High-order free vibration analysis of sandwich beams with a flexible core using dynamic stiffness method

In this paper, high-order free vibration of three-layered symmetric sandwich beam is investigated using dynamic stiffness method. The governing partial differential equations of motion for one element are derived using Hamilton's principle. This formulation leads to seven partial differential equations which are coupled in axial and bending deformations. For the harmonic motion, these equations are divided into two ordinary differential equations by considering the symmetrical sandwich beam. Closed form analytical solutions of these equations are determined. By applying the boundary conditions, the element dynamic stiffness matrix is developed. The element dynamic stiffness matrices are assembled and the boundary conditions of the beam are applied, so that the dynamic stiffness matrix of the beam is derived. Natural frequencies and mode shapes are computed by use of numerical techniques and the known Wittrick-Williams algorithm. Finally, some numerical examples are discussed using dynamic stiffness method.