SIAM Journal on Control and Optimization, Vol.50, No.2, 703-719, 2012
CLASSICAL SOLUTIONS OF NONLINEAR BEAM EQUATIONS: EXISTENCE AND STABILIZATION
In this paper we consider the large amplitude planar motion of a cantilevered beam with a feedback force and/or torque (proportional and acting opposite to the velocity/angular velocity, respectively) applied at the free end. We derive nonlinear equations of motion for such a beam based upon certain natural geometric assumptions. We then prove the existence of classical solutions for these equations and show that all classical solutions are uniformly exponentially stable.
Keywords:nonlinear beam;Euler-Bernoulli model;Rayleigh model;classical solutions;boundary feedback stabilization