固定边界条件下微曲液压管道的受迫振动

Forced Resonance of a Slightly-Curved Hydraulic Pipe Fixed at Two Ends

现实中理想的笔直管道是不可能存在的,由制造缺陷或者使役过程中的蠕变引起的初始位形会对液压管道系统的动力学特性产生较大影响。本文首次研究了两端固定约束下液压管道初始形状的影响,利用广义Hamilton原理建立系统动力学模型,并且基于该模型研究了管道势能随初始形状的变化。结果表明,初始形状使得系统势能曲线变得非对称,但系统依然是单稳态的,这与屈曲管道的性质不同。初始形状同样对系统的固有频率有较大影响,它硬化了一阶频率刚度。当初始形状高度超过一个临界值时,初始形状高度对该刚度不再产生影响。与此相反,二阶固有频率在初始形状高度较小时不受其影响,但是当初始形状高度超过临界值时,二阶频率开始增加。此外,由于初始形状的存在,系统动力学方程中产生了平方非线性,它使得系统响应远比理想笔直管道复杂。尽管通过调整初始形状高度以及液压流速建立了2∶1内共振条件,系统并未出现2∶1内共振典型的双跳跃现象,这与超临界输流管道特性有很大不同。研究表明液压管道建模过程中必须考虑管道的初始形状,并且对其动力学特性需要进行进一步的研究。

The ideally straight hydraulic pipe is inexistent in reality. The initial curve caused by the manufacturing or the creep deformation during the service life will change the dynamic character of the system. The current work discusses the effect of the initial curve on the hydraulic pipe fixed at two ends for the first time. Based on the governing equation obtained via the generalized Hamilton’s principle,the potential energy changing with the height of the initial curve is discussed. The initial curve makes the potential energy curve asymmetric,but the system is always monostable. The initial curve also has very important influence on natural frequencies. It hardens the stiffness of the first natural mode at first and then has no effect on this mode after a critical value. On the contrast,the second natural frequency is constant before the critical value but increases while the height of the initial curve exceeds the critical value. On account of the initial value,the quadratic nonlinearity appears in the system. Forced resonance is very different from that of the ideally straight pipe under the same condition. Although the 2∶1 internal resonance is established by adjusting the height of the initial curve and the fluid speed,the typical double-jumping phenomenon does not occur under the initial curve given in the current work. This is very different from the straight pipe in the supercritical region. The work here claims that the initial curve of the hydraulic pipe should be taken into consideration. Besides,more arduous work is needed to reveal the dynamic characters of it.