The present invention is directed to three dimensional weaves composed of wires or yarns that offer the potential for damping not achievable with solid materials, including high temperature damping. Three damping mechanisms have been identified: (1) Internal material damping, (2) Frictional energy dissipation (Coulomb damping), and (3) inertial damping (tuned mass damping). These three damping mechanisms can be optimized by modifying the wire material chemistries (metals, ceramics, polymers, etc.), wire sizes, wire shapes, wire coatings, wire bonding, and wire architecture (by removing certain wires). These have the effect of modifying the lattice and wire stiffnesses, masses, coefficients of friction, and internal material damping. Different materials can be used at different locations in the woven lattice. These design variables can also be modified to tailor mechanical stiffness and strength of the lattice, in addition to damping.