This paper studies the free bending vibration of cylindrical tank partially filled with liquid and submerged in water. The depths of liquid and water may be completely arbitrary. The exact calculating formulae of mode...This paper studies the free bending vibration of cylindrical tank partially filled with liquid and submerged in water. The depths of liquid and water may be completely arbitrary. The exact calculating formulae of mode shape functions and inherent frequencies are deduced. The results can be gained by means of computer. The analysis shows that the effect of liquid and water on vibration of cylindrical tank is respectively equivalent to a generalized distributive mass attached to the tank.展开更多
A theorem of solving a system of linear non-homogeneous differential equations through integrating and adding its basic solutions is put forward and proved, the mathematical role and physical nature of the theorem is ...A theorem of solving a system of linear non-homogeneous differential equations through integrating and adding its basic solutions is put forward and proved, the mathematical role and physical nature of the theorem is interpreted briefly. As an example, the theorem is applied to solve the problem of thermo-force bending of a thick plate.展开更多
Submerged vanes are installed on rivers and channel beds to protect the outer bank bends from scouring.Also,local scouring occurs around the submerged vanes over time,and identifying the effective factors on the scour...Submerged vanes are installed on rivers and channel beds to protect the outer bank bends from scouring.Also,local scouring occurs around the submerged vanes over time,and identifying the effective factors on the scouring phenomena around these submerged vanes is one of the important issues in river engineering.The most important aimof this study is investigation of scour pattern around submerged vanes located in 180°bend experimentally and numerically.Firstly,the effects of various parameters such as the Froude number(Fr),angle of submerged vanes to the flow(α),angle of submerged vane location in the bend(θ),distance between submerged vanes(d),height(H),and length(L)of the vanes on the dimensionless volume of the scour hole were experimentally studied.The submerged vanes were installed on a 180°bend whose central radius and channel width were 2.8 and 0.6 m,respectively.By reducing the Froude number,the scour hole volume decreased.For all Froude numbers,the biggest scour hole formed atθ=15°.In all models,by increasing the Froude number,the scour hole volume significantly increases.In addition,by increasing the submerged vanes’length and height,the scour hole dimensions also grow.Secondly,using gene expression programming(GEP),a relationship for determining the scour hole volume around the submerged vanes was provided.For this model,the determination coefficients(R2)for the training and test modes were computed as 0.91 and 0.9,respectively.In addition,this study performed partial derivative sensitivity analysis(PDSA).According to the results,the PDSA was calculated as positive for all input variables.展开更多
文摘This paper studies the free bending vibration of cylindrical tank partially filled with liquid and submerged in water. The depths of liquid and water may be completely arbitrary. The exact calculating formulae of mode shape functions and inherent frequencies are deduced. The results can be gained by means of computer. The analysis shows that the effect of liquid and water on vibration of cylindrical tank is respectively equivalent to a generalized distributive mass attached to the tank.
文摘A theorem of solving a system of linear non-homogeneous differential equations through integrating and adding its basic solutions is put forward and proved, the mathematical role and physical nature of the theorem is interpreted briefly. As an example, the theorem is applied to solve the problem of thermo-force bending of a thick plate.
文摘Submerged vanes are installed on rivers and channel beds to protect the outer bank bends from scouring.Also,local scouring occurs around the submerged vanes over time,and identifying the effective factors on the scouring phenomena around these submerged vanes is one of the important issues in river engineering.The most important aimof this study is investigation of scour pattern around submerged vanes located in 180°bend experimentally and numerically.Firstly,the effects of various parameters such as the Froude number(Fr),angle of submerged vanes to the flow(α),angle of submerged vane location in the bend(θ),distance between submerged vanes(d),height(H),and length(L)of the vanes on the dimensionless volume of the scour hole were experimentally studied.The submerged vanes were installed on a 180°bend whose central radius and channel width were 2.8 and 0.6 m,respectively.By reducing the Froude number,the scour hole volume decreased.For all Froude numbers,the biggest scour hole formed atθ=15°.In all models,by increasing the Froude number,the scour hole volume significantly increases.In addition,by increasing the submerged vanes’length and height,the scour hole dimensions also grow.Secondly,using gene expression programming(GEP),a relationship for determining the scour hole volume around the submerged vanes was provided.For this model,the determination coefficients(R2)for the training and test modes were computed as 0.91 and 0.9,respectively.In addition,this study performed partial derivative sensitivity analysis(PDSA).According to the results,the PDSA was calculated as positive for all input variables.
