  This article is to study the nonexistence of global solutions to semi-linear
structurally damped wave equation with nonlinear memory in $\R^n$ for any space
dimensions $n\ge 1$ and for the initial arbitrarily small data being subject to
the positivity assumption. We intend to apply the method of a modified test
function to establish blow-up results and to overcome some difficulties as well
caused by the well-known fractional Laplacian $(-\Delta)^{\sigma/2}$ in
structural damping terms.
