[雙語翻譯]--外文翻譯--模擬靜壓管道氣體泄漏引起的聲發(fā)射信號（英文）

1、J Nondestruct Eval (2013) 32:67–80 DOI 10.1007/s10921-012-0160-xModeling Acoustic Emission Signals Caused by Leakage in Pressurized Gas PipeSaman Davoodi · Amir MostafapourReceived: 26 May 2012 / Accepted: 19 July 2

2、012 / Published online: 9 November 2012 © Springer Science+Business Media New York 2012Abstract Leakage in high pressure pipes creates stress waves which transmitted through the pipe wall. These waves can be recorde

3、d by using acoustic sensor or accelerometer installed on the pipe wall. Knowing how these waves vi- brate pipe is very important in continuous leak source lo- cating process. In this paper the pipe radial displacement ca

4、used by acoustic emission due to leakage is modeled an- alytically. The standard form of Donnell’s nonlinear cylin- drical shell theory is used to derive the motion equation of the pipe for simply supported boundary cond

5、ition. Us- ing Galerkin method, the motion equation has been solved and a system of nonlinear equations with 7 degrees of free- dom is obtained. A MATLAB code according to Runge- Kutta numerical method is generated to so

6、lve these equa- tions and derive the pipe radial displacement. To check the theoretical results, acoustic emission testing with continu- ous leak source and linear array of two sensors positioned on two sides of the leak

7、age source were carried out. The major noise of recorded signals was removed through the wavelet transform and filtering technique. For better analy- sis, fast Fourier transform (FFT) was taken from theoretical and de-no

8、ised experimental results. Comparing the results showed that the frequency which carried the most amount of energy is the same that expresses excellent agreement be- tween the theoretical and experimental results validat

9、ing the analytical model.Keywords Acoustic emission · Wavelet transform · Donnell’s nonlinear theory · Galerkin methodS. Davoodi (? ) · A. MostafapourMechanical Engineering Department, University of T

10、abriz, Tabriz, Iran e-mail: Saman.davoodi@gmail.com1 IntroductionIn the fields of micromechanics and seismology the defor- mation such as micro cracks has been formulated analyt- ically. Leak detection is one of the most

11、 important prob- lems in the oil and gas pipelines, where it can lead to fi- nancial losses, severe human and environmental impacts. The technique to monitor defects and abnormal vibrations due to machine failures is vit

12、ally important for the safety of structures in the modern society. Acoustic emission (AE) has drawn a great attention because of its applicability to on-stream surveillance of structures. One important point is the capab

13、ility to acquire data very simply but with high sen- sitivity. The applicability is limited partly because the ac- curacy of solutions depends on the noise levels and partly because the phenomenon is usually irreproducib

14、le [1]. Pol- lock [2] has discussed the parameters which affect AE wave propagation in structures. He noted that in gas filled vessels, attenuation can be very low and a number of Lamb wave modes are experimentally obser

15、vable. In liquid filled ves- sels the increased attenuation of signals due to its effect on the waveform and the timing of the peak made source lo- cation more difficult. Elforjani and Mba [3] applied the AE technology t

16、o detect natural crack initiation and propagation on slow speed bearings which is one of the few publications that address natural mechanical degradation on rotating ma- chine components. Shehadeh and et al. [4] concentr

17、ated on the temporal aspects and on determining the arrival times of propagating waves generated from a simulated source, hence identifying the AE wave speeds. Maji [5] has dis- cussed AE wave propagation in plates and b

18、eams. He noted that it becomes more difficult to extract the arrival time of in- dividual frequency components from broad band transduc- ers and that it is preferable to use resonant transducers so that specific frequenc

19、ies dominate the recorded AE events. He found dominate peaks in the AE signals at around 100J Nondestruct Eval (2013) 32:67–80 69The strain-displacement relations are:? 1 ? ν2? NxEh = ?νwR + 12??w?x?2 + ν2? ?wR?θ?2+ ?u?x

20、 + νR??v?θ?? 1 ? ν2? NθEh = ?wR + ν2??w?x?2 + 12? ?wR?θ?2+ ν ?u?x + 1R?v?θ? 1 ? ν2?NxθEh = 2(1 ? ν)? 1R?w?x?w?θ + 1R?u?θ + ?v?x?(5)In these equations ν is Poisson ratio. According to Hamil- ton’s principle we can derive

