m javid - Instructor, Department of Mechanical Engineering, Germi Branch, Islamic Azad University, Germi, Iran
h biglari - Assistant Professor, Department of Mechanical Engineering, University of Tabriz, Tabriz, Iran

In this paper, a comprehensive and integrated approach to free vibration analysis of composite beam with general boundary conditions, according to the Euler-Bernoulli and deriving the natural frequencies is expressed. The boundary conditions at the end of the beam are modeled by linear and torsional springs, and these boundary conditionswill appear directly in the solution of lateral vibration equation of the beam. Initially, separate equations of motion for beam are obtained using Hamilton s principle. For solving, lateral deflection of the beam is considered as a linear superposition of Fourier cosine and Auxiliary polynomial. This auxiliary function compensates lack of convergence in boundary condition in the previous methods. By this method, natural frequencies and mode shapes are obtained for various modes of vibration. Comparing numerical results obtained by this method with the results of the previous classical methods shows that the pace of Fourier series and results accuracy has increased significantly.

Euler-Bernoulli theory, free vibration, general boundary conditions, mode shape, Fourier series