Km. Liew et al., VIBRATION OF PRETWISTED CANTILEVER SHALLOW CONICAL SHELLS, International journal of solids and structures, 31(18), 1994, pp. 2463-2476
Citations number
14
Categorie Soggetti
Construcion & Building Technology","Engineering, Civil
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.