Fuzzy response to SH guided-wave scattering by semicircular depressions on the boundary of a ribbon-shaped elastic plate

Abstract

In this paper, the fuzzy scattering problem with semicircular depressions on the boundary of a band-shaped elastic plate with steady SH guided wave incident is studied and an analytical solution is given. First, the SH guided wave is constructed by the guided wave expansion method, and then the scattered wave satisfying the free condition of the boundary stress of the strip domain is constructed by the cumulative mirror method. Finally, a definite solution equation is obtained based on the fact that the shear stress at the edge of the semi-circular recessed hole is zero. In this paper, the ambiguity of the number of waves and the width of the bands is taken into account. In order to avoid the irreversibility of interval algorithm and the difficulty of solving non-linear equations, the membership function of fuzzy quantity is segmented to make the membership degree and fuzzy quantity correspond respectively. A deterministic problem that translates into piecewise processing. Two numerical examples are given to examine the changes in fuzzy response of different numbers of fuzzy waves and fuzzy thicknesses to the dynamic stress concentration factor of the hoop at the collapse limit.