Forced Oscillations of a Piecewise‐Homogeneous Plane with an Interphase Inclusion Partially Detached from the Matrix

ABSTRACT

This paper discusses the plane stress state of a piecewise homogeneous elastic plane consisting of two dissimilar half‐planes containing an interphase absolutely rigid thin inclusion, one of the long sides of which has detached from the matrix, creating a crack. It is assumed that a piecewise homogeneous plane is deformed under the influence of a periodically changing concentrated load applied to the inclusion at some known point and a static normal concentrated load applied to the inclusion at its midpoint. On the basis of discontinuous solutions of the equations of motion of the plane theory of elasticity for a composite plane with defects, a governing system of singular integral equations of the problem is derived, the solution of which, in the case where the characteristic quadratic equation has two different roots, is constructed by the method of mechanical quadratures. A numerical analysis was conducted. Patterns of change in the moduli of contact stress amplitudes, the absolute value of intensity factors, crack opening, and inclusion rotation angle were identified depending on the frequency of forced vibrations.