This　paper　presents　the　study　on　the　chaotic　wave　and　chaotic　dynamics　of　the　nonlinear　wave　equations　for　a　simply　supported　truss　core　sandwich　plate　combined　with　the　transverse　and　in-plane　excitations.　Based　on　the　governing　equation　of　motion　for　the　simply　supported　sandwich　plate　with　truss　core,　the　reductive　perturbation　method　is　used　to　simplify　the　partial　differential　equation.　According　to　the　exact　solution　of　the　unperturbed　equation,　two　different　kinds　of　the　topological　structures　are　derived,　which　one　structure　is　the　resonant　torus　and　another　structure　is　the　heteroclinic　orbit.　The　characteristic　of　the　singular　points　in　the　neighborhood　of　the　resonant　torus　for　the　nonlinear　wave　equation　is　investigated.　It　is　found　that　there　exists　the　homoclinic　orbit　on　the　unperturbed　slow　manifold.　The　saddle-focus　type　of　the　singular　point　appears　when　the　homoclinic　orbit　is　broken　under　the　perturbation.　Additionally,　the　saddle-focus　type　of　the　singular　point　occurs　when　the　resonant　torus　on　the　fast　manifold　is　broken　under　the　perturbation.　It　is　known　that　the　dynamic　characteristics　are　well　consistent　on　the　fast　and　slow　manifolds　under　the　condition　of　the　perturbation.　The　Melnikov　method,　which　is　called　the　first　measure,　is　applied　to　study　the　persistence　of　the　heteroclinic　orbit　in　the　perturbed　equation.　The　geometric　analysis,　which　is　named　the　second　measure,　is　used　to　guarantee　that　the　heteroclinic　orbit　on　the　fast　manifold　comes　back　to　the　stable　manifold　of　the　saddle　on　the　slow　manifold　under　the　perturbation.　The　theoretical　analysis　suggests　that　there　is　the　chaos　for　the　Smale　horseshoe　sense　in　the　truss　core　sandwich　plate.　Numerical　simulations　are　performed　to　further　verify　the　existence　of　the　chaotic　wave　and　chaotic　motions　in　the　nonlinear　wave　equation.　The　damping　coefficient　is　considered　as　the　controlling　parameter　to　study　the　effect　on　the　propagation　property　of　the　nonlinear　wave　in　the　sandwich　plate　with　truss　core.　The　numerical　results　confirm　the　validity　of　the　theoretical　study.