Singular boundary method for wave propagation analysis in periodic structures

TLDR: In this article, a strong-form boundary collocation method, the singular boundary method (SBM), is developed for the wave propagation analysis at low and moderate wavenumbers in periodic structures.

About: This article is published in Journal of Sound and Vibration.The article was published on 2018-07-07 and is currently open access. It has received 140 citations till now. The article focuses on the topics: Singular boundary method & Boundary element method.

Figures

Fig. 3 Schematic configuration of periodic structure with one-line scatterers According to the property of the block Toeplitz matrix, it can be embedded into a larger block circulant matrix C

Table 1. The comparisons between these four approaches in the SBM

Fig. 9 Sketch of the 2D problem for water wave interaction with 2×2 circular cylinders

Fig. 15 Acoustic pressure amplitude u for one-line 7 m-shaped cylinder array at different wave

Fig. 4 The convergence rate of the present SBM in Example 3.1.

Fig. 5 Sketch of 3D wave radiation problem by a finite circular cylinder

Frequently asked questions

Q1. What are the contributions in "Singular boundary method for wave propagation analysis in periodic structures" ?

A strong-form boundary collocation method, the singular boundary method ( SBM ), is developed in this paper for the wave propagation analysis in periodic structures. 

Q2. What is the acoustic wave propagation behavior of the cylinders?

With the increasing normalized wave number ka , the dimensionless run-up on the surface of each cylinder becomes more oscillating. 

Q3. How many boundary nodes can be used on the surface of each kite-shaped obstacle?

incidence angle 0 = 4 and the non-dimensional wave number = 2ka by using 100boundary nodes on the surface of each kite-shaped scatterer. 

Q4. How many seconds does the SBM take to solve?

It can be found that 2D SBM model with 800,000 boundarynodes requires less than 1 second, and 3D SBM with 328,050 boundary nodes requires less than 6 minutes. 

Q5. What is the key issue in the implementation of the SBM?

It should be mentioned that the determination of the origin intensity factors(OIFs) is one of the key issues in the SBM implementation. 

Q6. What is the importance of control of wave propagation in periodic structures?

The control of wave propagation in periodic structures [1-3] is of greatimportance in the design and manufacture of modern acoustic and optical devices, such as photonic crystals, photovoltaic devices and metamaterials [4,5]. 

Q7. what is the acoustic pressure amplitude for the normal wave incidence?

12-14that the acoustic pressure amplitude for the normal wave incidence 0 =0 issymmetrical with respect to the line 2 0x , and the acoustic pressure amplitude forthe wave incidence angle 0 = 4 is symmetrical about the line 1 2x x .(a) infh ; (b) 3h ; (c) 2h ; (d) 1h on the 3 0x plane ( 0 =0 ).(a) infh ; (b) 3h ; (c) 2h ; (d) 1h on the 3 0x plane ( 0 = 6 ).(a) infh ; (b) 3h ; (c) 2h ; (d) 1h on the 3 0x plane ( 0 = 4 ). 

Q8. What is the importance of the determination of the efficient placement of the source nodes in the M?

In the MFS, the determination of the efficient placement of the source nodes is vital for numerical accuracy and reliability, and it requires an additional computational cost. 

Q9. What is the simplest way to solve the SBM?

According to the types of the SBM resultant matrix generated by different types of the periodic structures, three fast Toeplitz-type matrix solvers are implemented. 

Q10. What is the way to solve the Toeplitz matrix?

Ferreira andDominguez [28] proposed an logO n n algorithm, which extends a Toeplitz matrixto a circulant matrix by adding more equations, and implements the simple iterative algorithm in conjunction with the Fast Fourier Transform (FFT) to obtain the solution of Toeplitz matrix. 

Q11. How many amplitudes are there on the inner sides of the four cylinders?

As shown in Fig. 11, themaximum amplitudes appearing on the inner sides of the four cylinders are about 160 and 10 times higher than the incident wave amplitude for the aforementioned two specific parameter settings, respectively.