Understanding bend loss in single-ring hollow-core photonic crystal fibers(PCFs)is becoming of increasing importance as the fibers enter practical applications.While purely numerical approaches are useful,there is a n...Understanding bend loss in single-ring hollow-core photonic crystal fibers(PCFs)is becoming of increasing importance as the fibers enter practical applications.While purely numerical approaches are useful,there is a need for a simpler analytical formalism that provides physical insight and can be directly used in the design of PCFs with low bend loss.We show theoretically and experimentally that a wavelength-dependent critical bend radius exists below which the bend loss reaches a maximum,and that this can be calculated from the structural parameters of a fiber using a simple analytical formula.This allows straightforward design of single-ring PCFs that are bend-insensitive for specified ranges of bend radius and wavelength.It also can be used to derive an expression for the bend radius that yields optimal higher-order mode suppression for a given fiber structure.展开更多
A new method named the state space boundary element method （SSBEM） is estab- lished, in which the problem domain is divided into two parts. One is the boundary element domain which includes the interested inner poin...A new method named the state space boundary element method （SSBEM） is estab- lished, in which the problem domain is divided into two parts. One is the boundary element domain which includes the interested inner point, and the other is the state space domain. The boundary integral equation and the state space equation are combined together based on the interfacial continuity condition to form the system equation of the SSBEM. The SSBEM synthe- sizes both advantages of the boundary element method and the state space method. However, it can give inaccurate results when being used to evaluate the mechanical quantity of a point very close to the boundary element, because the Gaussian quadrature fails to calculate the nearly singular integrals. The analytical formulas were developed by part of the authors before intro- duced to deal with the nearly singular integrals. Thus, the SSBEM can yield accurate physical quantities for the points very close to the boundary element. The SSBEM results agree well with those of the finite element method （FEM）, while the discretized elements are far fewer than those of the FEM. Meanwhile, the SSBEM can analyze very thin coating, while the FEM fails due to the limitation of tolerance for Boolean operations.展开更多
Upheaval buckling of pipelines can occur under thermal expansion and differential ground settlement.Research on this phenomenon has usually assumed the pipes are buried in horizontal ground.For long-distance transmiss...Upheaval buckling of pipelines can occur under thermal expansion and differential ground settlement.Research on this phenomenon has usually assumed the pipes are buried in horizontal ground.For long-distance transmission pipelines across mountainous areas,the ground surface is commonly inclined.Based on the Rankine earth pressure theory and Mohr-Coulomb failure criterion,analytical formulae for calculating the peak uplift resistance and the slip surface angles for a buried pipe in inclined ground are presented in this paper.Analyses indicate that the slip surfaces in inclined ground are asymmetric and rotate towards the downhill side.Under a shallow burial depth,the failure plane angle is highly impacted by the ground inclination.When the embedment ratio(H/D)is more than 4,the influence of the ground slope on the failure plane angle is negligible.The peak uplift resistance reduces in inclined ground,especially when H/D is less than 1.Finally,a simple equation considering the impact of ground inclination is proposed to predict the peak uplift resistance.展开更多
A three-dimensional(3D)analytical formulation is proposed to put together magnetic,electric and elastic fields to analyze the vibration modes of simply-supported layered piezo-electro-magnetic plates.The present 3D mo...A three-dimensional(3D)analytical formulation is proposed to put together magnetic,electric and elastic fields to analyze the vibration modes of simply-supported layered piezo-electro-magnetic plates.The present 3D model allows analyses for layered smart plates in both open-circuit and closed-circuit configurations.The secondorder differential equations written in the mixed curvilinear reference system govern the magneto-electro-elastic free vibration problem for multilayered plates.This set consists of the 3D equations of motion and the 3D divergence equations for the magnetic induction and electric displacement.Navier harmonic forms in the planar directions and the exponential matrix method in the transversal direction of the plate are applied to solve the second-order differential equations in terms of displacements.For these reasons,simply-supported boundary conditions are considered.Imposition of interlaminar continuity conditions on primary variables(displacements,magnetic potential,electric potential),and some secondary variables(transverse normal and transverse shear stresses,transverse normal magnetic induction/electric displacement)allows the implementation of the layer-wise approach.Assessments for both load boundary configurations are proposed in the results section to validate the present 3D approach.3D electro-elastic and 3D magneto-elastic coupling validations are performed separately considering different models from the open literature.A new benchmark involving a full magneto-electro-elastic coupling for multilayered plates is presented considering both load boundary configurations for different thickness ratios.For this benchmark,circular frequency values and related vibration modes through the transverse direction in terms of displacements,magnetic and electric potential,transverse normal magnetic induction/electric displacement are shown to visualize the magneto-electroelastic coupling and material and thickness layer effects.The present formulation has been entirely implemented in an academic Matlab(R2024a)code developed by the authors.In this paper,for the first time,the second-order differential equations governing the magneto-electro-elastic problem for the free vibration analysis of plates has been solved considering the mixed mode of harmonic forms and exponential matrix.The exponential matrix permits computing the secondary variable of the problem(stresses,electric displacement components and magnetic induction components)exactly,directly from constitutive and geometrical equations.In addition,the very simple and elegant formulation permits having a code with very low computational costs.The present manuscript aims to fill the void in open literature regarding reference 3D solutions for the free vibration analysis of magneto-electro-elastic plates.展开更多
文摘Understanding bend loss in single-ring hollow-core photonic crystal fibers(PCFs)is becoming of increasing importance as the fibers enter practical applications.While purely numerical approaches are useful,there is a need for a simpler analytical formalism that provides physical insight and can be directly used in the design of PCFs with low bend loss.We show theoretically and experimentally that a wavelength-dependent critical bend radius exists below which the bend loss reaches a maximum,and that this can be calculated from the structural parameters of a fiber using a simple analytical formula.This allows straightforward design of single-ring PCFs that are bend-insensitive for specified ranges of bend radius and wavelength.It also can be used to derive an expression for the bend radius that yields optimal higher-order mode suppression for a given fiber structure.
