中文摘要：

论文引入一种新的、简单易行的近似方法,求解轴向非均匀变截面梁的自由振动固有频率.将位移展开成切比雪夫多项式,从而变系数控制微分方程转化为含未知系数的齐次线性方程组.利用非零解的存在条件,进而得到含固有频率的特征方程.通过和特定梯度下已有的精确解进行比较,验证了该方法的精度和有效性,并分析了梯度参数、支承条件等对固有频率的影响.

英文摘要：

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.