The following nonlinear beam equation is considered: \[ u_{tt}+\Delta^2 u+m^2 u+f(u)=0, \] where \(m \neq 0,\, u=u(x,t),\, x \in \mathbb R^n\) and \[ uf(u)-\int^u_0 f(s)ds \geq 0. \] Using a variational method, the author establishes a Moravetz type identity which presents a simple proof of the time decay estimates for a nonlinear term with repelling sign as \(t \rightarrow\infty\). As a consequence, the time-integrablility of the local energy is proved.