Present of Analytical Solution for Free Vibration of the Curved Thick Sandwich Beam with Flexible Core Using Higher Order Theory and the Dynamic Stiffness Method

Document Type : Research Paper

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Abstract

In this paper, free vibration of the thick sandwich beams with flexible cores is investigated using the dynamic stiffness method and a new higher order theory. First the governing partial differential equations of motion for one element are derived using Hamilton’s principle. Closed form analytical solution of these equations is determined. After applying the effect of boundary condition of the element on the obtained equations, the element dynamic stiffness matrix is developed. These 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 the use of numerical techniques and the well-known Wittrick–Williams algorithm. Finally, some numerical examples are discussed using the dynamic stiffness method and the analytical formulation. For verification of the present model, the obtained results are compared with the latest exact analytical and approximate finite element results.

References

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