A hydrodynamic model is used to study Kelvin-Helmholtz(KH)instability of the interface between two particle-laden inviscid fluids moving with two different uniform mean velocities.Explicit eigen-equation is derived to...A hydrodynamic model is used to study Kelvin-Helmholtz(KH)instability of the interface between two particle-laden inviscid fluids moving with two different uniform mean velocities.Explicit eigen-equation is derived to study the effect of suspended particles on the growth rate of KH instability.For dusty gases with negligible volume fraction of heavy particles and small particle-to-fluid mass ratio,the real and imaginary parts of leading-order asymptotic expression derived by the present model for the growth rate are shown to be identical to the earlier results derived by the classical Saffman model established for dusty gases.Beyond the known results,explicit leading-order asymptotic expressions for the effect of suspended particles on the growth rate are derived for several typical cases of basic interest.It is shown that the suspended particles can decrease or increase the growth rate of KH instability depending on the Stokes numbers of the particles and whether the particles are heavier or lighter than the clean fluid.Compared to the mass density of the clean fluid,our results based on leading-order asymptotic solutions show that heavier particles and lighter particles have opposite effects on the growth rate of KH instability,while the effect of neutrally buoyant particles on the growth rate of KH instability is negligible.展开更多
Wetting of a liquid droplet on another liquid substrate is governed by the well-known Neumann equations.The present work aims to develop an explicit modified version of the Neumann equations for axisymmetric wetting o...Wetting of a liquid droplet on another liquid substrate is governed by the well-known Neumann equations.The present work aims to develop an explicit modified version of the Neumann equations for axisymmetric wetting of a liquid droplet on a highly stretched elastic membrane of non-zero bending rigidity.An explicit modified form of the Neumann equations is derived to determine the two contact angles,which is reduced to Young's equation for a liquid droplet on a rigid membrane or to the Neumann equations for a liquid droplet on another liquid substrate.Further implications of the modified Neumann equations are examined by comparison with some previous results reported in the recent literature,particularly considering the ranges of material and geometrical parameters of the liquid droplet-membrane system which have not been recently addressed in the literature.展开更多
The internal stress field of an inhomogeneous or homogeneous inclusion in an infinite elastic plane under uniform stress-free eigenstrains is studied. The study is restricted to the inclusion shapes defined by the pol...The internal stress field of an inhomogeneous or homogeneous inclusion in an infinite elastic plane under uniform stress-free eigenstrains is studied. The study is restricted to the inclusion shapes defined by the polynomial mapping functions mapping the exterior of the inclusion onto the exterior of a unit circle. The inclusion shapes, giving a polynomial internal stress field, are determined for three types of inclusions, i.e., an inhomogeneous inclusion with an elastic modulus different from the surrounding matrix, an inhomogeneous inclusion with the same shear modulus but a different Poisson＇s ratio from the surrounding matrix, and a homogeneous inclusion with the same elastic modulus as the surrounding matrix. Examples are presented, and several specific conclusions are achieved for the relation between the degree of the polynomial internal stress field and the degree of the mapping function defining the inclusion shape.展开更多
Inspired by recent research interest in the interface wrinkling of bonded materials in diverse areas of 3D printing,the present work studies the interfacial instability of two bonded elastic bodies driven by negative ...Inspired by recent research interest in the interface wrinkling of bonded materials in diverse areas of 3D printing,the present work studies the interfacial instability of two bonded elastic bodies driven by negative interfacial tension or compressible bulk residual stress.For interfacial instability modes decaying exponentially with distance from the interface,the present model is formulated for two bonded elastic half-spaces with a planar interface under plane strain.An explicit expression is given for the wavenumber of interfacial instability driven by negative interfacial tension,and a critical condition is derived for interfacial instability driven by compressive bulk residual stress.The derived results are validated with comparison to known results on surface instability of an elastic half-space,and the role of shear modulus ratio and Poisson’s ratios of two bonded elastic bodies in interfacial instability,an issue to be addressed in literature,is studied with specific reference to material parameters used in some areas of 3D printing.展开更多
The existing theories of finite-time stability depend on a prescribed bound on initial disturbances and a prescribed threshold for allowable responses. It remains a challenge to identify the critical value of loading ...The existing theories of finite-time stability depend on a prescribed bound on initial disturbances and a prescribed threshold for allowable responses. It remains a challenge to identify the critical value of loading parameter for finite time instability observed in experiments without the need of specifying any prescribed threshold for al- lowable responses. Based on an energy balance analysis of a simple dynamic system, this paper proposes a general criterion for finite time stability which indicates that finite time stability of a linear dynamic system with constant coefficients during a given time interval [0, tf] is guaranteed provided the product of its maximum growth rate （determined by the maximum eigen-root pl 〉0） and the duration tf does not exceed 2, i.e., pltf 〈2. The proposed criterion （pltf=2） is applied to several problems of impacted buckling of elastic columns： （i） an elastic column impacted by a striking mass, （ii） longitudinal impact of an elastic column on a rigid wall, and （iii） an elastic column compressed at a constant speed （＂Hoff problem＂）, in which the time-varying axial force is replaced approximately by its average value over the time duration. Comparison of critical parameters predicted by the proposed criterion with available experimental and simulation data shows that the proposed criterion is in robust reasonable agreement with the known data, which suggests that the proposed simple criterion （pltf---2） can be used to estimate critical parameters for finite time stability of dynamic systems governed by linear equations with constant coefficients.展开更多
文摘A hydrodynamic model is used to study Kelvin-Helmholtz(KH)instability of the interface between two particle-laden inviscid fluids moving with two different uniform mean velocities.Explicit eigen-equation is derived to study the effect of suspended particles on the growth rate of KH instability.For dusty gases with negligible volume fraction of heavy particles and small particle-to-fluid mass ratio,the real and imaginary parts of leading-order asymptotic expression derived by the present model for the growth rate are shown to be identical to the earlier results derived by the classical Saffman model established for dusty gases.Beyond the known results,explicit leading-order asymptotic expressions for the effect of suspended particles on the growth rate are derived for several typical cases of basic interest.It is shown that the suspended particles can decrease or increase the growth rate of KH instability depending on the Stokes numbers of the particles and whether the particles are heavier or lighter than the clean fluid.Compared to the mass density of the clean fluid,our results based on leading-order asymptotic solutions show that heavier particles and lighter particles have opposite effects on the growth rate of KH instability,while the effect of neutrally buoyant particles on the growth rate of KH instability is negligible.
