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The truncated conical shell segments made from multi-scale epoxy/carbon nanotube/fiberglass material are studied in this research in the view of evaluating nonlinear free vibration behavior. Incorporating random dispersion of carbon nanotubes (CNTs) and parallel alignment of glass fibers, a three-dimensional (3D) Mori–Tanaka micro-mechanic method has been utilized for defining the hybrid material properties. For defining the configuration of truncated conical shell segments, a semi-vertex angle and also an open angle are used in the thin shell formulation. With the usage of Jacobi elliptic functions, exact values of nonlinear vibration frequencies have been derived which are more accurate compared to familiar approximate solutions. A specific attention is drawn to the impacts of fiber volume, fiber directions, semi-vertex angle, CNT weight fraction, and CNT aspect ratio on nonlinear free vibrations of multi-scale truncated conical shell segments. Communicated by Jie Yang

Analysis of nonlinear vibrations of CNT- /fiberglass-reinforced multi-scale truncated conical shell segments