Nonlinear dynamic behaviors of viscoelastic shallow arches

The nonlinear dynamic behaviors of nonlinear viscoelastic shallow arches subjected to external excitation are investigated. Based on the d’Alembert principle and the Euler-Bernoulli assumption, the governing equation of a shallow arch is obtained, where the Leaderman constitutive relation is applied. The Galerkin method and numerical integration are used to study the nonlinear dynamic properties of the viscoelastic shallow arches. Moreover, the effects of the rise, the material parameter and excitation on the nonlinear dynamic behaviors of the shallow arch are investigated. The results show that viscoelastic shallow arches may appear to have a chaotic motion for certain conditions.