Free vibration and buckling behavior of sandwich tapered columns with square cross-section

This paper aims to study the free vibration and buckling behavior of a sandwich tapered column. The sandwich members are laterally-symmetrically laminated against the mid-depth of a square cross-section with the side length varying according to a parabolic function along the column axis. The closed-form stiffness of sandwich members is provided as a function of axial rigidity, flexural rigidity, mass per unit length, and mass moment of inertia. This formulated stiffness is implemented to the free vibration problem of the column under axial load. The differential equations governing vibrational and buckled mode shapes are derived. Numerical methods are presented to calculate natural frequencies and buckling loads of the column. The numerical results of this study are tabulated and illustrated in figures, accompanied by an extensive discussion of parametric study regarding natural frequencies and buckling loads. Natural frequencies and buckling loads increase with increasing the material property ratio and taper ratio, while decrease with increasing slenderness ratio and load parameter.