正弦型黏弹性拱的非线性动力学行为研究

利用分数导数的本构关系建立了粘弹性拱的控制方程，采用Galerkin方法简化了拱的数学模型。提出一种求解含分数算子的非线性方程的数值方法，并利用该方法对控制方程进行求解。考察载荷参数、材料参数对拱动力响应的影响。运用非线性动力学中各种经典的分析方法，如时程曲线、功率谱、相图、庞加莱截面等，判别并揭示了粘弹性拱的丰富的动力学行为。

Study On Nonlinear Dynamic Behavior Of Sine Type Viscoelastic Arch

The motion equation governing the dynamical behavior of a viscoelastic arch is derived. The viscoelastic material is assumed to obey fractional derivative constitutive relation. The motion equation is simplified by Galerkin method. An effective numerical method for solving nonlinear equations with fractional operator is developed and the motion equation governing the dynamical behavior of the viscoelastic arch is solved with the method. The influences of the load parameters and the material parameters on the dynamic response of arch are considered respectively. By using some classical methods in nonlinear dynamics, such as the time history curves, power spectrum, phase diagram, Poincare section,  The complex dynamic behaviors of viscoelastic arch are discriminated and revealed in this paper.