Exact free vibration of symmetric three-layered curved sandwich beams using dynamic stiffness matrix

Abstract

In the present study, the governing differential equations of motion are developed by using the Hamilton principle for a three-layered curved sandwich beam with symmetric face layers. To develop the dynamic stiffness matrix, the face layers are considered to behave like Euler–Bernoulli beams although only shear deformation occurs in the core. In this research, for computing the natural frequencies of curved sandwich beams, the Wittrick–Williams algorithm is applied. After the procedure is validated by comparison with various published results, to indicate its range of application, natural frequencies of a complex frame are computed. Finally, a parametric study investigated the effect of thickness and curvature for various boundary conditions on the natural frequencies.

Keywords

• Free vibration
• Curved sandwich beam
• Wittrick–Williams algorithm
• Exact dynamic stiffness matrix
• Natural frequency