基金Project supported by the Natural Science&Engineering Research Council(NSERC)of Canada(No.NSERC-RGPIN204992)。
文摘Wetting of a liquid droplet on another liquid substrate is governed by the well-known Neumann equations.The present work aims to develop an explicit modified version of the Neumann equations for axisymmetric wetting of a liquid droplet on a highly stretched elastic membrane of non-zero bending rigidity.An explicit modified form of the Neumann equations is derived to determine the two contact angles,which is reduced to Young's equation for a liquid droplet on a rigid membrane or to the Neumann equations for a liquid droplet on another liquid substrate.Further implications of the modified Neumann equations are examined by comparison with some previous results reported in the recent literature,particularly considering the ranges of material and geometrical parameters of the liquid droplet-membrane system which have not been recently addressed in the literature.
基金Project supported by the National Natural Science Foundation of China(No.11372363)the Fundamental Research Funds for the Central Universities of China(No.0241005202006)+1 种基金the Natural Science&Engineering Research Council of Canadathe Open Research Foundation of the State Key Laboratory of Structural Analysis for Industrial Equipment(No.GZ1404)
文摘The internal stress field of an inhomogeneous or homogeneous inclusion in an infinite elastic plane under uniform stress-free eigenstrains is studied. The study is restricted to the inclusion shapes defined by the polynomial mapping functions mapping the exterior of the inclusion onto the exterior of a unit circle. The inclusion shapes, giving a polynomial internal stress field, are determined for three types of inclusions, i.e., an inhomogeneous inclusion with an elastic modulus different from the surrounding matrix, an inhomogeneous inclusion with the same shear modulus but a different Poisson＇s ratio from the surrounding matrix, and a homogeneous inclusion with the same elastic modulus as the surrounding matrix. Examples are presented, and several specific conclusions are achieved for the relation between the degree of the polynomial internal stress field and the degree of the mapping function defining the inclusion shape.
基金support of Natural Science and Engineering Research Council of Canada(NSERCRGPIN204992).
文摘Inspired by recent research interest in the interface wrinkling of bonded materials in diverse areas of 3D printing,the present work studies the interfacial instability of two bonded elastic bodies driven by negative interfacial tension or compressible bulk residual stress.For interfacial instability modes decaying exponentially with distance from the interface,the present model is formulated for two bonded elastic half-spaces with a planar interface under plane strain.An explicit expression is given for the wavenumber of interfacial instability driven by negative interfacial tension,and a critical condition is derived for interfacial instability driven by compressive bulk residual stress.The derived results are validated with comparison to known results on surface instability of an elastic half-space,and the role of shear modulus ratio and Poisson’s ratios of two bonded elastic bodies in interfacial instability,an issue to be addressed in literature,is studied with specific reference to material parameters used in some areas of 3D printing.
基金Project supported by the Natural Science and Engineering Research Council (NSERC) of Canada (No.NSERC-RGPIN204992)
文摘The existing theories of finite-time stability depend on a prescribed bound on initial disturbances and a prescribed threshold for allowable responses. It remains a challenge to identify the critical value of loading parameter for finite time instability observed in experiments without the need of specifying any prescribed threshold for al- lowable responses. Based on an energy balance analysis of a simple dynamic system, this paper proposes a general criterion for finite time stability which indicates that finite time stability of a linear dynamic system with constant coefficients during a given time interval [0, tf] is guaranteed provided the product of its maximum growth rate （determined by the maximum eigen-root pl 〉0） and the duration tf does not exceed 2, i.e., pltf 〈2. The proposed criterion （pltf=2） is applied to several problems of impacted buckling of elastic columns： （i） an elastic column impacted by a striking mass, （ii） longitudinal impact of an elastic column on a rigid wall, and （iii） an elastic column compressed at a constant speed （＂Hoff problem＂）, in which the time-varying axial force is replaced approximately by its average value over the time duration. Comparison of critical parameters predicted by the proposed criterion with available experimental and simulation data shows that the proposed criterion is in robust reasonable agreement with the known data, which suggests that the proposed simple criterion （pltf---2） can be used to estimate critical parameters for finite time stability of dynamic systems governed by linear equations with constant coefficients.
