E. Esmailzadeh et al., EXISTENCE OF PERIODIC-SOLUTION FOR BEAMS WITH HARMONICALLY VARIABLE-LENGTH, Journal of vibration and acoustics, 119(3), 1997, pp. 485-488
The transverse oscillatory motion of a simple beam with one end fixed
while driven harmonically at the other end along its longitudinal axis
is investigated. For a special case of zero value for the rigidity of
beam, the problem reduces to that of a vibrating string with its corr
esponding equation of motion. The sufficient condition for the periodi
c solution of the beam was determined using the Green's function and S
chauder's fixed point theorem. The criterion for the stability of the
system is well defined and the condition for which the performance of
the beam behaves as a nonlinear function is stated.