Font Size: 

This paper establishes dynamical partial differential equation for the nonlinear viscoelastic simply supported beam suffering transverse simple harmonic excitation. The generalized Duffing equation with two fractional order differential iterms by using the Galerkin approximation method to discretize the partial differential equation.The system’s amplitude-frequency response equation is obtained by average method.The instability criterion requirement of the system is deduced by studying its local stability. At last, the paper researches parameter analysis of amplitude-frequency response equation through the singularity analysis and compares the theory solution with the numerical solution to verify accuracy of the theory solution.