Parametric instability of a rotating truncated conical shell subjected to periodic axial loads

• Parametric instability of periodic axial loaded conical shells is studied.
• Current rotating conical shell model is corrected.
• Primary instability regions for various natural modes are obtained.
• Effects of various system parameters on the instability regions are examined.

Parametric instability of a rotating truncated conical shell subjected to periodic axial loads is studied in the paper. Through deriving accurate expressions of inertial force and initial hoop tension, a rotating conical shell model is presented based upon the Love's thin shell theory. Considering the periodic axial loads, equations of motion of the system with periodic stiffness coefficients are obtained utilizing the generalized differential quadrature (GDQ) method. Hill's method is introduced for parametric instability analysis. Primary instability regions for various natural modes are computed. Effects of rotational speed, constant axial load, cone angle and other geometrical parameters on the location and width of various instability regions are examined.