We prove the exponential decay in the case $n>2$ , as time goes to
infinity, of regular solutions for the nonlinear beam equation
with memory and weak damping $u_{tt}+\Delta^{2}u-$ $M(\|\nabla u\|^{2}_{L^2(\Omega_t)})\Delta u+\int_{0}^{t}g(t-s)\Delta u(s)ds+\alpha u_{t}=0\text{ in } \overset{\wedge}{Q}$ in a noncylindrical domain of $\R^{n+1}\ (n\geq 1)$ under suitable hypothesis on the scalar
functions $M$ and $g$ , and where $\alpha$ is a positive constant.
We establish existence and uniqueness of regular solutions for any
$n\geq 1$ .