In this study,a theoretical approach is used to investigate the scattering problem of circular holes under a scalene triangle on the surface.The wave displacement function is obtained by solving the Helmholtz equation...In this study,a theoretical approach is used to investigate the scattering problem of circular holes under a scalene triangle on the surface.The wave displacement function is obtained by solving the Helmholtz equation that meets the zero-stress boundary conditions by adopting the method of separation of variables.Based on the complex function,multi-polar coordinate method,and region-matching technique,algebraic equations are established at auxiliary boundaries and free boundaries conditions in a complex domain.The auxiliary circle is used to solve the singularity of the reflex angle at the triangle corner.Then,according to sample statistics,the least squares method is used instead of the Fourier expansion method to solve the undetermined coefficient of the algebraic equations by discrete boundary.Numerical results show that the continuity of the auxiliary boundaries and the accuracy of the zero-stress boundaries are adequate,and the displacement of the free surface and the stress of the circular hole are related to the shape of the triangle,the position of the circular hole,the direction of the incident wave,and the frequency content of the excitation.Finally,time-domain responses are calculated by FFT based on the frequency domain theory,and the results reveal the wave propagation mechanism in a complicated structure.展开更多
基金National Natural Science Foundation of China under Grant No. 12072085Research Team Project of Heilongjiang Natural Science Foundation under Grant No. TD2020A001+2 种基金the Opening Fund of Acoustics Science and Technology Laboratory under Grant No. SSKF2020011the Fundamental Research Funds for the Central Universities under Grant No. 3072021CF0206the program for Innovative Research Team in China Earthquake Administration
文摘In this study,a theoretical approach is used to investigate the scattering problem of circular holes under a scalene triangle on the surface.The wave displacement function is obtained by solving the Helmholtz equation that meets the zero-stress boundary conditions by adopting the method of separation of variables.Based on the complex function,multi-polar coordinate method,and region-matching technique,algebraic equations are established at auxiliary boundaries and free boundaries conditions in a complex domain.The auxiliary circle is used to solve the singularity of the reflex angle at the triangle corner.Then,according to sample statistics,the least squares method is used instead of the Fourier expansion method to solve the undetermined coefficient of the algebraic equations by discrete boundary.Numerical results show that the continuity of the auxiliary boundaries and the accuracy of the zero-stress boundaries are adequate,and the displacement of the free surface and the stress of the circular hole are related to the shape of the triangle,the position of the circular hole,the direction of the incident wave,and the frequency content of the excitation.Finally,time-domain responses are calculated by FFT based on the frequency domain theory,and the results reveal the wave propagation mechanism in a complicated structure.
