广义模糊粗糙集的不确定性度量

研究广义模糊粗糙集的不确定性问题,利用一种新的信息熵定义模糊粗糙集的模糊性度量,并给出这种度量的性质,证明当且仅当A是经典可定义集合时其模糊粗糙集的模糊性度量FR(A)等于0。     

Size and temperature effects on band gaps in periodic fluid-filled micropipes

A new model is proposed for determining the band gaps of flexural wave propagation in periodic fluid-filled micropipes with circular and square thin-wall cross-sectional shapes, which incorporates temperature, microstructure, and surface energy effects. The band gaps depend on the thin-wall cross-sectional shape, the microstructure and surface elastic material constants, the pipe wall thickness, the unit cell length, the volume fraction, the fluid velocity in the pipe, the temperature change,and the thermal expansion coefficient. A systematic parametric study is conducted to quantitatively illustrate these factors. The numerical results show that the band gap frequencies of the current non-classical model with both circular and square thin-wall cross-sectional shapes are always higher than those of the classical model. In addition,the band gap size and frequency decrease with the increase of the unit cell length according to all the cases. Moreover, the large band gaps can be obtained by tailoring these factors.