A NEW ANALYTICAL METHOD FOR FREE VIBRATION ANALYSIS OF SANDWICH BEAMS

摘要

This work provides a bending free vibration analysis of sandwich beams with three layered, using a proposed new analytical method based on energy approach and spectral analysis. Zig-zag displacement model is used to define the face and core layers displacements. The upper and lower layers are assumed to be Euler-Bernoulli beams, while the central layer is considered to be a Timoshenko beam. Two boundary conditions (Simply supported and clamped ends) are assumed. Assuming a harmonic motion, the governing equations of the sandwich beam are derived by applying Hamilton's principle. Two differential equations coupled in axial and transverse deformations are obtained. The present model is validated by comparing the obtained results with those available in the literature. A parametric study is done to show the effects of some parameters such as face/core thickness ratio and face/core density ratio on the natural frequencies of sandwich beams.