boundaries’’ of validity of the different models the vibration modes certainly will
interact. Observe that for the boundary value problems that are considered in this paper .. is equal to
...., and so ... and ..... Based upon the aforementioned considerations the following approach
will be proposed. For small values of n in Eq. (34) a string-like model should be used, that is, for ...
(and .. is of order ...)