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Research Papers: Seismic Engineering

Steady-State Response of a Piping System Under Harmonic Excitations Considering Pipe-Support Friction With Variable Normal Loads

[+] Author and Article Information
José Argüelles

Sinclair Knight Merz Ltd.,
Santiago 7500011, Chile
e-mail: JArguelles@globalskm.com

Euro Casanova

Professor
Department of Mechanics,
Universidad Simón Bolívar,
Caracas 1080, Venezuela
e-mail: ecasanov@usb.ve

1Corresponding author.

Contributed by the Pressure Vessel and Piping Division of ASME for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received September 6, 2013; final manuscript received December 13, 2014; published online February 24, 2015. Assoc. Editor: Chong-Shien Tsai.

J. Pressure Vessel Technol 137(5), 051801 (Oct 01, 2015) (10 pages) Paper No: PVT-13-1153; doi: 10.1115/1.4029403 History: Received September 06, 2013; Revised December 13, 2014; Online February 24, 2015

Dynamic loads in piping systems are mainly caused by transient phenomena generated by operating conditions or installed equipment. In most cases, these dynamic loads may be modeled as harmonic excitations, e.g., pulsating flow. On the other hand, when designing piping systems under dynamic loads, it is a common practice to neglect strong nonlinearities such as shocks and friction between pipe and support surfaces, mainly because of the excessive cost in terms of computational time and the complexity associated with the integration of the nonlinear equations of motion. However, disregarding these nonlinearities for some systems may result in overestimated dynamic amplitudes leading to incorrect analysis and designs. This paper presents a numerical approach to calculate the steady-state response amplitudes of a piping system subjected to harmonic excitations and considering dry friction between the pipe and the support surfaces, without performing a numerical integration. The proposed approach permits the analysis of three dimensional piping systems, where the normal forces may vary in time and is based in the hybrid frequency–time domain method (HFT). Results of the proposed approach are compared and discussed with those of a full integration scheme, confirming that HFT is a valid and computationally feasible option.

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References

Jangid, R., 2001, “Response of Sliding Structures to Bi-Directional Excitation,” J. Sound Vib., 243(5), pp. 929–944. [CrossRef]
Hong, H., and Liu, C., 2001, “Non–Sticking Oscillation Formulae for Coulomb Friction Under Harmonic Loading,” J. Sound Vib., 244(5), pp. 883–898. [CrossRef]
Xia, F., 2003, “Modeling of a Two-Dimensional Coulomb Friction Oscillator,” J. Sound Vib., 265(5), pp. 1063–1074. [CrossRef]
Sobieszczanski, J., 1972, “Inclusion of Support Friction into a Computerized Solution of Self-Compensating Pipeline,” ASME J. Manuf. Sci. Eng., 94(3) pp. 797–802. [CrossRef]
Kobayashi, H., Yoshida, M., and Ochi, Y., 1989, “Dynamic Response of Piping System on Rack Structure With Gaps and Frictions,” Nucl. Eng. Des., 111(3), pp. 341–350. [CrossRef]
Bakre, S., Jangid, R., and Reddy, G., 2007, “Response of Piping System on Friction Support to Bi-Directional Excitation,” Nucl. Eng. Des., 237(2), pp. 124–136. [CrossRef]
Oliver, K., 2007, “Modelado de la Respuesta Dinámica de Sistemas de Tuberías Considerando Fricción en Los Soportes,” M.Sc. thesis, Universidad Simón Bolívar, Caracas, Venezuela.
Mickens, R., 1984, “Comments on the Method of Harmonic Balance,” J. Sound Vib., 94(3), pp. 456–460. [CrossRef]
Pierre, C., and Ferri, A., 1985, “Multi-Harmonics of Dry Friction Damped Systems Using an Incremental Harmonic Balance Method,” ASME J. Appl. Mech., 52(4), pp. 958–964. [CrossRef]
Ostachowicz, W., 1989, “The Harmonic Balance Method for Determining the Vibration Parameters in Damped Dynamic Systems,” J. Sound Vib., 131(3), pp. 465–473. [CrossRef]
Menq, C., and Chidamparam, P., 1991, “Friction Damping of Two-Dimensional Motion and Its Application in Vibration Control,” J. Sound Vib., 144(3), pp. 427–447. [CrossRef]
Chen, J., Yang, B., and Menq, C., 2000, “Periodic Forced Response of Structures Having Three Dimensional Frictional Constraints,” J. Sound Vib., 229(4), pp. 775–792. [CrossRef]
Sanliturk, K., and Ewins, D., 1996, “Modelling Two Dimensional Friction Contact and Its Application Using Harmonic Balance Method,” J. Sound Vib., 193(2), pp. 511–523. [CrossRef]
Petrov, E., and Ewins, D., 2005, “Method for Analysis of Nonlinear Multiharmonic Vibrations of Mistuned Bladed Disks With Scatter of Contact Interface Characteristics,” ASME J. Turbomach., 127(1), pp. 128–136. [CrossRef]
Cameron, T., and Griffin, J., 1989, “An Alternating Frequency/Time Domain Method for Calculating the Steady-State Response of Nonlinear Dynamic Systems,” ASME J. Appl. Mech., 56(1), pp. 149–154. [CrossRef]
Guillen, J., and Pierre, C., 1999, “An Efficient, Hybrid, Frequency-Time Domain Method for the Dynamics of Large-Scale Dry-Friction Damped Structural Systems,” IUTAM Symposium on Unilateral Multibody Contacts, Kluwer Academic Publishers, Dordrecht, Netherlands, pp. 169–178. [CrossRef]
Powell, M., 1970, A Hybrid Method for Nonlinear Equations; Numerical Methods for Nonlinear Algebraic Equations, Gordon & Breach Science Publishers, London, UK.
Poudou, O., Pierre, C., and Reisser, B., 2004, “A New Hybrid Frequency-Time Domain Method for the Forced Vibration of Elastic Structures With Friction and Intermittent Contact,” Proceedings of the 10th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery (ISROMAC), Honolulu, HI, Paper No. 10-2004-068.
Poudou, O., and Pierre, C., 2005, “A New Method for the Analysis of the Nonlinear Dynamics of Structures With Cracks,” Proceedings of the NOVEM, Saint-Raphäel, France.
Saito, A., Castanier, M., and Pierre, C., 2008, “Vibration Analysis of Cracked Cantilevered Plates Near Natural Frequency Veerings,” AIAA Paper No. 2008-1872. [CrossRef]
Argüelles, J., Casanova, E., and Asuaje, M., 2011, “Harmonic Response of a Piping System Considering Pipe-Support Friction via HFT Method,” ASME Paper No. PVP2011-57172. [CrossRef]
Follan, G., 1992, Fourier Analysis and Its Applications, Wadsworth & Brooks/Cole, Pacific Grove, CA.
Broyden, C. G., 1965, “A Class of Methods for Solving Nonlinear Simultaneous Equations,” Math. Comput., 19(92), pp. 577–593. [CrossRef]
Bathe, K., 1996, Finite Element Procedures, Prentice–Hall, Upper Saddle River, NJ.
Pascal, M., 2014, “Finite Sticking and Nonsticking Orbits for a Two-Degree-of-Freedom Oscillator Excited by Dry Friction and Harmonic Loading,” Nonlinear Dyn., 77(1–2), pp. 267–276. [CrossRef]

