Adjacent mode resonance of a hydraulic pipe system consisting of parallel pipes coupled at middle points

The coupling vibration of a hydraulic pipe system consisting of two pipes is studied.The pipes are installed in parallel and fixed at their ends,and are restrained by clips to one bracket at their middle points.The pipe subjected to the basement excitation at the left end is named as the active pipe,while the pipe without excitation is called the passive pipe.The clips between the two pipes are the bridge for the vibration energy.The adjacent natural frequencies will enhance the vibration coupling.The governing equation of the coupled system is deduced by the generalized Hamilton principle,and is discretized to the modal space.The modal correction is used during the discretization.The investigation on the natural characters indicates that the adjacent natural frequencies can be adjusted by the stiffness of the two clips and bracket.The harmonic balance method(HBM)is used to study the responses in the adjacent natural frequency region.The results show that the vibration energy transmits from the active pipe to the passive pipe swimmingly via the clips together with a flexible bracket,while the locations of them are not node points.The adjacent natural frequencies may arouse wide resonance curves with two peaks for both pipes.The stiffness of the clip and bracket can release the vibration coupling.It is suggested that the stiffness of the clip on the passive pipe should be weak and the bracket should be strong enough.In this way,the vibration energy is reflected by the almost rigid bracket,and is hard to transfer to the passive pipe via a soft clip.The best choice is to set the clips at the pipe node points.The current work gives some suggestions for weakening the coupled vibration during the dynamic design of a coupled hydraulic pipe system.

An Efficient Reliability-Based Optimization Method Utilizing High-Dimensional Model Representation and Weight-Point Estimation Method

The objective of reliability-based design optimization(RBDO)is to minimize the optimization objective while satisfying the corresponding reliability requirements.However,the nested loop characteristic reduces the efficiency of RBDO algorithm,which hinders their application to high-dimensional engineering problems.To address these issues,this paper proposes an efficient decoupled RBDO method combining high dimensional model representation(HDMR)and the weight-point estimation method(WPEM).First,we decouple the RBDO model using HDMR and WPEM.Second,Lagrange interpolation is used to approximate a univariate function.Finally,based on the results of the first two steps,the original nested loop reliability optimization model is completely transformed into a deterministic design optimization model that can be solved by a series of mature constrained optimization methods without any additional calculations.Two numerical examples of a planar 10-bar structure and an aviation hydraulic piping system with 28 design variables are analyzed to illustrate the performance and practicability of the proposed method.

Main Gas Pipelines： Fracture Resistance Assessment of Pipes

This paper proposes an estimation method of fracture resistance of oil ＆ gas pipes, based on the results of full scale hydraulic pressure pipe testing with the artificial notch, made by the authors at 2002-2006. It shows that the fracture process at the stage of stripping （initialization） of crack can be characterized by Critical Fracture Diagram （CFD）. Calculating and experimental way to construct CFD is suggested and discussed. The fracture resistance requirements for oil ＆ gas pipes in terms of fracture mechanics （Kc, Lc） are formulated and proved. The results of full scale hydraulic pressure pipe testing, based on metal testing data of the standard Charpy specimens （KCV） and pipe＇s specification requirements are interrelated. The way to estimate the admissible temperature operation conditions of oil ＆ gas pipes by means of based metal ＂KCV-temperature＂ dependence is proposed.

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

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.