The dual boundary element method is used to obtain an efficient solution of
the Helmholtz equation in the presence of geometric singularities. In part
icular, time-harmonic waves in a membrane which contains one or more fixed
edge stringers (or cracks) are investigated. The hypersingular integral equ
ation is used in the procedure to ensure a unique solution for the problem
with a degenerate boundary. The method yields a solution for the entire mem
brane as well as the dynamic stress intensity factor. Numerical results are
presented for a circular membrane containing a single edge stringer, two e
dge stringers and an internal stringer. Also, the first three critical wave
numbers of the membrane with the homogeneous boundary condition are determ
ined, and the dynamic stress intensity factors are found for problems with
the nonhomogeneous boundary condition. Good agreement is found after compar
ing the results with exact solutions, and with results obtained using DtN-F
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