2∶1内共振下超临界输流管道的强迫振动

Forced Vibration of Supercritical Fluid-conveying Pipe with 2∶1 Internal Resonance

高流速输流管道广泛应用于航空航天发动机等领域。为了掌握其在超临界流速下的动力学响应特征,基于坐标变换法建立了超临界输流管道的运动方程,并使用Galerkin截断法将运动方程离散为非线性常微分方程。通过增量谐波平衡法求解系统具有2∶1内共振时的非线性动力学响应,通过Floquet理论研究系统响应的稳定性和分岔行为,并使用数值积分法模拟了系统的拟周期响应。研究结果表明:当系统存在2∶1内共振时,系统响应发生不对称的双跳跃现象;而且2∶1内共振会导致能量在模态间相互转移,导致系统发生鞍结点分岔和Hopf分岔行为,引起系统响应的拟周期行为。分析系统参数对响应的影响表明,增加阻尼和减小激励幅值可以降低系统发生拟周期响应的可能性。可见,2∶1内共振是影响输流管道动力学特征的重要因素,因此设计中应该避免系统存在2∶1内共振,也可通过增加阻尼或减小激励的方式减少系统发生拟周期响应。

Pipes with high-velocity flow are widely used in aerospace engines and other fields.In order to understand its dynamical response characteristics under supercritical velocity of flow,the motion equation of supercritical fluid conveying pipe based on coordinate transformation method was established.Galerkin truncation method was used to discrete the motion equation into nonlinear ordinary differential equation.The nonlinear dynamical response of the system with 2∶1 internal resonance was solved by the incremental harmonic balance method.The stability and bifurcation behavior of the system response were studied by the Floquet theory,and the quasi-periodic response of the system was simulated by the numerical integration method.The results show that when the system has 2∶1 internal resonance,the system response occurs asymmetric double jump phenomenon.Moreover,2∶1 internal resonance leads to the transfer of energy between the modes,resulting in saddle node bifurcation and Hopf bifurcation of the system,resulting in quasi-periodic behavior of the system response.The analysis of the influence of system parameters on the response shows that increasing damping and reducing excitation amplitude reduce the possibility of quasi-periodic response of the system.It can be seen that 2∶1 internal resonance is an important factor affecting the dynamic characteristics of the fluid transmission pipeline.Therefore,2∶1 internal resonance of the system should be avoided in the design.The quasi-periodic response of the system can be reduced by increasing damping or reducing excitation.