Figures

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Fig. 1

Piping system under study

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Fig. 2

Second normal mode

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Fig. 3

Orbits in plane X-Z for S1 (μ = 0.3, F = 1 × 104 N, and Ω = 10.15 Hz)

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Fig. 4

Response amplitude for E1 and S1 (μ = 0.1 and F = 2.5 × 103N)

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Fig. 5

Response amplitude for E1 and S1 (μ = 0.3 and F = 2.5 × 103N)

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Fig. 6

Response amplitude for E2 and E3 (μ = 0.1 and F = 2.5 × 103N)

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Fig. 7

Response amplitude for E2 and E3 (μ = 0.3 and F = 2.5 × 103N)

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Fig. 8

Response amplitude for E1 and S1 (μ = 0.1 and F = 2 × 104 N)

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Fig. 9

Response amplitude for E1 and S1 (μ = 0.3 and F = 2 × 104 N)

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Fig. 10

Response amplitude for E2 and E3 (μ = 0.1 and F = 2 × 104 N)

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Fig. 11

Response amplitude for E2 and E3 (μ = 0.3 and F = 2 × 104 N)

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Fig. 12

Friction effect in harmonic response for E1 (F = 2.5 × 103 N)

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Fig. 13

Friction effect in harmonic response for S1 (F = 2.5 × 103N)

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Fig. 14

Amplitude reduction due to friction for E1 (F = 2 × 104N)

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Fig. 15

Amplitude reduction due to friction for S1 (F = 2 × 104N)

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Fig. 16

Force effect in harmonic response of E1 and S1 (μ = 0.3)

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Fig. 17

Force effect in harmonic response of E2 and E3 (μ = 0.3)

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Fig. 18

Response amplitude for E1 and S1 considering constant and variable normal forces (μ = 0.3 and F = 2 × 104N)

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Fig. 19

Response amplitude for E2 and E3 considering constant and variable normal forces (μ = 0.3 and F = 2 × 104N)

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Fig. 20

Response amplitude for E1 (μ = 0.3 and F = 2.5 × 103N)

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Fig. 21

Response amplitude for S1 (μ = 0.3 and F = 2.5 × 103N)

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