Out-of-plane free vibration analysis of three-layer sandwich beams using dynamic stiffness matrix

Abstract

Abstract This paper has been devoted to exact calculation of the natural frequencies for out-of-plane free vibration of three-layer symmetric sandwich beams by using dynamic stiffness matrix method. Governing differential equations of motion have been derived using Euler-Bernoulli beam theory and St. Venant’s torsion theory, so that the effects of shear deformation in the face layers and rotary inertia are not taken into account and the cross-section is allowed to warp without restraint. Wittrick-Williams algorithm has been used to calculate the natural frequencies. Accuracy and ability of the dynamic stiffness matrix method have been illustrated in form of several examples. Results are verified through comparison with the natural frequencies obtained from ABAQUS software. Full independence of out-of-plane bending and torsional modes of vibration for three-layer symmetric sandwich beams has been proven.