Analysis of Dynamical Behavior of Nonlinear Viscoelastic Timoshenko Beam

The dynamical behaviors of a viscoelastic Timoshenko beam with finite deformation were discussed in details Applying the Timoshenko's theory of beams and the fractional derivative constitutive relation, the governing motion equations were derived. Galerkin method is used to simplify the governing e-quations. The dynamical behaviors of the reduced systems with first order and second order were compared and they are uniform quality. It is shown that Galerkin method is reasonable. A new numerical method for the integro-differential equation included fractional integral was presented, which can be used to get a long-time solution of the equations. The numerical methods in nonlinear dynamics are synthetically applied to reveal plenty dynamical behaviors of the beam with finite deformation. The influences of load and material parameters on the dynamical behavior of the structure are considered respectively.