Analysis method of multi-hole piezoelectric material electro-elastic field

A piezoelectric material and electric material technology, applied in the direction of electrical digital data processing, special data processing applications, instruments, etc., can solve the problems of unguaranteed accuracy, consuming a lot of manpower and calculation time, consuming large computer time and manpower, etc. , to achieve flexible adaptation, enhance engineering practicability, and reduce the amount of calculation

Active Publication Date: 2015-02-18
NANJING UNIV OF AERONAUTICS & ASTRONAUTICS
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  • Application Information

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Problems solved by technology

[0008] (3) Multiple grid models with different densities and qualities must be prepared, and the convergence results can be obtained by calculating the results of these models separately, which will consume a lot of manpower and computing time
[0009] Therefore, generally speaking, although the finite element method can approximate the electroelastic field of piezoelectric materials with non-elliptical holes, it takes a lot of time and manpower, and the accuracy cannot be guaranteed.

Method used

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  • Analysis method of multi-hole piezoelectric material electro-elastic field
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  • Analysis method of multi-hole piezoelectric material electro-elastic field

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Experimental program
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Effect test

Embodiment 1

[0038] This embodiment is a PZT-4 piezoelectric material containing a triangular hole and a square hole (such as figure 2 and image 3 shown), subject to x 2 Uniform electrical load in the direction The medium in the two holes is air. Material constants of PZT-4 (including elastic matrix A, piezoelectric matrix B and dielectric matrix C) and air permittivity ε 0 as follows:

[0039] A 11 =8.205×10 -12 ,A 12 =-3.144×10 -12 ,A 22 =7.495×10 -12 ,

[0040] A 33 =19.3×10 -12 (Pa -1 );

[0041] B 13 =39.4×10 -3 ,B 21 =-16.62×10 -3 ,B 22 =23.96×10 -3 (m 2 / C); (1)

[0042] C 11 =7.66×10 7 ,C 22 =9.82×10 7 (mF);

[0043] ε 0 =8.85×10 -12 F / m.

[0044] Step 1: Calculate the corresponding conformal mapping function according to the Schwarz-Christoffel mapping and using Maple software as

[0045]

[0046] Step 2: based on the electroelastic constant of the given piezoelectric material and the dielectric constant (see formula (1)) of the medium in the h...

Embodiment 2

[0082] Present embodiment is the PZT-4 piezoelectric material that contains an oval hole and an ellipse hole (such as Figure 4 and Figure 5 shown), subject to x 2 Uniform electrical load in the direction The medium in the two holes is air. The conformal mapping function of these two holes is

[0083]

[0084] The specific solution process is similar to that of Embodiment 1. First, the electroelastic constant of the piezoelectric material is obtained, and the complex potential function of the piezoelectric material and the perturbation series expression of the potential function of the medium in the two holes are established, and then the boundary conditions are established. Then carry out the Fourier series expansion of the boundary conditions, obtain the equations about the undetermined complex coefficients in the perturbation series expression, and solve all the undetermined coefficients, so as to determine the complex potential function of the piezoelectric materia...

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Abstract

The invention discloses an analysis method of a multi-hole piezoelectric material electro-elastic field. The method comprises the steps of presetting the shapes and positions of a plurality of holes in a piezoelectric material to be analyzed and then building a conformal mapping function corresponding to the holes; giving a perturbation expression of a complex potential function of the piezoelectric material and the perturbation expression of an electrical potential function of a medium in the holes in a precondition of taking the mutual effect of the holes into account; respectively spreading the complex potential function of the piezoelectric material and the electrical potential function of the medium in the holes to form a Fourier series, so as to obtain the semi-analytical solutions of all the potential functions; calculating the stress field and electric field of the piezoelectric material and the electric field of the medium in the holes according to the solved potential functions. The method is applicable to the shapes and positions of any given holes. Compared with the finite element method, the method disclosed by the invention has the advantages that tedious geometric modeling and mesh generation are not needed, and great advantages of speed and precision calculation are realized; the built complex variables function perturbation method can be used for solving multi-hole isotropic and anisotropic materials.

Description

technical field [0001] The invention relates to a piezoelectric material electroelastic field analysis method, in particular to a semi-analytic analysis method for stress concentration and electric field concentration at the edge of a piezoelectric material hole. Background technique [0002] Since the Curie brothers first discovered the piezoelectric effect on quartz crystals in the 1880s, the research and development of piezoelectric materials has been carried out rapidly. Piezoelectric materials are an important class of high-tech new materials with fierce international competition, and are widely used in high-tech fields such as information lasers, navigation and biology. [0003] During the manufacture and use of piezoelectric materials, holes are inevitable; on the other hand, due to artificial needs, some piezoelectric structures need to open holes. Since most piezoelectric materials are brittle materials, when they are subjected to external mechanical loads and elec...

Claims

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Application Information

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IPC IPC(8): G06F17/50
Inventor 戴明黄成高存法王爽宋坤范文荣
Owner NANJING UNIV OF AERONAUTICS & ASTRONAUTICS
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