Dynamic Analysis of Laminated Composite Rhombic Elliptic Paraboloid due to Mass Variation

Abstract

The present paper is the first study of free vibration analysis of laminated composite rhombic (skew) elliptic paraboloids with mass variation via multiple cutouts and concentrated mass. To solve the vibration problem of a laminated composite skew elliptic paraboloid with multiple cutouts and concentrated mass, cubic variation in the displacement field and cross-curvature effects of the shell are considered. The parabolic variation of transverse shear strain is considered; hence, no shear correction factor is required. The zero transverse shear stress conditions at the top and bottom of the shell are imposed in the mathematical model. The finite-element implementation of the present realistic mathematical model is done using a nine-noded curved isoparametric element with seven unknowns at each node. The C finite-element (FE) implementation of the present mathematical model has been done and coded in FORTRAN. The present model results are compared and found in good agreement with experimental, analytical, and other solutions published in the literature. A free vibration study has been done for skew elliptic paraboloids with multiple cutouts and concentrated mass having different curvatures, ply orientations, and thickness ratios.