非均匀杆纵向自由振动的高频渐近性质

The High Frequency Asymptotic Characteristics of Axial Free Vibrations of Non-uniform Bars

本文将非均匀杆纵向自由振动的特征值微分方程化为积分方程。通过对积分项的估计,分析了一般边界条件下非均匀杆纵向自由振动的高频渐近性质,给出了高阶时特征值问题的渐近解。

In this paper, the differential equation of the eigenvalue problem derived from axial free vibrations of non-uniform bars is converted into an integral equation. By estimating the integral term, the high frequency asymptotic characteristics of free vibrations of non-uniform bars are explored under the general boundary conditions, and an asymptotic solution to the eigenvalue problem is derived for high frequencies.