THE STUDY OF NONLINEAR FLEXINGS IN A FLOATING BEAM BY VARIATIONAL-METHODS

[摘要] The equation of a floating beam u(u) + u(xxxx) + bu(+) = c with free-end boundary conditions is studied, using the variational methods. We show the existence of at least one nontrivial solution which is of the mountain-pass type. Also considered is 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 that some of these solutions have local asymptotic stability properties.

[发布日期] 1994-07-20

[关键词] NONLINEAR PDE;VARIATIONAL METHOD