FINITE VOLUME METHOD FOR DETERMINING THE NATURAL CHARACTERISTICS OF STRUCTURES

Abstract

In this paper a finite volume based formulation is developed to calculate the structural natural characteristics including the natural frequencies and the critical buckling loads of slender beam/beam-columns in which the shear effects are taken into account. For natural frequency calculations, both shear effects and rotational inertia effects are considered. In this finite volume based approach, the equilibrium equations of control volumes are expressed and used with the boundary conditions to obtain the eigenvalue equation in the standard format. Then, the natural characteristics of beam/beam-columns are obtained by solving the eigenvalue equations. The formulation is tested on a number of benchmark problems. Accordingly, the proposed formulation has been found to accurately predict the natural frequencies and the critical buckling loads of the test problems. Also, the formulation is tested for the very thin and thick beams. It is found that the formulation is also able to analyze the thin beams in which no shear locks is observed.

Keywords

• Finite volume
• Natural frequency
• Buckling load
• Beam-column
• Shear effect