Rock　masses　consist　of　nesting　rock　blocks　with　various　scales　separated　by　weak　structural　layers,　and　their　complex　hierarchical　structures　play　a　significant　role　in　dynamic　deformation　and　stress　wave　propagation.　In　this　paper,　based　on　the　Cosserat　theory,　a　dynamic　model　of　pendulum-type　and　rotational　waves　in　blocky　rock　mass　with　complex　hierarchical　structures　is　established　to　determine　the　influence　of　hierarchical　structures　on　dynamic　deformation.　Then,　aiming　at　low-frequency　and　low-velocity　characteristics　of　pendulum-type　waves,　dispersion　equations　of　waves　are　determined　and　solved　in　different　hierarchical　structures　based　on　the　Bloch　theorem,　and　furthermore,　the　dispersion　relation　and　velocity　characteristics　of　waves　are　investigated.　Finally,　mechanism　of　low-frequency　characteristics　of　pendulum-type　waves　is　revealed　on　the　basis　of　solid　energy　band　theory,　and　the　possibility　of　pendulum-type　and　rotational　waves　inducing　rock　bursts　is　discussed　based　on　the　research　results.　It　is　indicated　that　ignoring　higher-order　hierarchical　structures　of　rock　masses　may　underestimate　displacement　and　overall　deformation　of　rock　masses,　resulting　in　unsafe　numerical　results.　Under　the　action　of　long　wave　disturbance,　for　the　first　mode　pendulum-type　waves(the　acoustic　branches),　the　dispersion　is　not　significant　and　propagation　velocity　decreases,　and　higher-order　hierarchical　structures　inside　rock　masses　hinder　the　wave　propagation.　However,　the　dispersion　of　other　waves(the　optical　branches)　is　significant　so　that　they　hardly　exist　and　propagate　independently.　The　low-frequency　pendulum-type　waves　are　dominant,　which　have　slower　attenuation　and　longer　propagation　distance　than　the　high-order　mode　waves　and　traditional　P　and　S-waves.　©　2024　Academia　Sinica.　All　rights　reserved.