21、the motion equations as:?Nx ?η + ?Nxθ?θ= R2ρh¯ ¨ u?Nθ?θ + ?Nxθ?η + Qθ= R2ρh¯ ¨ v ?Qx?η + ?Qθ?θ ? Nθ = ρhR2 ¯ ¨ w + f?Bx ?η + ?Bxθ?θ ? RQx = 0?Bxθ?η + ?Bθ?θ ? RQθ = 0(6)where Bx, Bθ, Bxθ are

22、equivalent static couples, Qx, Qθ are equivalent static shearing and η = x/R, ¯ u = u/R, ¯ v = v/R, ¯ w = w/R. Donnell’s theory represents a simplification of the theory. There are two assumptions in Donne

23、ll’s theory to solve Eqs. (6). It is argued that in the equations of motion (6) the transverse shearing stress resultant Qθ make a negli- gible contribution to the equilibrium forces in the circumfer- ential direction an

24、d hence Qθ may be neglected. Secondly it is argued that v has no effect on the relationship between curvature and the displacements. So we can rewrite Eqs. (6) as:?2 ¯ u?η2 + K0 ?2 ¯ u?θ2 + K? 0 ?2 ¯ v?θ?η

25、 + υ ? ¯ w?η = R2c2 ¯ ¨ uK? 0 ?2 ¯ u?θ?η + K0 ?2 ¯ v?η2 + ?2 ¯ v?θ2 + ? ¯ w?θ = R2c2 ¯ ¨ v?υ ? ¯ u?η ? ? ¯ v?θ ? ε?4 ¯ w = R2c2 ¯ ¨ w + RfK(7)where ε

26、= h2/12R2, K? 0 = (1+υ)/2,K0 = (1?υ)/2, K = Eh/(1 ? υ2). By some calculations we can obtain Eq. (1) from Eqs. (7). The perturbation pressure is calculated by using Paidousis and Dennis model [13] and the method of vari-

27、ables separation:pr = ρf LmπIn(mπr/L)I ? n(mπR/L)? ??t?2 w (8)where ρf is the gas density. Pipelines and piping system are important in the infrastructure of modern society. Pipelines networks frequently cross highly pop

28、ulated regions water, oil and gas supplies or natural reserves. So knowing the vi- bration behavior of the gas and fluid-filled pipes caused by leakage is very important to detect the leakage and prevent the explosion, e

29、nvironmental pollution and saving energies and water supplies. This model can be used to model the fluid and gas filled pipe vibrations and be useful in several industrial fields. Applied force to the pipe caused by leak

30、ing fluid is con- sidered as follows:f = Fδ(x ? x0)δ(θ ? θ0)eiωt (9)where x0, θ0 denote leak source coordinates and ω is the fre- quency of applied force caused by leaking gas. By replacing w in the right hand side of Eq

31、. (2), a partial difference equa- tion (PDE) for in-plane stress function is defined as:F = Fh + Fp (10)where Fp and Fh denote particular and homogeneous solu- tions of in-plane stress function. To determine Fp and Fh, M

32、athematica software is used [12]. By replacing w(x,θ,t), F , f and pr in right hand side of Eq. (1) and by using the Galerkin technique with weight- ing functions, the partial differential equation of motion is solved an

33、d a system of non-linear ordinary differential equations with 7 degree of freedom is obtained in Math- ematica. By using the Galerkin method, seven second or- der ordinary, coupled non-linear differential equations are o

34、btained. The Galerkin projection of Eq. (1) has been per- formed by using the Mathematica computer software. The Runge-Kutta method was used to solve the system of equa- tions (Appendix). In this model the non-linear int

35、eraction among linear modes of the chosen basis involves only the asymmetric modes having a given n value, and all the axisymmetric modes is considered. Then the obtained theoretical results were compared with de-noised

36、experimental results. Liu et al. [14] and Kandasamy et al. [15] used the computer sim- ulation source or a point excitation source (a small piezo- electric disc) in their experimental set-up for theoretical re- sults val

37、idation and in some other researches [16] a linear interaction among the modes were used to study the vibra- tion behavior of pipe caused by simulated leak source. In our previous work [11] we studied the validation of t

38、he an- alytical model by noisy experimental results. The boundary conditions were as:u = 0 at x = 0,L and v = 0 at x = 0,L (11)In this study we used a non-linear model with a differ- ent boundary conditions (as mentioned