Free vibration of fully functionally graded carbon nanotube reinforced graphite/epoxy laminates

This study provides the first-known vibration analysis of fully functionally graded carbon nanotube reinforced hybrid composite (FFG-CNTRHC) laminates. CNTs are non-uniformly distributed to reinforce the graphite/epoxy laminates. Some CNT distribution functions in the plane and thickness directions are proposed to more efficiently increase the stiffening effect. The rule of mixtures is modified by considering the non-homogeneous material properties of FFG-CNTRHC laminates. The formulation of the location dependent stiffness matrix and mass matrix is derived. The effects of CNT volume fraction and distribution on the natural frequencies of FFG-CNTRHC laminates are discussed. The results reveal that the FFG layout may significantly increase the natural frequencies of FFG-CNTRHC laminate.