Force Vibration Analysis of Thick Beams on Two Parameter Elastic Foundation by Finite Element Method

Abstract

In the present work, the free vibration analysis of rectangular cross-section uniform beams on two-parameter elastic foundation, considering shear deformation and rotatory inertia is made by the finite element method. In this analysis, two different thick beam elements are used. The first 4 degrees of freedom thick beam element has two nodes with two degrees of freedom at each node such as transverse displacements and cross-section rotations. In the second beam element, the nodal variables are the transverse displacement, the cross-section rotation and shear deformation. The elastic foundation is idealized as a constant two-parameter model characterized by two moduli, i.e., the Winkler foundation modulus k and the shear foundation modulus kG. In the case kG = 0, this model reduces to the Winkler model, i.e., the elastic foundation is idealized as a constant one-parameter model. Axial displacement of the beam is also considered. Three kinds of end conditions, i.e., simply-supported, clamped-clamped and clamped-free ends are considered in this study. The effects of axial force, foundation stiffness parameters and partial elastic foundation on the natural frequencies of the beam are examined. In this analysis, the vibration calculation results are presented in the tables and their importance in design are discussed. The numerical results obtained from this analysis are compared with the exact or available solutions, wherever possible. Numerical results and comparisons show the effectiveness of the proposed method.