Vibration of pretwisted cantilever shallow conical shells

This paper presents a mathematical model to investigate the effects of initial twist on the vibratory characteristics of cantilever shallow conical shells. The energy functional is minimized according to the Ritz procedure to arrive at the governing eigenvalue equation. A set of orthogonally generated two-dimensional polynomials associated with a basic function, which accounts for the boundary expressions and constraints, is introduced to approximate the in-plane and transverse displacement amplitude functions. The complete procedure has been automated to compute the vibration frequencies and mode shapes for exemplary problems. In the numerical experiments, the convergence of eigenvalues is confirmed by increasing the degrees of polynomials employed in the admissible shape functions. To enhance the existing literature, a set of first known frequency parameters is presented. The paper highlights the important effects of angle of twist on the vibration frequencies and mode shapes of conical shells. The fundamental physical frequency ω decreases monotonically for a longer conical shell. The result shows that an increase in the angle of twist does not ensure higher torsional stiffness for a conical shell, which is in contradiction with previous observation for a pretwisted beam or plate. The symmetry of modes is absent when the angle of twist is non-zero. © 1994.