  This paper generalizes the earlier work on the energy-based discontinuous
Galerkin method for second-order wave equations to fourth-order semilinear wave
equations. We first rewrite the problem into a system with a second-order
spatial derivative, then apply the energy-based discontinuous Galerkin method
to the system. The proposed scheme, on the one hand, is more computationally
efficient compared with the local discontinuous Galerkin method because of
fewer auxiliary variables. On the other hand, it is unconditionally stable
without adding any penalty terms, and admits optimal convergence in the $L^2$
norm for both solution and auxiliary variables. In addition, the
energy-dissipating or energy-conserving property of the scheme follows from
simple, mesh-independent choices of the interelement fluxes. We also present a
stability and convergence analysis along with numerical experiments to
demonstrate optimal convergence for certain choices of the interelement fluxes.
