Effect of Bimodularity on Dynamic Response of Cross-ply Conical Panels

Abstract

The effect of bimodularity ratio on free vibration characteristics of cross-ply conical panels of various geometry and lamination scheme is studied. Forced vibration response is also studied for a typical case. The formulation is based on first order shear deformation theory and Bert’s constitutive model. An iterative eigenvalue approach is employed to obtain the positive and negative half cycle free vibration frequencies. Galerkin’s approach in time domain is used to obtain the frequency response. It is interesting to note that there is a significant difference between positive and negative half cycle frequencies depending on panel parameters. Also, there is a significant difference in positive and negative half cycle forced response amplitudes due to bimodularity. Bimodularity, the different behavior of material in tension and compression, affects the static and dynamic response of structures. Few studies on static analysis of bimodulus laminated cross-ply composite shells and dynamic analysis of cross-ply panels have been presented [1-4]. To the best of the authors’ knowledge, the work on the analysis of bimodular laminated cross-ply conical shell panels is not dealt in the literature. The effect of bimodularity ratio on free and forced vibration characteristics of cross-ply conical panel is important for design of such structures under dynamic loading condition. Here, the dynamic analysis of cross-ply laminated conical panels of bimodulus material is carried out using finite element method and Bert’s constitutive model. The effect of semi-cone angle, number of layers and bimodularity ratio (E 2t /E 2c ) on free vibration frequencies and frequency response is investigated. 2. FORMULATION The geometry and dimensions of a conical panel is shown in Fig. 1 with total thickness h, small end radius r 1 , large end radius r 2 , meridional length L, circumferential length b at small end, sector angle y, and semi-cone angle a. Displacements u, v, w at a point (s, q, z) are expressed as functions of middle surface displacements u 0 , v 0 , w 0 and independent rotation b s , b q of the meridional and hoop sections, respectively, as: u (s, q, z, t) = u 0 (s, q, t) + z b s (s, q, t) v (s, q, z, t) = v 0 (s, q, t) + z b q (s, q, t) (1) w (s, q, z, t) = w 0 (s, q, t)