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Band gap design method for two-dimensional phononic crystal plate structure based on wavelet finite element model

A two-dimensional phononic crystal, wavelet finite element technology, applied in design optimization/simulation, special data processing applications, etc., can solve the problems of slow convergence, low precision, restricting the band gap design of phononic crystal plate structure, etc. The effect of good computational efficiency, convergence, and high computational accuracy

Active Publication Date: 2020-06-26
WENZHOU UNIVERSITY
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Problems solved by technology

[0007] Although some of the above algorithms have been widely used, the common disadvantages are low precision and slow convergence, which restricts the bandgap design of phononic crystal plate structures and can be applied in engineering practice.

Method used

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  • Band gap design method for two-dimensional phononic crystal plate structure based on wavelet finite element model
  • Band gap design method for two-dimensional phononic crystal plate structure based on wavelet finite element model
  • Band gap design method for two-dimensional phononic crystal plate structure based on wavelet finite element model

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Embodiment 1

[0107] Embodiment 1: This embodiment mainly verifies the calculation accuracy of the wavelet finite element numerical solution model for calculating the band gap of the two-dimensional phononic crystal plate structure. In order to verify the correctness and effectiveness of the constructed BSWI plate element in the calculation of the bandgap of the phononic crystal, this section will give an example verification. As shown in Figure 2, the scatterers are periodically arranged in rectangular lead plates (Part B) and embedded in the epoxy resin (Part A) matrix to form a two-dimensional phononic crystal plate, and the filling rate is f=(L a × L b ) / (L x × L y)=11%, limited lattice constant L x with L y Both are equal to 0.03m. For the material parameters of lead and epoxy resin, see Image 6 .

[0108] First use 9 (m=3, n=3) BSWI4 3 The plate unit is used to calculate the bandgap characteristics of the two-dimensional phononic crystal. The BSWI scaling function used here is...

Embodiment 2

[0109] Embodiment 2: This embodiment mainly verifies the calculation efficiency of the wavelet finite element numerical solution model for calculating the band gap of a two-dimensional rectangular plate phononic crystal. Rectangular plates are also widely used in engineering practice as structural components. This paper will use BSWI wavelet finite element method to study the band gaps of phononic crystals with different lattice forms. For material parameters of lead and epoxy resin, see Image 6 .

[0110] We use a rectangular lattice to study the effect of the bandgap of phononic crystals, where L x not equal to L y . The corresponding structural parameters are: L x =0.03m, L y = 0.02m, L a = L b =0.01m, filling rate f=16.7%. 9 BSWI4 respectively 3 Plate unit (m=3, n=3), 20×20, 40×40 traditional rectangular plate units to calculate the band gap of phononic crystal, the results are shown in Figure 4 , the results are represented by dots, solid lines, and square box...

Embodiment 3

[0111] Embodiment 3: This embodiment mainly provides the scale range of the phononic crystal structure of a two-dimensional rectangular plate with a relatively wide bandgap calculated by using the wavelet finite element model. For material parameters of lead and epoxy resin, see Image 6 . Without loss of generality, the fixed structure parameters are: L x =0.03m, L y = 0.02m.

[0112] Adopt 9 BSWI4 3 Plate elements (m=3, n=3) are used to calculate the bandgap of phononic crystals. In order to obtain the bandgap characteristics that meet the requirements of a specific frequency band, the structural size of the two-dimensional phononic crystal plate is continuously calculated and adjusted. Under the premise of fixing the lattice constant, the relationship between the geometric dimensions of the scatterer is determined by obtaining the best filling rate, and finally the two-dimensional phononic crystal plate is completed. The bandgap design of the two-dimensional phononic c...

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Abstract

The invention discloses a design method for the band gap of a two-dimensional phonon crystal plate structure based on a wavelet finite element model. The wavelet finite element model uses the interval B-spline wavelet combined with the finite element method, replaces the polynomial interpolation of the traditional finite element with the BSWI scaling function, and combines the unit cell technology and the periodic boundary condition PBCs to establish the real symmetry of the discrete structure of the two-dimensional phononic crystal The eigenvalue problem is then calculated to obtain the bandgap characteristics of the phononic crystal. The wavelet finite element model for calculating the bandgap of the two-dimensional phononic crystal plate structure absorbs the advantages of the finite element method that can deal with complex solution domains and wavelet multi-scale approximation characteristics, and can obtain a numerical calculation model with high precision and fast convergence. The wavelet finite element model of the bandgap design of the two-dimensional phonon crystal plate structure proposed by the invention has high calculation accuracy and fast convergence, and is suitable for the bandgap design of the two-dimensional phonon crystal plate structure.

Description

technical field [0001] The invention belongs to the field of structural design of acoustic functional materials, and in particular relates to a method for designing a band gap of a two-dimensional phonon crystal plate structure based on a wavelet finite element model. Background technique [0002] In recent years, based on the theory of electronic energy bands in natural crystals, scholars have become very interested in the propagation of elastic waves in periodic structures, and are bound to find a good way to control vibrations. In 1993, Kushwaha et al. used the concept of phononic crystals for the first time when they studied the periodic structure of materials. It is also pointed out that the bandgap characteristic of phononic crystals can be applied to high-precision, vibration-free environments. In 1995, when R.Martinez-Sala et al. performed an acoustic test on the sculpture "Flowing Melody", they first verified the existence of an elastic band gap experimentally. Si...

Claims

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Application Information

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Patent Type & Authority Patents(China)
IPC IPC(8): G06F30/23
CPCG06F30/23
Inventor 向家伟刘帽钟永腾
Owner WENZHOU UNIVERSITY
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