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 Ri tz procedure to arrive at the governing eigenvalue equation. A set of orthogonally generated two-dimensional polynomials associated with a b asic function, which accounts for the boundary expressions and constra ints. is introduced to approximate the in-plane and transverse displac ement amplitude functions. The complete procedure has been automated t o compute the vibration frequencies and mode shapes for exemplary prob lems. In the numerical experiments, the convergence of eigenvalues is confirmed by increasing the degrees of polynomials employed in the adm issible shape functions. To enhance the existing literature, a set of first known frequency parameters is presented. The paper highlights th e important effects of angle of twist on the vibration frequencies and mode shapes of conical shells. The fundamental physical frequency ome ga decreases monotonically for a longer conical shell. The result show s that an increase in the angle of twist does not ensure higher torsio nal stiffness for a conical shell, which is in contradiction with prev ious observation for a pretwisted beam or plate. The symmetry of modes is absent when the angle of twist is non-zero.