Vibration of Elastic Structures With Cracks

Abstract

An analytical algorithm is proposed to represent eigensolutions [λm 2 , ψm (r )]m=1 ∞ of an imperfect structure C containing cracks in terms of crack configuration σc and eigensolutions [ωn 2 , 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 λm 2 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.