中文摘要：

研究有限长周期参数梁的动力学特性。建立周期参数梁的运动微分方程，得到梁高度周期性的参变方程，运用伽辽金法转化为多自由度状态方程，然后得到周期参数梁的固有频率方程。最后通过数值结果说明梁位移展开项数对于固有频率与动力学特性的影响，特别是周期参数为低周期或高频率情况时，固有频率随周期参数频率与幅度的变化及频带间隙（固有频率随周期参数频率变化的空隙）的退化与梁弯曲波的弥散等。

英文摘要：

The dynamic characteristics of finite-length periodic parameter beams are studied. The differential equation of motion of the periodic parameter beams is presented, and the partial differential equation with spatial varying parameters for the periodic- height beam is obtained. Then, the equation is converted into a multi-DOF state equation using Galerkin method, and a set of algebraic equations for natural frequencies of the periodic beam is obtained. Numerical results are given. The influence of the number of series expansion terms of the displacement on the natural frequencies and dynamic characteristics of the beam is analyzed. Variation of the natural frequencies with the change of the frequency and amplitude of the periodic parameter, degeneration of the band gaps among the natural frequencies, and the bending waves scattering are analyzed in the case of large periodic parameter frequencies.