Seismic analysis of structures with a fractional derivative model of viscoelastic dampers

Viscoelastic dampers are now among some of the preferred energy dissipation devices used for passive seismic response control.To evaluate the performance of structures installed with viscoelastic dampers,different analytical models have been used to characterize their dynamic force deformation characteristics.The fractional derivative models have received favorable attention as they can capture the frequency dependence of the material stiffness and damping properties observed in the tests very well.However,accurate analytical procedures are needed to calculate the response of structures with such damper models.This paper presents a modal analysis approach,similar to that used for the analysis of linear systems,for solving the equations of inotion with fractional derivative terms for arbitrary forcing functions such as those caused by earthquake induced ground motions.The uncoupled modal equations still have fractional derivatives,but can be solved by numerical or analytical procedures.Both numerical and analytical procedures are formulated.These procedures are then used to calculate the dynamic response of a multi-degree of fleedom shear beam structure excited by ground motions. Numerical results demonstrating the response reducing effect of viscoelastic dampers are also presented.

一类含有p-Laplace算子的分数阶时滞微分方程非局部共振边值问题解的存在性

研究了一类含有p-Laplace算子的时滞分数阶微分方程非局部共振边值问题,利用Mawhin连续性定理获得了该边值问题解存在的充分条件,得到了一些新的结果,推广了一些已有的工作.

一类分数阶Laplacian方程边值问题解的存在性与唯一性

研究了一类分数阶p-Laplacian方程2点边值问题解的存在性,利用Leray-Schauder非线性抉择和Banach压缩映射原理获得了该边值问题解存在性和唯一性的充分条件,得到了一些新的结果.

一类具有时滞的高阶分数阶微分方程积分边值问题解的存在唯一性

研究了一类高阶分数阶微分方程积分边值问题解的存在性和唯一性,利用Banach压缩映射原理得到了该边值问题解存在唯一的充分条件。

一类具有时滞的分数阶微分方程边值问题正解的存在性

研究了一类具有时滞的分数阶微分方程两点边值问题解的存在性,利用一个锥上的不动点定理和一些分析技巧获得了该边值问题正解存在的充分条件,补充和完善了一些已有的结果。