The study of nonlinear flexings in a floating beam by variational methods

The equation of a floating beam $u\sb{tt}$ + $u\sb{xxxx}$ + $bu\sp+$ = c with free-end boundary conditions was studied using the variational methods. We showed the existence of at least one nontrivial solution which is of the mountain pass type. Also considered was the beam with one end clamped and the other end free, in this case there exist at least two nontrivial solutions.

The numerical results show the presence of both small and large amplitude flexings. Moreover, they persist in the presence of small damping, and arise as solutions of an initial value problem, thereby suggesting some of these solutions have local asymptotic stability properties.