Free Vibration Analysis of Curved Sandwich Beams

Abstract

A study of free vibrations of singly curved sandwich beams is presented. The model takes into consideration both radial and circumferential displacements of the beam core with the assumption of linear distribution across the thickness. The faces of the sandwich are treated as thin beams. Linear equations of motion as well as the boundary conditions are derived with the help of calculus of variations. Verification of the model is performed via a number of asymptotic cases. It is shown that there exist four types of eigen modes. Numerical analyses of free vibrations of the simply supported and clamped beams are carried out. Effect of the curvature on the eigen modes and their frequencies is investigated. A coupling coefficient is introduced to study the dynamic coupling of different types of motions in an eigen mode.