In this study,the vibration stability of fluid conveying pipe resting on two-parameter foundation is in-vestigated under four different elastic support boundary conditions.The harmonic differential quadrature(HDQ)meth...In this study,the vibration stability of fluid conveying pipe resting on two-parameter foundation is in-vestigated under four different elastic support boundary conditions.The harmonic differential quadrature(HDQ)method is applied to solve the governing vibration equation derived based on Euler–Bernoulli beam theory subject to the elastic foundation and boundary conditions.As a result,a general set of second-order ordinary differential equations emerges,and by appropriately setting the stiffness of the end springs,one can easily study the dynamics of various systems with classical or non-classical bound-ary conditions.The numerical simulations are conducted to study the pipe instability performance with respect to various boundary conditions,elastic support parameters,elastic foundation parameters and fluid mass ratios.The numerical model is validated by comparison with published data.It is found that the elastic support boundary conditions have significant effects on the stability of pipe resting on elas-tic foundation.The pipe stability performance is very sensitive to the two elastic foundation parameters.Larger fluid mass ratio enhances the pipe flutter stability performance but has no effects on the diver-gence.展开更多
This work presents a numerical methodology for modeling the Winkler supports and nonlinear conditions by proposing new boundary conditions. For the boundary conditions of Winkler support model, the surface tractions a...This work presents a numerical methodology for modeling the Winkler supports and nonlinear conditions by proposing new boundary conditions. For the boundary conditions of Winkler support model, the surface tractions and the displacements normal to the surface of the solid are unknown, but their relationship is known by means of the ballast coefficient, whereas for nonlinear boundary conditions, the displacements normal to the boundary of the solid are zero in the positive direction but are allowed in the negative direction. In those zones, detachments of nodes might appear, leading to a nonlinearity, because the number of nodes that remain fixed or of the detached ones (under tensile tractions) is unknown. The proposed methodology is applied to the 3D elastic receding contact problem using the boundary element method. The surface t r actions and the displacements of the common int erface bet ween the two solids in contac t under the influence of different supports are calculated as well as the boundary zone of the solid where the new boundary conditions are applied. The problem is solved by a double-iterative met hod, so in the final solut ion, t here are no t r act ions or pene trations between the two solids or at the boundary of the solid where the nonlinear boundary conditions are Simula ted. The effectiveness of the proposed method is verified by examples.展开更多
A supported framework of a gyroscope＇s rotor is designed and the B-Spline wavelet finite element model of nonlinear supported magnetic field is worked out. A new finite element space is studied in which the scaling f...A supported framework of a gyroscope＇s rotor is designed and the B-Spline wavelet finite element model of nonlinear supported magnetic field is worked out. A new finite element space is studied in which the scaling function of the B-spline wavelet is considered as the shape function of a tetrahedton. The magnetic field is spited by an artificial absorbing body which used the condition of field radiating, so the solution is unique. The resolution is improved via the varying gradient of the B-spline function under the condition of unchanging gridding. So there are some advantages in dealing with the focus flux and a high varying gradient result from a nonlinear magnetic field. The result is more practical. Plots of flux and in the space is studied via simulating the supported system model. The results of the study are useful in the research of the supported magnetic system for the gyroscope rotor.展开更多
[摘要]给出了一种陀螺仪转子悬浮结构.建立了悬浮磁场 B 样条小波有限元模型;研究了一类新的有限元空间.它以 B 样条小波函数作为正四面体有限等参元的形状函数。利用 B 样条小波函数的变尺度特性在不改变网格的剖分下提高分辨率。最后...[摘要]给出了一种陀螺仪转子悬浮结构.建立了悬浮磁场 B 样条小波有限元模型;研究了一类新的有限元空间.它以 B 样条小波函数作为正四面体有限等参元的形状函数。利用 B 样条小波函数的变尺度特性在不改变网格的剖分下提高分辨率。最后对悬浮系统模型进行了仿真,给出了磁力线的走向、分布及空间各点的磁场强度,并对结果进行了分析。展开更多
文摘In this study,the vibration stability of fluid conveying pipe resting on two-parameter foundation is in-vestigated under four different elastic support boundary conditions.The harmonic differential quadrature(HDQ)method is applied to solve the governing vibration equation derived based on Euler–Bernoulli beam theory subject to the elastic foundation and boundary conditions.As a result,a general set of second-order ordinary differential equations emerges,and by appropriately setting the stiffness of the end springs,one can easily study the dynamics of various systems with classical or non-classical bound-ary conditions.The numerical simulations are conducted to study the pipe instability performance with respect to various boundary conditions,elastic support parameters,elastic foundation parameters and fluid mass ratios.The numerical model is validated by comparison with published data.It is found that the elastic support boundary conditions have significant effects on the stability of pipe resting on elas-tic foundation.The pipe stability performance is very sensitive to the two elastic foundation parameters.Larger fluid mass ratio enhances the pipe flutter stability performance but has no effects on the diver-gence.
