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
Based on the standard spaces of the physical presentation, both the quasi-static mechanical approximation and the quasi-static electromagnetic approximation of piezoelectric solids are studied here. The complete set o...Based on the standard spaces of the physical presentation, both the quasi-static mechanical approximation and the quasi-static electromagnetic approximation of piezoelectric solids are studied here. The complete set of uncoupled elastic wave and electromagnetic wave equations are deduced. The results show that the number and propagation speed of elastic waves and electromagnetic waves in anisotropic piezoelectric solids are determined by both the subspaces of electromagnetically anisotropic media and ones of mechanically anisotropic media. Based on these laws, we discuss the propagation behaviour of elastic waves and electromagnetic waves in the piezoelectric material of class 6 mm.展开更多
Static electromagnetic fields are studied based on standard spaces of the physical presentation, and the modal equations of static electromagnetic fields for anisotropic media are derived. By introducing a new set of ...Static electromagnetic fields are studied based on standard spaces of the physical presentation, and the modal equations of static electromagnetic fields for anisotropic media are derived. By introducing a new set of first-order potential functions, several novel theoretical results are obtained. It is found that, for isotropic media, electric or magnetic potentials are scalar; while for anisotropic media, they are vectors. Magnitude and direction of the vector potentials are related to the anisotropic subspaces. Based on these results, we discuss the laws of static electromagnetic fields for anisotropic media.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Based on the standard spaces of the physical presentation, both the quasi-static mechanical approximation and the quasi-static electromagnetic approximation of piezoelectric solids are studied here. The complete set of uncoupled elastic wave and electromagnetic wave equations are deduced. The results show that the number and propagation speed of elastic waves and electromagnetic waves in anisotropic piezoelectric solids are determined by both the subspaces of electromagnetically anisotropic media and ones of mechanically anisotropic media. Based on these laws, we discuss the propagation behaviour of elastic waves and electromagnetic waves in the piezoelectric material of class 6 mm.
基金supported by the National Natural Science Foundation of China (No.50778179)
文摘Static electromagnetic fields are studied based on standard spaces of the physical presentation, and the modal equations of static electromagnetic fields for anisotropic media are derived. By introducing a new set of first-order potential functions, several novel theoretical results are obtained. It is found that, for isotropic media, electric or magnetic potentials are scalar; while for anisotropic media, they are vectors. Magnitude and direction of the vector potentials are related to the anisotropic subspaces. Based on these results, we discuss the laws of static electromagnetic fields for anisotropic media.
