ارائه یک مدل غیرخطی برای تحلیل ارتعاشات آکوستیک یک پوسته استوانه‌ای متحرک در عمق سیال

نوع مقاله : مقاله پژوهشی

نویسندگان

دانشکده ی مهندسی مکانیک، دانشگاه یزد

10.24200/j40.2024.64818.1715

چکیده

در این مقاله، ارتعاشات آکوستیک غیرخطی پوسته استوانه‌ای دو سر گیردار متحرک در راستای محوری در عمق سیال بررسی شده است. سطح بیرونی پوسته که در تماس با سیال است؛ در معرض موج صوتی تابشی از نوع تخت مورب قرار می‌گیرد. تئوری غیر خطی پوسته نازک دانل برای استخراج معادله دیفرانسیل جزئی غیرخطی پوسته استوانه‌ای برای ارتعاشات در راستای شعاعی استفاده می‌شود. همچنین از رابطه‌ برنولی برای سیال غیر پایدار، فشار وارد بر پوسته استوانه‌ای محاسبه می‌شود. روش گالرکین برای تبدیل معادلات حرکت به دستگاه معادلات دیفرانسیل مرتبه دوم معمولی غیرهمگن غیرخطی استفاده می‌شود. پس از آن با در نظر گرفتن هر دو شکل مودهای تحریک شده و همراه، از روش مقیاس‌های چندگانه برای به دست آوردن پاسخ فرکانسی سیستم استفاده می‌شود. اثرات شدت صوت، زاویه برخورد موج تابشی و سرعت محوری پوسته بر پاسخ فرکانسی سیستم و افت توان صوتی مورد مطالعه قرار می‌گیرد. نتایج شبیه‌سازی نشان داده است که در سرعت‌های پایین پوسته استوانه-ای، پاسخ فرکانسی تحت تأثیر تحریک هر دو مود تحریک شده و همراه می‌باشد.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

A nonlinear model for vibro-acoustic analysis of a submerged axially moving cylindrical shell

نویسندگان [English]

  • A. H. Orafa
  • M.M. Jalili
  • A.R. Fotuhi
Ph.D Student of Yazd University, Yazd, Iran
چکیده [English]

Investigating the acoustic vibrations of moving cylindrical shells in fluid is of interest to researchers due to their many applications in marine structures. Underwater vehicles, submarine pipelines, and oil and gas industries are examples of shells used in the marine industry. Analyzing the acoustic vibration of submerged structures and investigating the effect of various parameters on their sound energy absorption is of great importance. If most of the radiated sound intensity is transferred to the structure due to its reflection, the possibility of identifying it will decrease. For this reason, much research has been conducted to investigate the acoustic behavior of submerged structures, especially cylindrical shells, due to their many uses in underwater vehicles. In this study, the nonlinear vibro-acoustic dynamics and stability of doubly-clamped axially moving cylindrical shells are investigated. The exterior surface of the shell is in contact with the fluid and subjected to oblique incident plane sound waves. Donnell’s nonlinear shallow shell theory is used to derive the nonlinear partial differential equation of the cylindrical shell for the radial motion. Also, the pressure on the cylindrical shell is calculated from Bernoulli's equation for unstable fluid. The Galerkin method is employed to discretize the equations of motion into the set of coupled nonlinear, nonhomogeneous ordinary second-order differential equations. Considering both driven and companion modes, the Multiple Scales Method is used to obtain the response of the system. The effects of sound level, incident angle, and axial velocity on the frequency response of the system are studied. Comparing the frequency response of the nonlinear model presented in this article with the frequency response of the linearized model shows that for the high intensity and high angle of the incident sound and also the low speed of the shell movement in the depth of the fluid, the error of the linear model in determining the resonance frequency and the stable response range of the cylindrical shell is large.

کلیدواژه‌ها [English]

