Free Vibration Analysis of Beams Considering Different Geometric Characteristics and Boundary Conditions

Abstract

In this study, free vibration of square cross-sectioned aluminum beams is investigated analytically and numerically under four different boundary conditions: Clamped-Clamped (C-C), Clamped-Free (C-F), Clamped-Simply Supported (C-SS) and Simply Supported-Simply Supported (SS-SS). Analytical solution is carried out using Euler-Bernoulli beam theory and Newton Raphson Method. First, the equations of motion are provided. Then, solutions including the effects of the geometric characteristics, and boundary conditions are obtained and discussed for the natural frequencies of the first three modes. To confirm the reliability of the vibration analysis carried out in the present paper as well, all the analytical results are checked with the corresponding numerical results obtained from the finite-element-method (FEM) based software called ANSYS. Numerical and analytical results are found to be good agreement.