A generalized nonlinear equation of elastic beam with both structural damping and external damping was considered.By using Galerkin method combined with prior estimates

the existence and uniqueness of global strong solutions were proved under hinged boundary conditions and initial conditions.Through the prior estimates and some inequality

the existence of the bounded absorbing set of above-mentioned system was obtained.By taking the proposed method for compact property verification

the compactness of group determined by the above system was proved

and the existence of the strong global attractor of beam equation was proved.