一种新型变截面杆的纵振动

Longitudinal Vibration of a New Type of Variable Cross-section Rod

用一种新的试探函数方法,研究了变截面杆的纵振动问题.首先用试探函数方法,研究一般变截面杆的纵振动控制方程,得到了一种新型变截面杆,并给出了此杆控制方程的贝塞尔函数形式的精确解析解.其次,求出了两端自由边界条件下的频率方程,计算出了无量纲固有频率,并绘制位移振幅变化曲线,分析了节点位置、放大系数和形状因数等性能参量.结果表明,新型变截面杆有较大的形状因数,放大系数也有一定的提高.结果对一种新型变截面杆的设计具有一定的理论参考价值.

In this thesis, the problem on longitudinal vibration of variable cross-section rod is studied by using a new kind of trial function method. First, the longitudinal vibration of variable cross-section rod’s general governing equa-tion is studied by using trial function method, and a new type of variable cross-section rod is obtained, and then exact analytical solution in Bessel function form to governing equation is given. Second, according to the both ends free boundary conditions, the frequency equation is established, and the dimensionless natural frequencies are calculated, and then the graphs of displacement amplitudes are plotted, the performance factors such as, displacement node, am-plitude amplification factor and form factor are analyzed. Results indicate that new type of variable cross-section rod’ s form factor is larger and it is better in amplitude amplification factor. The results will provide a valuable theoretical reference for the design of new type of variable cross-section rod.