Anisotropic viscoelastic mechanics is studied under anisotropicsubspace. It is proved that there also exist the eigen properties forviscoelastic medium. The modal Maxwell's equation, modal dynamicalequation (or mo...Anisotropic viscoelastic mechanics is studied under anisotropicsubspace. It is proved that there also exist the eigen properties forviscoelastic medium. The modal Maxwell's equation, modal dynamicalequation (or modal equilibrium equation) and modal compatibilityequation are ob- tained. Based on them, a new theory of anisotropicviscoelastic mechanics is presented. The advan- tages of the theoryare as follows: 1) the equations are all scalar, and independent ofeach other. The number of equations is equal to that of anisotrpicsubspaces, 2) no matter how complicated the anisotropy of solids maybe, the form of the definite equation and the boundary condition arein com- mon and explicit, 3) there is no distinction between theforce method and the displacement method for statics, that is, theequilibrium equation and the compatibility equation areindistinguishable under the mechanical space, 4) each modal equationhas a definite physical meaning, for example, the modal equations oforder one and order two express the value change and sheardeformation respec- tivley for isotropic solids, 5) there also existthe potential functions which are similar to the stress functions ofelastic mechanics for viscoelastic mechanics, but they are notman-made, 6) the final so- lution of stress or strain is given in theform of modal superimposition, which is suitable to the proxi- matecalculation in engineering.展开更多
Using the eigen theory of solid mechanics, the eigen properties of anisotropic viscoelastic bodies with Kelvin-Voigt model were studied, and the generalized Stokes equation of anisotropic viscoelastic dynamics was obt...Using the eigen theory of solid mechanics, the eigen properties of anisotropic viscoelastic bodies with Kelvin-Voigt model were studied, and the generalized Stokes equation of anisotropic viscoelastic dynamics was obtained, which gives the three-dimensional pattern of viscoelastical waves. The laws of viscoelastical waves of different anisotropical bodies were discussed.Several new conclusiones are given.展开更多
Kármán Vortex Street, a fascinating phenomenon of fluid dynamics, has intrigued the scientific community for a long time. Many researchers have dedicated their efforts to unraveling the essence of this intri...Kármán Vortex Street, a fascinating phenomenon of fluid dynamics, has intrigued the scientific community for a long time. Many researchers have dedicated their efforts to unraveling the essence of this intriguing flow pattern. Here, we apply the lattice Boltzmann method with curved boundary conditions to simulate flows around a circular cylinder and study the emergence of Kármán Vortex Street using the eigen microstate approach, which can identify phase transition and its order-parameter. At low Reynolds number, there is only one dominant eigen microstate W_(1) of laminar flow. At Re_(c)^(1)= 53.6, there is a phase transition with the emergence of an eigen microstate pair W^(2,3) of pressure and velocity fields. Further at Re_(c)^(2)= 56, there is another phase transition with the emergence of two eigen microstate pairs W^(4,5) and W^(6,7). Using the renormalization group theory of eigen microstate,both phase transitions are determined to be first-order. The two-dimensional energy spectrum of eigen microstate for W^(1), W^(2,3) after Re_(c)^(1), W^(4-7) after Re_(c)^(2) exhibit-5/3 power-law behavior of Kolnogorov's K41 theory. These results reveal the complexity and provide an analysis of the Kármán Vortex Street from the perspective of phase transitions.展开更多
文摘Anisotropic viscoelastic mechanics is studied under anisotropicsubspace. It is proved that there also exist the eigen properties forviscoelastic medium. The modal Maxwell's equation, modal dynamicalequation (or modal equilibrium equation) and modal compatibilityequation are ob- tained. Based on them, a new theory of anisotropicviscoelastic mechanics is presented. The advan- tages of the theoryare as follows: 1) the equations are all scalar, and independent ofeach other. The number of equations is equal to that of anisotrpicsubspaces, 2) no matter how complicated the anisotropy of solids maybe, the form of the definite equation and the boundary condition arein com- mon and explicit, 3) there is no distinction between theforce method and the displacement method for statics, that is, theequilibrium equation and the compatibility equation areindistinguishable under the mechanical space, 4) each modal equationhas a definite physical meaning, for example, the modal equations oforder one and order two express the value change and sheardeformation respec- tivley for isotropic solids, 5) there also existthe potential functions which are similar to the stress functions ofelastic mechanics for viscoelastic mechanics, but they are notman-made, 6) the final so- lution of stress or strain is given in theform of modal superimposition, which is suitable to the proxi- matecalculation in engineering.
文摘Using the eigen theory of solid mechanics, the eigen properties of anisotropic viscoelastic bodies with Kelvin-Voigt model were studied, and the generalized Stokes equation of anisotropic viscoelastic dynamics was obtained, which gives the three-dimensional pattern of viscoelastical waves. The laws of viscoelastical waves of different anisotropical bodies were discussed.Several new conclusiones are given.
基金supported by the National Natural Science Foundation of China (Grant No.12135003)。
文摘Kármán Vortex Street, a fascinating phenomenon of fluid dynamics, has intrigued the scientific community for a long time. Many researchers have dedicated their efforts to unraveling the essence of this intriguing flow pattern. Here, we apply the lattice Boltzmann method with curved boundary conditions to simulate flows around a circular cylinder and study the emergence of Kármán Vortex Street using the eigen microstate approach, which can identify phase transition and its order-parameter. At low Reynolds number, there is only one dominant eigen microstate W_(1) of laminar flow. At Re_(c)^(1)= 53.6, there is a phase transition with the emergence of an eigen microstate pair W^(2,3) of pressure and velocity fields. Further at Re_(c)^(2)= 56, there is another phase transition with the emergence of two eigen microstate pairs W^(4,5) and W^(6,7). Using the renormalization group theory of eigen microstate,both phase transitions are determined to be first-order. The two-dimensional energy spectrum of eigen microstate for W^(1), W^(2,3) after Re_(c)^(1), W^(4-7) after Re_(c)^(2) exhibit-5/3 power-law behavior of Kolnogorov's K41 theory. These results reveal the complexity and provide an analysis of the Kármán Vortex Street from the perspective of phase transitions.
