Free vibration of a three-layered sandwich beam using the dynamic stiffness method and experiment

In this paper, an accurate dynamic stiffness model for a three-layered sandwich beam of unequal thicknesses is developed and subsequently used to investigate its free vibration characteristics. Each layer of the beam is idealised by the Timoshenko beam theory and the combined system is reduced to a tenth-order system using symbolic computation. An exact dynamic stiffness matrix is then developed by relating amplitudes of harmonically varying loads to those of the responses. The resulting dynamic stiffness matrix is used with particular reference to the Wittrick–Williams algorithm to carry out the free vibration analysis of a few illustrative examples. The accuracy of the theory is confirmed both by published literature and by experiment. The paper closes with some concluding remarks