Study on the true and spurious eigensolutions of two-dimensional cavities using the dual multiple reciprocity method

In this paper, true and spurious eigensolutions for a circular cavity using the dual multiple reciprocity method (MRM) are analytically derived and numerically verified by the developed program. The roots of spurious eigenequation are found analytically by using symbolic manipulation software. A more efficient method is proposed by choosing a fewer number of equations from the dual MRM instead of all of the equations in the dual MRM. Numerical experiments are performed by using dual MRM program for comparison purposes. A circular cavity of radius 1 m with Neumann boundary conditions is considered, and the results match very well between the theoretical prediction and the numerical experiments for the first four true eigenvalues and the first two spurious eigenvalues. Also, a noncircular case of square cavity is numerically implemented. The true eigensolutions can be easily solved by the dual MRM program in conjunction with the singular value decomposition technique. At the same time, the boundary modes and the multiplicities of the true eigenvalues can also be determined.