This　study　proposes　a　new　trans-scale　dynamic　shear-lag　model　that　integrates　the　strain　gradient　linear　viscoelasticity　theory　to　investigate　the　effects　of　size　and　viscous　softening　on　the　dynamic　mechanical　properties　and　energy　absorption　characteristics　of　fiber-reinforced　composites　with　micro-　and　nano-structures.　The　proposed　model　clarifies　how　the　strain　gradient　effect　can　decrease　energy　dissipation　in　the　matrix.　Our　investigation　suggests　that　both　classical　and　higher-order　viscosities　of　the　submicron-scale　matrix　can　synergistically　optimize　energy　dissipation.　Furthermore,　parametric　studies　demonstrate　that　the　attenuation　efficiency　of　absorbed　energy　changes　non-monotonically　with　microstructure　and　constituent　properties,　such　as　matrix　thickness,　strain　gradient　elasticity　parameter,　classical　viscosity,　and　high-order　viscosity.　The　trans-scale　dynamic　shearlag　model　advances　our　understanding　of　the　energy　dissipation　in　the　submicron-scale　viscoelastic　matrix　of　fiber-reinforced　composites　and　provides　valuable　guidance　for　developing　composites　with　micro-　and　nanostructures　that　display　exceptional　dynamic　properties.