Vibration of Axially Loaded and Partially Interacting Composite Beams

The vibrations of axially loaded composite beams with partial interaction are considered. The equations of motion and the pertaining boundary conditions are derived from Hamilton's principle. Mainly free — but also forced — vibrations are considered. The natural frequencies are calculated as a function of the axial force and the stiffness of the interaction between the layers. The analytical result obtained for the eigenfrequencies of the simply supported beam is taken as a starting point for an approximation of the eigenfrequencies of beams subject to other boundary conditions. The proposed approximation — which has no numerical fitting parameters — is shown to be in good agreement with the exact solutions, especially for the case of a beam clamped at both ends.