  This paper is concerned with the study of the nonlinear viscoelastic
evolution equation with strong damping and source terms, described by \[u_{tt}
- \Delta_{\mathbb{B}}u + \int_{0}^{t}g(t-\tau)\Delta_{\mathbb{B}}u(\tau)d\tau +
f(x)u_{t}|u_{t}|^{m-2} = h(x)|u|^{p-2}u , \hspace{1 cm} x\in int\mathbb{B}, t >
0,\] where $\mathbb{B}$ is a stretched manifold. First, we prove the solutions
of problem {1.1} in cone Sobolev space
$\mathcal{H}^{1,\frac{n}{2}}_{2,0}(\mathbb{B}),$ admit a blow up in finite time
for $p > m$ and positive initial energy. Then, we construct a lower bound for
obtained blow up time under appropriate assumptions on data.
