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A system for damping vibrations in a turbine includes a first rotating blade having a first ceramic airfoil, a first ceramic platform connected to the first ceramic airfoil, and a first root connected to the first ceramic platform. A second rotating blade adjacent to the first rotating blade include

A system for damping vibrations in a turbine includes a first rotating blade having a first ceramic airfoil, a first ceramic platform connected to the first ceramic airfoil, and a first root connected to the first ceramic platform. A second rotating blade adjacent to the first rotating blade includes a second ceramic airfoil, a second ceramic platform connected to the second ceramic airfoil, and a second root connected to the second ceramic platform. A non-metallic platform damper has a first position in simultaneous contact with the first and second ceramic platforms.

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1. A system for damping vibrations in a turbine, comprising a. a first rotating blade having a first ceramic airfoil, a first ceramic platform connected to the first ceramic airfoil, and a first root connected to the first ceramic platform;b. a second rotating blade adjacent to the first rotating bl

1. A system for damping vibrations in a turbine, comprising a. a first rotating blade having a first ceramic airfoil, a first ceramic platform connected to the first ceramic airfoil, and a first root connected to the first ceramic platform;b. a second rotating blade adjacent to the first rotating blade, wherein the second rotating blade includes a second ceramic airfoil, a second ceramic platform connected to the second ceramic airfoil, and a second root connected to the second ceramic platform; andc. a non-metallic platform damper having a first position in simultaneous contact with the first and second ceramic platforms, the non-metallic platform damper comprising a plurality of spheres connected to one another. 2. The system as in claim 1, wherein the first and second roots are ceramic. 3. The system as in claim 2, further comprising a non-metallic root damper having a first position in simultaneous contact with the first and second roots. 4. The system as in claim 2, further comprising a non-metallic root damper having a first position in simultaneous contact with the first root and a rotor wheel. 5. The system as in claim 1, wherein the non-metallic platform damper comprises at least one of zirconia, polycrystalline alumina, sapphire, silicon carbide, or silicon nitride. 6. The system as in claim 1 wherein the non-metallic platform damper has at least one of a triangular or hexagonal cross-section. 7. The system as in claim 1, wherein the non-metallic platform damper comprises a plurality of segments. 8. The system as in claim 1, wherein the non-metallic platform damper is hollow. 9. A system for damping vibrations in a turbine, comprising: a. a first rotating blade having a first ceramic airfoil and a first ceramic root connected to the first ceramic airfoil;b. a first adaptor configured to connect the first rotating blade to a rotor wheel, the first adaptor having a slot for receipt of the first ceramic root, the slot and the first ceramic root having complementary shapes;c. a second rotating blade adjacent to the first rotating blade, wherein the second rotating blade includes a second ceramic airfoil and a second ceramic root connected to the second ceramic airfoil;d. a first non-metallic root damper extending axially within the slot in simultaneous contact with the first ceramic root and the first adaptor; ande. a second non-metallic root damper extending radially in simultaneous contact with the first ceramic root and the second ceramic root. 10. The system as in claim 9, wherein the first non-metallic root damper comprises at least one of zirconia, polycrystalline alumina, sapphire, silicon carbide, or silicon nitride. 11. The system as in claim 9, wherein the first non-metallic root damper has at least one of a triangular or hexagonal cross-section. 12. The system as in claim 9, wherein the first non-metallic, root damper comprises a plurality of spheres connected to one another. 13. The system as in claim 9, wherein the first non-metallic root damper comprises a plurality of segments. 14. The system as in claim 9, wherein the first non-metallic, root damper is hollow. 15. The system as in claim 9, further comprising a second adaptor configured to connect the second rotating blade to the rotor wheel, wherein the second non-metallic root damper extends radially in simultaneous contact with the first adaptor and the second adaptor. 16. A system for damping vibrations in a turbine, comprising: a. a first rotating blade having a first ceramic airfoil and a first ceramic root connected to the first ceramic airfoil, the first ceramic root received within a first slot of a rotor wheel, the first slot and the first ceramic root having complementary shapes;b. a second rotating blade adjacent to the first rotating blade, wherein the second rotating blade includes a second ceramic airfoil and a second ceramic root connected to the second ceramic airfoil; andc. a non-metallic root damper extending axially in the first slot in simultaneous contact with the first ceramic root and the rotor wheel such that a gap is formed between the first ceramic root and the rotor wheel. 17. The system as in claim 16, wherein the non-metallic root damper comprises at least one of zirconia, polycrystalline alumina, sapphire, silicon carbide, or silicon nitride. 18. The system as in claim 16, wherein the non-metallic root damper has at least one of a triangular or hexagonal cross-section. 19. The system as in claim 16, wherein the non-metallic root damper comprises a plurality of spheres connected to one another. 20. The system as in claim 16, wherein the non-metallic root damper comprises a plurality of segments.