Abstract: 
We consider the nonlinear wave equation
u_{tt}u_{xx}=±u^{3}
and the beam equation
u_{tt}+u_{xxxx}=±u^{3}
on an interval.
Numerical observations indicate that timeperiodic solutions
for these equations are organized into structures that resemble branches
and seem to undergo bifurcations.
Besides describing our observations,
we prove the existence of timeperiodic solutions
for various periods (a set of positive measure
in the case of the beam equation)
along the main nontrivial "branch".
