摘要
A kind of addition formulae for the spherical wave functions is generated by using the bicentric expansion of Green function in spherical coordinates. For an acoustical system with multiple spheres, the addition formulae permit the field expansions all referred to the center of one of the spheres, whose boundary conditions can be consequently used to study the multiple scattering easily. The two-sphere acoustical system with different boundary conditions is considered and the field scattered by each sphere can be obtained by solving an infinite set of two linear, complex, algebraic equations, whose coefficients are coupled through double sums in the spherical wave functions. Finally, the form functions of two spheres insonified by a plane wave at arbitrary angles of incidence are calculated and the addition formulae presented are validated by comparing the corresponding numerical results with those of the existing literature.
A kind of addition formulae for the spherical wave functions is generated by using the bicentric expansion of Green function in spherical coordinates. For an acoustical system with multiple spheres, the addition formulae permit the field expansions all referred to the center of one of the spheres, whose boundary conditions can be consequently used to study the multiple scattering easily. The two-sphere acoustical system with different boundary conditions is considered and the field scattered by each sphere can be obtained by solving an infinite set of two linear, complex, algebraic equations, whose coefficients are coupled through double sums in the spherical wave functions. Finally, the form functions of two spheres insonified by a plane wave at arbitrary angles of incidence are calculated and the addition formulae presented are validated by comparing the corresponding numerical results with those of the existing literature.
基金
National Natural Science Foundation of China (10174037)
