  We consider the semi-linear beam equation on the d dimensional irrational
torus with smooth nonlinearity of order n -- 1 with n $\ge$ 3 and d $\ge$ 2. If
$\epsilon$ $\ll$ 1 is the size of the initial datum, we prove that the lifespan
T$\epsilon$ of solutions is O($\epsilon$ --A(n--2) --) where A $\not\equiv$
A(d, n) = 1 + 3 d--1 when n is even and A = 1 + 3 d--1 + max(4--d d--1 , 0)
when n is odd. For instance for d = 2 and n = 3 (quadratic nonlinearity) we
obtain T$\epsilon$ = O($\epsilon$ --6 --), much better than O($\epsilon$ --1),
the time given by the local existence theory. The irrationality of the torus
makes the set of differences between two eigenvalues of $\sqrt$ $\Delta$ 2 + 1
accumulate to zero, facilitating the exchange between the high Fourier modes
and complicating the control of the solutions over long times. Our result is
obtained by combining a Birkhoff normal form step and a modified energy step.
