Band structure analysis of phononic crystals based on the Chebyshev interval method

Area of Science:

• Materials Science
• Computational Physics
• Acoustics

Background:

• Phononic crystals are susceptible to uncertainties in material properties and geometry due to manufacturing and environmental factors.
• Accurate band structure analysis is crucial for designing effective phononic crystals.
• Existing methods like Monte Carlo simulation (MCM) can be computationally expensive.

Purpose of the Study:

• To develop and validate efficient methods for analyzing phononic crystal band structures under uncertainty.
• To compare the computational efficiency and accuracy of proposed methods against traditional approaches.
• To provide reliable tools for phononic crystal design despite inherent variability.

Main Methods:

• Proposed the Simplex Chebyshev Polynomial Expansion (SPCE) method for band structure analysis.
• Introduced a simplified incremental sampling strategy to enhance the Chebyshev surrogate model's efficiency and accuracy.
• Utilized samples from the Monte Carlo method (MCM) to establish interval ranges for band structures within the Chebyshev model.

Main Results:

• The SPCE method demonstrated significantly higher computational efficiency compared to the MCM.
• The simplified incremental sampling strategy successfully balanced calculation accuracy and computational speed.
• Validated the effectiveness and efficiency of the SPCE method through numerical examples of 2D and 3D phononic crystals.

Conclusions:

• The SPCE method is a computationally efficient and accurate approach for phononic crystal band structure analysis with uncertainties.
• This method provides a valuable tool for overcoming the limitations of traditional methods, especially when dealing with limited information.
• The findings support the practical application of the SPCE method in the design and optimization of phononic crystal devices.