Parametric stability of symmetrically laminated composite super-elliptical plates

Abstract

Static and parametric stability of thin symmetrically laminated composite super-elliptical plates resting on Winkler-type foundation and subjected to uniform in-plane harmonic loads, under clamped, simply supported and free boundary conditions, are investigated based on the classical laminated plate theory. The governing equations are obtained from a variational approach and then the classical Ritz method is used to reduce the problem into a set of coupled Mathieu–Hill equations. Hsu’s technique is utilized to determine the dynamic instability regions of principal and combination resonance frequencies. Extensive numerical data are provided to examine the effects of plate aspect ratio, super-ellipticity power, foundation stiffness parameter, stacking sequence, and fiber orientation on the vibrational, static, and parametric stability characteristics of symmetrically laminated super-elliptical composite plates. Furthermore, three-dimensional buckling mode shapes are illustrated. The accuracy of formulation is checked by performing convergence studies and the validity of results is established by comparison with the existing results in the literature, exact results obtained from the analytical approach, and as well as from FEM results.