The dimensionless fractional dynamics model of a smart viscoelastic shallow arch under harmonic loads, in which fractional derivative model introduced to simulate the materials’ characteristics, is proposed. The simplified differential equation of the single-mode system is developed combined with boundary conditions and the Galerkin method. Dynamic behaviors of the fractional single-mode system with 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, frequency and damping and other state parameters are fixed but the initial conditions are different.