Abstract
An analytical algorithm is proposed to represent eigensolutions [λm2, ψm(r)]m=1∞ of an imperfect structure C containing cracks in terms of crack configuration σc and eigensolutions [ωn2, φn(r)]n=1∞ of a perfect structured without P the cracks. To illustrate this algorithm on mechanical systems governed by the two-dimensional Helmholtz operator, the Green’s identity and Green’sfunction of P are used to represent ψm(r) in terms of an infinite series of φn(r). Substitution of the ψn(r) representation into the Kamke quotient of C and stationarity of the quotient result in a matrix Fredholm integral equation. The eigensolutions of the Fredholm integral equation then predict λm2 and ψm(r) of C. Finally, eigensolutions of two rectangular elastic solids under antiplane strain vibration, one with a boundary crack and the other with an oblique internal crack, are calculated numerically.
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