Free vibration of initially stressed composite laminates

Abstract

The characteristics of fundamental modes of vibration of initially stressed composite laminated plates are presented in this paper. The semiloof finite element is used in this formulation. Angle-ply and cross-ply rectangular laminates with simply supported and clamped edge conditions have been analyzed for which results have not been reported in the literature earlier. The effect of using “the same” and “different” boundary conditions for the calculation of initial stress and for the subsequent vibration analysis is studied. The number of layers in the laminate has been taken as a parameter for the study. The formulation of the geometric stiffness matrix includes moment resultants induced due to bending-stretching coupling. Its effect on the frequencies is also studied. Considerable differences are found in the frequencies of vibration between the cases of “the same” and “different” boundary conditions; the differences are greater for the simply supported (S2) and clamped (C2) boundary conditions. There is no difference in the case of S4 conditions. The variation of frequencies with initial stresses, whether fully linear or piecewise linear, depends not only on the aspect ratio of the plate but also on the orthotropy ratio and on the angle of fibre orientation. In the present paper, results for simple uniaxial loading alone are presented. However, the program developed has the capability to handle other complicated loading cases also.