文摘This work presents a numerical methodology for modeling the Winkler supports and nonlinear conditions by proposing new boundary conditions. For the boundary conditions of Winkler support model, the surface tractions and the displacements normal to the surface of the solid are unknown, but their relationship is known by means of the ballast coefficient, whereas for nonlinear boundary conditions, the displacements normal to the boundary of the solid are zero in the positive direction but are allowed in the negative direction. In those zones, detachments of nodes might appear, leading to a nonlinearity, because the number of nodes that remain fixed or of the detached ones (under tensile tractions) is unknown. The proposed methodology is applied to the 3D elastic receding contact problem using the boundary element method. The surface t r actions and the displacements of the common int erface bet ween the two solids in contac t under the influence of different supports are calculated as well as the boundary zone of the solid where the new boundary conditions are applied. The problem is solved by a double-iterative met hod, so in the final solut ion, t here are no t r act ions or pene trations between the two solids or at the boundary of the solid where the nonlinear boundary conditions are Simula ted. The effectiveness of the proposed method is verified by examples.
文摘A supported framework of a gyroscope＇s rotor is designed and the B-Spline wavelet finite element model of nonlinear supported magnetic field is worked out. A new finite element space is studied in which the scaling function of the B-spline wavelet is considered as the shape function of a tetrahedton. The magnetic field is spited by an artificial absorbing body which used the condition of field radiating, so the solution is unique. The resolution is improved via the varying gradient of the B-spline function under the condition of unchanging gridding. So there are some advantages in dealing with the focus flux and a high varying gradient result from a nonlinear magnetic field. The result is more practical. Plots of flux and in the space is studied via simulating the supported system model. The results of the study are useful in the research of the supported magnetic system for the gyroscope rotor.
文摘[摘要]给出了一种陀螺仪转子悬浮结构.建立了悬浮磁场 B 样条小波有限元模型;研究了一类新的有限元空间.它以 B 样条小波函数作为正四面体有限等参元的形状函数。利用 B 样条小波函数的变尺度特性在不改变网格的剖分下提高分辨率。最后对悬浮系统模型进行了仿真,给出了磁力线的走向、分布及空间各点的磁场强度,并对结果进行了分析。
文摘针对超前支护存在的问题,通过叠加原理和有限差分原理,研究了超前支护装备-顶板之间相互作用力.采用叠加原理建立超前支护装备横、纵梁变形协调方程,并将其作为小支撑组的绝对位移.采用有限差分理论,并根据顶板的"三边固支,一边简支"的边界条件对建立了顶板的力学模型.采用ANSYS对超前支护装备-顶板耦合体系进行求解,结果表明:超前支护装备的最大应力发生于后部横、纵梁接触处为258 MPa,最大位移发生于中间纵梁后部及中纵梁与后部横梁连接处为2.219 mm.顶板的最大应力位于后部两角处为7.11 MPa,变形从迎头向后逐渐增大为7.77 mm.
