Free vibration of sandwich beams using the dynamic stiffness method

The free vibration analysis of three-layered symmetric sandwich beams is carried out using the dynamic stiffness method. First the governing partial differential equations of motion in free natural vibration are derived using Hamilton's principle. The formulation leads to two partial differential equations that are coupled both in axial and bending deformations. For harmonic oscillation, the two equations are combined into one ordinary differential equation, which applies to both axial and bending displacements. A closed form analytical solution is then sought in its most general form. By applying the boundary conditions the dynamic stiffness matrix is developed. The Wittrick–Williams algorithm is used as a solution technique to compute the natural frequencies and mode shapes of an example sandwich beam. The discussion of results is followed by some concluding remarks.