Viscoelastic material damping characteristics of carbon nanotubes based functionally graded composite shell structures

This work deals with the study of viscoelastic modeling and vibration analysis of functionally graded nanocomposite shell panels where carbon nanotubes are reinforced in the polymer matrix based on the functionally graded distributions of carbon nanotubes. Five types of grading of carbon nanotubes (such as UD, FGX, FGV, FGO, and FGΛ) in the thickness directions have been considered in order to investigate the vibration damping performance of such composite shell panels. A detailed mathematical formulation for the determination viscoelastic properties is presented. The Mori–Tanaka micromechanics in conjunction with weak interface theory has been developed for the mathematical formulations of the viscoelastic modeling of carbon nanotubes based polymer matrix phase. An eight-noded shell element with five degrees-of-freedom per node has been formulated to study the vibration damping characteristics of various panels made by such functionally graded nanocomposite materials. The shell finite element formulation is based on the transverse shear effects as per the Mindlin’s hypothesis, and stress resultant-type Koiter’s shell theory. Impulse and frequency responses of such structures have been performed to study the effects of various important parameters (such as volume fraction of carbon nanotubes, interfacial condition, agglomeration, temperature, geometries of shell panel) on the dynamic responses. Obtained results demonstrate that quick vibration mitigation may be possible using such carbon nanotubes based proposed composite materials.