Nonlinear dynamic behaviors of viscoelastic shallow arch with fractional derivative constitutive relationship.

The dynamics equation of a viscoelastic shallow arch under lateral loads, in which fractional derivative model is introduced to simulate the material characteristics, is established. The simplified differential equations of the first and second order Galerkin systems are developed combining Galerkin method with boundary conditions. Nonlinear dynamic behaviors of the first order Galerkin system under harmonic loads are discussed by numerical calculations. The results show that the system may lead to chaotic motion via period--doubling bifurcations or intermittent routes; In addition, the coexistences of multiple periodic solutions and the coexistences of periodic solutions with chaos solutions are found in this system when the excitation amplitude and frequency, damping and other state parameters are fixed but the initial conditions are changed. [ABSTRACT FROM AUTHOR]