Abstract：Abstract: A new and simple approximate method is introduced to solve natural frequencies of free vibration of beams with axially inhomogeneity in this paper. The governing differential equation is transformed to a system of linear algebraic equations by changing the form of the expression of displacement with the Chebyshev polynomials expansion. Under the non-zero solution of existence conditions, the characteristic equations are numerically obtained to get the natural frequency. The effectiveness and accuracy of present method are confirmed by comparing numerical results with the exact solution of some specific gradient. Furthermore, the influences of gradient parameter and support conditions on natural frequency are studied.
2015, Vol. 36 
