Applications of FEM on Free and Forced Vibration of Laminated Shells

Performance Evaluation of Free Vibration of Laminated Composite Stiffened Hyperbolic Paraboloid Shell Panel with Cutout

“…Free vibration of corner point supported, simply supported and clamped spherical shells of (0/90) 4 lamination with cutouts is also considered. The fundamental frequencies of spherical shell with cutout obtained by the present method agree well with those reported by Chakravorty et al [22] as evident from Table 2, establishing the correctness of the cutout formulation in doubly curved shells. Thus it is evident that the finite element model proposed here can successfully analyze vibration problems of stiffened composite hyperbolic paraboloid shell panels with cutout which is reflected by close agreement of present results with benchmark ones.…”

“…The effects of these parametric variations on the fundamental frequencies and mode shapes are considered in details to conclude a set of inferences of practical engineering significance. depth of x and y stiffeners respectively {d e } element displacement e sx , e sy eccentricities of x and y -stiffeners with respect to shell mid-surface respectively E 11 , E 22 elastic moduli G 12 , G 13 , G 23 shear moduli of a lamina with respect to 1, 2 and 3 axes of fibre h shell thickness M x , M y moment resultants M xy torsion resultant np number of plies in a laminate N 1 -N 8 shape functions N x , N y inplane force resultants N xy inplane shear resultant Q x , Q y transverse shear resultant R xx , R yy , R xy radii of curvature and cross curvature of shell respectively u, v, w translational degrees of freedom x, y, z local co-ordinate axes X, Y, Z global co-ordinate axes z k distance of bottom of the kth ply from mid-surface of a laminate , rotational degrees of freedom  x ,  y inplane strain component  xy , xz ,  yz shearing strain components It is noted from the literature review that free vibration study of laminated composite hyperbolic paraboloid shell panels with cutout is not reported by any researcher so far although the importance of this shell form is mentioned. Thus the present study intends to study the free vibration behaviour of stiffened hyperbolic paraboloid shell panels with cutout by varying the size and position of the cutouts.…”

Behaviour and Optimization Aids of Composite Stiffened Hypar Shell Roofs with Cutout under Free Vibration

“…Thus, it is found that results of free vibration characteristics of isotropic as well as composite stiffened composite shell panels with cutout are scanty in the existing body of literature. Only Chakravorty et al [8] deals with some results of free vibration of hypar shell with concentric cutout, but to the best of author knowledge information regarding the free vibration behaviour of composite stiffened hypar shell with cutout is missing in the literature. In the present paper the free vibration of stiffened hypar shell with cutouts ( Figure 1) is studied considering different boundary conditions.…”

“…Later Sivakumar et al [4], Rossi [5], Huang and Sakiyama [6], and Hota and Padhi [7] studied free vibration of plate with various cutout geometries. Chakravorty et al [8] reported some results in order to study the effect of concentric cutout on natural frequency of different shell options. In 1999, Sivasubramonian et al [9] studied the free vibration characteristics of longitudinally stiffened square panels with symmetrical square cutouts by using the finite element method.…”

Static and Dynamic Characteristics of Composite Conoidal Shell Roofs

“…The authors used finite element method and reported deflections and stress resultants of the conoidal shells. Chakravorty et al [8] studied fundamental frequencies of composite conoidal shells with cut-outs. They also reported forced vibration responses of laminated conoidal shells with point supported boundaries.…”