CAJ | 학술논문

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。
이용분수도수적본구관계건립료점탄성공적공제방정，채용Galerkin방법간화료공적수학모형。제출일충구해함분수산자적비선성방정적수치방법，병이용해방법대공제방정진행구해。고찰재하삼수、재료삼수대공동력향응적영향。운용비선성동역학중각충경전적분석방법，여시정곡선、공솔보、상도、방가래절면등，판별병게시료점탄성공적봉부적동역학행위。
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.