利用分数导数的本构关系建立了黏弹性拱的控制方程，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，判别并揭示了黏弹性拱的丰富的动力学行为。%The motion equation governing the dynamical behaviors of a viscoelastic arch was derived.The viscoelastic material was assumed to obey the fractional derivative constitutive relation.The motion equation was simplified by Galerkin method.An effective numerical method for solving the nonlinear equation with fractional operator was developed and the motion equation governing the dynamical behaviors of the viscoelastic arch was solved with the method. The influences of load parameters and material parameters on the dynamic responses of arch were considered respectively. By using some classical methods in nonlinear dynamics,such as the methods of time history curves,power spectrum, phase diagram,Poincare section,etc.,the complex dynamic behaviors of viscoelastic arch were discriminated and revealed.
展开▼
