A method that series perturbations approximate solutions to N-S equations with boundary conditions was discussed and adopted. Then the method was proved in which the asymptotic solutions of viscous fluid flow past a s...A method that series perturbations approximate solutions to N-S equations with boundary conditions was discussed and adopted. Then the method was proved in which the asymptotic solutions of viscous fluid flow past a sphere were deducted. By the ameliorative asymptotic expansion matched method, the matched functions, are determined easily and the ameliorative curve of drag coefficient is coincident well with measured data in the case that Reynolds number is less than or equal to 40 000.展开更多
Recently application of functionally graded materials（FGMs） have attracted a great deal of interest. These materials are composed of various materials with different micro-structures which can vary spatially in FGMs...Recently application of functionally graded materials（FGMs） have attracted a great deal of interest. These materials are composed of various materials with different micro-structures which can vary spatially in FGMs. Such composites with varying thickness and non-uniform pressure can be used in the aerospace engineering. Therefore, analysis of such composite is of high importance in engineering problems. Thermoelastic analysis of functionally graded cylinder with variable thickness under non-uniform pressure is considered. First order shear deformation theory and total potential energy approach is applied to obtain the governing equations of non-homogeneous cylinder. Considering the inner and outer solutions, perturbation series are applied to solve the governing equations. Outer solution for out of boundaries and more sensitive variable in inner solution at the boundaries are considered. Combining of inner and outer solution for near and far points from boundaries leads to high accurate displacement field distribution. The main aim of this paper is to show the capability of matched asymptotic solution for different non-homogeneous cylinders with different shapes and different non-uniform pressures. The results can be used to design the optimum thickness of the cylinder and also some properties such as high temperature residence by applying non-homogeneous material.展开更多
A narrow open channel resonant phenomenon, newly found by the authors in corresponding numerical calculations , was proved to exist based on the method of matching asymptotic expansions for three different channel co...A narrow open channel resonant phenomenon, newly found by the authors in corresponding numerical calculations , was proved to exist based on the method of matching asymptotic expansions for three different channel configurations. It is shown that the resonant wave numbe rk emerges around kL=nπ, n=1,2,3,…∞ with a corresponding frequency s hift, where L is the length of the channel. It is also clear that the resona nce in a narrow open channel is an essential property of a channel as long as it is uniformly narrow.展开更多
We explore the use of PDE constrained nonlinear optimization techniques to optimize and design electromagnetic crystals which exhibit frozen mode behavior.This is characterized by Van Hove singularities in the dispers...We explore the use of PDE constrained nonlinear optimization techniques to optimize and design electromagnetic crystals which exhibit frozen mode behavior.This is characterized by Van Hove singularities in the dispersion relation,e.g.,stationary reflection points and degenerate band edge points.Hence,the optimization process modifies the dispersion relation by adjusting the geometries and material parameters.The resulting algorithm is found to be capable of recovering all known crystal configurations as well as many new configurations,some of which display dramatically improved properties over previously used configuration.We investigate both gyrotropic photonic crystals and degenerate band edge crystals as well as the more complex case of the oblique incidence.In this latter case,we extend the investigation to the three-dimensional case to identify the first three-dimensional crystal exhibiting frozen mode behavior.展开更多
文摘A method that series perturbations approximate solutions to N-S equations with boundary conditions was discussed and adopted. Then the method was proved in which the asymptotic solutions of viscous fluid flow past a sphere were deducted. By the ameliorative asymptotic expansion matched method, the matched functions, are determined easily and the ameliorative curve of drag coefficient is coincident well with measured data in the case that Reynolds number is less than or equal to 40 000.
文摘Recently application of functionally graded materials（FGMs） have attracted a great deal of interest. These materials are composed of various materials with different micro-structures which can vary spatially in FGMs. Such composites with varying thickness and non-uniform pressure can be used in the aerospace engineering. Therefore, analysis of such composite is of high importance in engineering problems. Thermoelastic analysis of functionally graded cylinder with variable thickness under non-uniform pressure is considered. First order shear deformation theory and total potential energy approach is applied to obtain the governing equations of non-homogeneous cylinder. Considering the inner and outer solutions, perturbation series are applied to solve the governing equations. Outer solution for out of boundaries and more sensitive variable in inner solution at the boundaries are considered. Combining of inner and outer solution for near and far points from boundaries leads to high accurate displacement field distribution. The main aim of this paper is to show the capability of matched asymptotic solution for different non-homogeneous cylinders with different shapes and different non-uniform pressures. The results can be used to design the optimum thickness of the cylinder and also some properties such as high temperature residence by applying non-homogeneous material.
基金Project supported by the National Natural Science Foundation of China (No: 59879011, 19732004) the Foundation of the Mnistry
文摘A narrow open channel resonant phenomenon, newly found by the authors in corresponding numerical calculations , was proved to exist based on the method of matching asymptotic expansions for three different channel configurations. It is shown that the resonant wave numbe rk emerges around kL=nπ, n=1,2,3,…∞ with a corresponding frequency s hift, where L is the length of the channel. It is also clear that the resona nce in a narrow open channel is an essential property of a channel as long as it is uniformly narrow.
基金the U.S.Air Force Office of Scientific Research under the grant FA9550-04-1-0359.
文摘We explore the use of PDE constrained nonlinear optimization techniques to optimize and design electromagnetic crystals which exhibit frozen mode behavior.This is characterized by Van Hove singularities in the dispersion relation,e.g.,stationary reflection points and degenerate band edge points.Hence,the optimization process modifies the dispersion relation by adjusting the geometries and material parameters.The resulting algorithm is found to be capable of recovering all known crystal configurations as well as many new configurations,some of which display dramatically improved properties over previously used configuration.We investigate both gyrotropic photonic crystals and degenerate band edge crystals as well as the more complex case of the oblique incidence.In this latter case,we extend the investigation to the three-dimensional case to identify the first three-dimensional crystal exhibiting frozen mode behavior.