基金This work was supported by National Natural Science Foundation of China （No.11772114） and Grants from China Scholarship Council （No. 201706690019）.
文摘A new method named the state space boundary element method （SSBEM） is estab- lished, in which the problem domain is divided into two parts. One is the boundary element domain which includes the interested inner point, and the other is the state space domain. The boundary integral equation and the state space equation are combined together based on the interfacial continuity condition to form the system equation of the SSBEM. The SSBEM synthe- sizes both advantages of the boundary element method and the state space method. However, it can give inaccurate results when being used to evaluate the mechanical quantity of a point very close to the boundary element, because the Gaussian quadrature fails to calculate the nearly singular integrals. The analytical formulas were developed by part of the authors before intro- duced to deal with the nearly singular integrals. Thus, the SSBEM can yield accurate physical quantities for the points very close to the boundary element. The SSBEM results agree well with those of the finite element method （FEM）, while the discretized elements are far fewer than those of the FEM. Meanwhile, the SSBEM can analyze very thin coating, while the FEM fails due to the limitation of tolerance for Boolean operations.
基金Project supported by the National Natural Science Foundation of China(Nos.51988101 and 51178427)the Natural Science Foundation of Zhejiang Province(No.LCZ19E080002)the Fundamental Research Funds for the Central Universities(No.2019FZA4016),China。
文摘Upheaval buckling of pipelines can occur under thermal expansion and differential ground settlement.Research on this phenomenon has usually assumed the pipes are buried in horizontal ground.For long-distance transmission pipelines across mountainous areas,the ground surface is commonly inclined.Based on the Rankine earth pressure theory and Mohr-Coulomb failure criterion,analytical formulae for calculating the peak uplift resistance and the slip surface angles for a buried pipe in inclined ground are presented in this paper.Analyses indicate that the slip surfaces in inclined ground are asymmetric and rotate towards the downhill side.Under a shallow burial depth,the failure plane angle is highly impacted by the ground inclination.When the embedment ratio(H/D)is more than 4,the influence of the ground slope on the failure plane angle is negligible.The peak uplift resistance reduces in inclined ground,especially when H/D is less than 1.Finally,a simple equation considering the impact of ground inclination is proposed to predict the peak uplift resistance.
文摘A three-dimensional(3D)analytical formulation is proposed to put together magnetic,electric and elastic fields to analyze the vibration modes of simply-supported layered piezo-electro-magnetic plates.The present 3D model allows analyses for layered smart plates in both open-circuit and closed-circuit configurations.The secondorder differential equations written in the mixed curvilinear reference system govern the magneto-electro-elastic free vibration problem for multilayered plates.This set consists of the 3D equations of motion and the 3D divergence equations for the magnetic induction and electric displacement.Navier harmonic forms in the planar directions and the exponential matrix method in the transversal direction of the plate are applied to solve the second-order differential equations in terms of displacements.For these reasons,simply-supported boundary conditions are considered.Imposition of interlaminar continuity conditions on primary variables(displacements,magnetic potential,electric potential),and some secondary variables(transverse normal and transverse shear stresses,transverse normal magnetic induction/electric displacement)allows the implementation of the layer-wise approach.Assessments for both load boundary configurations are proposed in the results section to validate the present 3D approach.3D electro-elastic and 3D magneto-elastic coupling validations are performed separately considering different models from the open literature.A new benchmark involving a full magneto-electro-elastic coupling for multilayered plates is presented considering both load boundary configurations for different thickness ratios.For this benchmark,circular frequency values and related vibration modes through the transverse direction in terms of displacements,magnetic and electric potential,transverse normal magnetic induction/electric displacement are shown to visualize the magneto-electroelastic coupling and material and thickness layer effects.The present formulation has been entirely implemented in an academic Matlab(R2024a)code developed by the authors.In this paper,for the first time,the second-order differential equations governing the magneto-electro-elastic problem for the free vibration analysis of plates has been solved considering the mixed mode of harmonic forms and exponential matrix.The exponential matrix permits computing the secondary variable of the problem(stresses,electric displacement components and magnetic induction components)exactly,directly from constitutive and geometrical equations.In addition,the very simple and elegant formulation permits having a code with very low computational costs.The present manuscript aims to fill the void in open literature regarding reference 3D solutions for the free vibration analysis of magneto-electro-elastic plates.
