Dynamic stability of graded graphene reinforced truncated conical shells under both periodic spinning speeds and axial loads considering thermal effects

Abstract

This paper is concerned with dynamic stability of graded graphene reinforced truncated conical shells under both periodic spinning speeds and axial loads considering thermal effects. The volume fraction of graphene platelets (GPLs) varies continuously along the shell’s thickness direction, which induces the position-dependent effective material properties. Based upon Love’s thin shell theory and Galerkin approach, the equations of motion of the conical shells are derived by considering thermal environment, both time-variable spinning speeds and axial loads. The method of multiple scales is adopted to obtain an analytical solution on the instability boundaries under combination parametric resonances. Then, comprehensive parametric studies are conducted focusing on the instability regions, natural frequencies and critical spinning speeds of the conical shell. The sensitivities of dynamic stabilities on the thermal expansion deformation, thermal conductivity and temperature-dependent material properties are also analyzed. Results show that the conical shell system would be always instability if parametric phase is not equal to integer multiple of π. The GPL parameters, temperature variation, spinning speeds and axial loads have a significant influence on dynamic stability of the conical shell, and thermal conductivity and thermal expansion deformation are nonnegligible in the dynamic stability analysis.