Estimation of Vibration Decay Rates for a Nonlinear Flexible Beam with Nonlinear Boundary Damping

Abstract

In this paper, the decay rate estimation of solution and energy function for a nonlinear flexible beam with nonlinear boundary damping are investigated. The nonlinear boundary damping criterion, which includes a large class of nonlinear functions, is relied on a negative feedback of the right boundary velocity of the nonlinear flexible beam. The decay rate for the solution and energy is estimated by the solution of an ordinary differential equation when nonlinear boundary damping has different growth restriction at the origin. To validate the effectiveness of the results, the numerical simulation test is presented by the finite element method.