Will electric field intensity vector poisson equation is 本文来自辣/文(论"文?网，
毕业论文 www.751com.cn 加7位QQ324~9114找原文 converted into the potential neumann boundary value problem of elliptic partial differential equations. Using the finite element method solving the constrained electric field intensity produced by electric charge distribution in the piezoelectric body and boundary, and the linear polarization is very different results are obtained. The theoretical analysis results for the strong support of the test results. See [63
L 3 a variety of energy between the physical effects of touch type research
Now commonly used machine an electricity an hot three hodginsii material effect model (figure 3) is Heekmann 19th \"~ 5 years. It vividly and intuitively describe the three types of energy: the material effect relations between any physical effects are the result of energy conversion and information transformation, gives the main effect and cross effect concept and expression effect. Although the model via Srastl miserably to 0 1994, replaced by the optical thermal capacity, I and gains and losses according to the light wave is part of the electromagnetic wave, the optical quantity as similar to the electrical signal, and use similar symbols, this is unreasonable. In fact, related to the amount of optical property effect is mainly using the particle nature of light, and
Not volatility. Therefore, the modified model has not been a hawser is widely accepted. In practice, found Heekrn ~ nn model also have disadvantages: first, it does not include magnetism. Of course, in the model can't reflect the effect of physical properties related to the magnetic energy. Such as electromagnetic effect, piezomagnetic effect and thermomagnetic effect, etc. Second, because of a lack of magnetism, the thermodynamic equation and it cannot be the gibbs free energy (expression) of 4 kinds of energy. In order to make the model more perfect, in 1998, the author puts forward as shown in figure 4. Machine an electricity an thermal - magnetic effect of four kinds of physical properties between the energy model, and physical effect constitutive equation is presented. The model of the relationship between energy and gibbs free energy expression is completely consistent, but each symbol. Type (1) for the gibbs free energy expression: G, U a sun 'a TfE a one (1) : can U for crystal inherent thermodynamics} the subscript to the dimensions of the parameters. = 1, 2,' f,..., 6} ^,, m, n = 1, 2, 3} other symbolic figure 4 model is composed of double square, outside the square 4 vertices is intensive variables (also called constraint variables and independent variables, the intensity or generalized force)} in a square 4 vertices is shown capacity variable (also called variable, dependent variable, dependent variable or generalized displacement nan). The two vertices corresponding attachment (indicated by the arrows) of the relationship between two variables, namely the same energy as primary effect in relations between the system parameters. The main effect: thermodynamics' = c0, main effect: for heat capacity c} mechanics, a, s for smooth coefficient I electrical main effect: Df = high. As the dielectric constant, the polarizability tensor I
Magnetism main effects: B = for permeability. The coupling relations between the rest of the various parameters (as shown in figure with thin lines) for cross effect, in the form of a matrix can be expressed as table 1 (subscript ditto) in formula. The effect of expression is a rigid boundary conditions, namely the type from the variables and the dependent variable is the only, in all other coupled with the parameters are considered to be constant or zero. In addition, for Jane stand see, the above formula are the following written in an approximate conditions, does not take into account more than 2 times higher order term, the influence of the coupling relationship of any two parameters to control within the linear Fan Gu. In the four kinds of physical properties between the energy effect model on the basis of the author in 2000 and puts forward as shown in figure 5 machine, electrical, thermal, magnetic, optical, acoustic, \"six energy property effect between the new model, the diagram of light field intensity, y for light displacement} P for sound pressure, sound for displacement. Other symbols with figure 4. It comprehensively reflects the common effects of the relationship between various energy. The model not only bag in front of the ancient three energy physical effects (namely Heekmann and Srasti) model and four kinds of can
Physical effect model, and a new extension, and give the corresponding effect of material constitutive equation. Ask the physical effects of 6 kinds of energy model, each physical property parameters (including all of the generalized forces and generalized displacements) with other constitutive relation of parameters. The general expression (phenomenological equation) in the first approximation for
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