Generalized scattering matrix method for Lamb wave scattering analysis at cascaded notches

2021 ◽  
pp. 107754632110377
Author(s):  
Xuwei Cao ◽  
Liang Zeng ◽  
Jing Lin
Keyword(s):  
Matrix Method ◽  
Recurrence Relations ◽  
Lamb Waves ◽  
Scattering Matrix ◽  
Scattering Coefficients ◽  
Mode Control ◽  
Scattering Matrices ◽  
The Time Domain ◽  
Scattering Matrix Method ◽  
Generalized Scattering Matrix

A thorough understanding of the scattering mechanism of Lamb waves at discontinuities is of interest for quantitative evaluation of structural properties and mode control. This study extends the generalized scattering matrix method to investigate the interaction of straight crested Lamb waves with multiple cascaded rectangular notches. Based on the orthogonality and completeness of Lamb modes, the mode matching method is utilized to determine the scattering matrices of downward and upward step discontinuities. After that, the generalized scattering matrix method is employed to determine the scattering matrices of a single rectangular notch and the recurrence relations between the scattering matrices of n + 1 cascaded notches and those of n cascaded notches. Finally, the scattering matrices of multiple cascaded notches can be easily obtained taking advantage of the recurrence relations. As the number of cascaded notches increases, more and sharper peaks appear in the scattering coefficient curves. The finite element simulations conducted in the time domain validate the theoretical results for cascaded notches with identical or different depths, which demonstrate that this method can be applied to find the scattering coefficients at piece-wise periodic or nonperiodic waveguides. The generalized scattering matrix method may have potential applications in quantitative nondestructive evaluation and mode control.

LES-Based Scattering Matrix Method for Low-Order Acoustic Network Models

2017 ◽  
Author(s):  
Changjin Yoon ◽  
Owen Graham ◽  
Fei Han ◽  
Kwanwoo Kim ◽  
Katsuo Maxted ◽  
...  
Keyword(s):  
Experimental Data ◽  
Phase Angle ◽  
Traveling Wave ◽  
Matrix Method ◽  
Scattering Matrix ◽  
Acoustic Energy ◽  
Upstream Region ◽  
Downstream Region ◽  
Scattering Matrices ◽  
Scattering Matrix Method

The identification of scattering matrix method is conducted using high fidelity Large Eddy Simulations. From a series of LES results, the scattering matrices of a plain orifice and a lean premixed nozzle are evaluated and compared with the corresponding experimental data. It is confirmed that LES simulations are capable of predicting the acoustic scattering matrix, with some limitations. The magnitude of the scattering matrices imply that the acoustic energy transfer across the orifice and mixer agree fairly well with that of the scattering matrices from the experimental data. Moreover, the phase angle of transmission/reflection elements for the traveling wave in the upstream region consistently follows the experimental trends. The phase angle of transmission/reflection elements for traveling waves in the downstream region, however, shows a significant discrepancy with the experimental measurements. For the direct use of the LES-based scattering matrix method, the accuracy of determination of the phase angle of reflection/transmission of the traveling wave in the downstream region needs further study.

Sign in / Sign up

Export Citation Format

Share Document