  • Nonlinear vibro-acoustics
  • Submerged moving cylindrical shell
  • Transmission loss
  • Method of multiple scales
1. Tang, D., Yao, X., Jin, Y. and Pang, F., 2016. Acoustic radiation from shear deformable ring-stiffened laminated composite cylindrical shell submerged in flowing fluid. Appl. Ocean Res, 61, pp. 65-80. doi.org/10.1016/j.apor.2016.10.006 2. Guo, W., Li, T., Zhu, X., Miao, Y. and Zhang, G., 2017. Vibration and acoustic radiation of a finite cylindrical shell submerged at finite depth from the free surface. J Sound Vib, 393, pp. 338-352. doi.org/10.1016/j.jsv.2017.01.003 3. Wang, X., Chen, D., Xiong, Y., Jiang, Q. and Zuo, Y. 2018. Experiment and modeling of vibro-acoustic response of a stiffened submerged cylindrical shell with force and acoustic excitation. Results Phys, 11, pp. 315–324. doi.org/10.1016/j.rinp.2018.09.017 4. Jin, G., Mab, X., Wang. W. and Liu, Z., 2018. An energy-based formulation for vibro-acoustic analysis of submerged submarine hull structures. Ocean Eng, 164, pp. 402-413. doi.org/10.1016/j.oceaneng.2018.06.057 5. Sua, J., Lei, Z., Qu, Y. and Hu, H., 2018. Effects of non-axisymmetric structures on vibro-acoustic signatures of a submerged vessel subject to propeller forces. Appl. Acoust, 133, pp. 28-37. doi.org/10.1016/j.apacoust.2017.12.006 6. Xie, K., Chen, M., Zhang, L., Li., W. and Dong, W., 2019. A unified semi-analytic method for vibro-acoustic analysis of submerged shells of revolution. Ocean Eng, 189, pp. 1-16. doi.org/10.1016/j.oceaneng.2019.106345 7. Zhao, K., Fan, J., Wang, B. and Tang, W., 2020. Analytical and experimental study of the vibro-acoustic behavior of a semi-submerged finite cylindrical shell. J Sound Vib, 482, pp. 1-20. doi.org/10.1016/j.jsv.2020.115466 8. Pan, C., Sun, X. and Zhang, Y., 2020. Vibro-acoustic analysis of submerged ring-stiffened cylindrical shells based on a symplectic wave-based method. Thin Wall Struct, 150, pp. 1-15. doi.org/10.1016/j.tws.2020.106698 9. Marsick, A., Sharma, GS., Eggler, D., Maxit, L., Meyer, V. and Kessissoglou, N., 2021. On the vibro-acoustic response of a cylindrical shell submerged near a free sea surface. J Sound Vib, 511, pp. 1–15. doi.org/10.1016/j.jsv.2021.116359 10. Yang, H. and Seong, W., 2021. Acoustic radiation efficiency of a submerged periodic ring-stiffened cylindrical shell with finite vibration loading. Appl. Acoust, 171, pp. 1-8. doi.org/10.1016/j.apacoust.2020.107664 11. Zhang, S., Li, T., Zhu, X., Yin, C. and Li, Q., 2022. Far field acoustic radiation and vibration analysis of combined shells submerged at finite depth from free surface. Ocean Eng, 252, pp. 1–14. doi.org/10.1016/j.oceaneng.2022.111198 12. Jia, W., Chen, M., Xie, K. and Dong, W., 2022. Experimental and analytical investigations on vibro-acoustic characteristics of a submerged submarine hull coupled with multiple inner substructures. Ocean Eng, 259, pp. 1-20. doi.org/10.1016/j.oceaneng.2022.111960 13. Jia, W., Chen, M., Zhou, Z. and Xie, K., 2022. Effects of non-axisymmetric internal structures on vibro-acoustic characteristics of a submerged cylindrical shell using wavenumber analysis. Thin Wall Struct, 171, pp. 883-899. doi.org/10.1016/j.tws.2021.108758 14. Gao, C., Zhang, H., Li, H., Pang, F. and Wang, H., 2022. Numerical and experimental investigation of vibro-acoustic characteristics of a submerged stiffened cylindrical shell excited by a mechanical force. Ocean Eng, 249, pp. 112-128. doi.org/10.1016/j.oceaneng.2022.110913 15. Pan, C. and Zhang, Y., 2022. Coupled vibro-acoustic analysis of submerged double cylindrical shells with stringers, rings, and annular plates in a symplectic duality system. Thin Wall Struct, 171, pp. 1–16. doi.org/10.1016/j.tws.2021.108671 16. Qu, Y., Zhang, W., Peng, Z. and Meng, G., 2019. Nonlinear structural and acoustic responses of three-dimensional elastic cylindrical shells with internal mass-spring systems. Appl. Acoust, 149, pp.143-155. doi.org/10.1016/j.apacoust.2019.01.009 17. Qu, Y., Xie, F. and Meng, G., 2019. Nonlinear dynamic and acoustic analysis of orthogonally stiffened composite laminated cylindrical shells containing piecewise isolators. J Sound Vib, 456, pp. 199–220. doi.org/10.1016/j.jsv.2019.05.023 18. Orafa, A.H., Jalili, M.M. and Fotuhi, A.R., 2021. Nonlinear vibro-acoustic behavior of cylindrical shell under primary resonances. Int J Non Linear Mech, 130, pp. 1-21. doi.org/10.1016/j.ijnonlinmec.2021.103682 19. Orafa, A.H., Jalili, M.M. and Fotuhi, A.R., 2023. Nonlinear analysis of sound transmission loss through cylindrical shell considering companion modes. Int Journal of Vibration and Control, 130, 1-21. https://doi.org/10.1177/10775463231203442 20. Zou, M.S., Jiang, L.W. and Tang, H.C., 2022. Computational method of underwater acoustic radiation from a spherical shell coupled with nonlinear systems. J Sound Vib, 533, pp. 1–21. doi.org/10.1016/j.jsv.2022.117020 21. Amabili, M., Pellicano, F. and Paidoussis, M.P., 1998. Nonlinear vibrations of simply supported, circular cylindrical shells, coupled to quiescent fluid. J Sound Vib, 12, pp. 883-918. doi.org/10.1006/jfls.1998.0173 22. Dowell, E.H. and Ventres, C.S., 1968. Modal equations for the nonlinear flexural vibrations of a cylindrical shell. International Journal of Solids and Structures, 4, pp. 975–991. doi.org/10.1016/0020-7683(68)90017-6 23. Daneshjou, K., Talebitooti, R. and Tarkashvand, A., 2016. Analysis of sound transmission loss through thick-walled cylindrical shell using three-dimensional elasticity theory. Int J Mech Sci, 106, pp. 286-296. doi.org/10.1016/j.ijmecsci.2015.12.019 24. White, F. M., 2011. Fluid Mechanics, 7th Edn., McGraw- Hill, New York, USA. 25. Linge, S. and Langtangen, H.P., 2010. Programming for Computations – MATLAB/Octave, 1st Edn., Springer, Heidelberg, Germany. 26. Talebitooti, R., Gohari, H.D. and Zarastvand, M.R., 2017. Multi objective optimization of sound transmission across laminated composite cylindrical shell lined with porous core investigating non-dominated sorting genetic algorithm. Aerosp. Sci. Technol, 69, pp. 269–280. doi.org/10.1016/j.ast.2017.06.008 27. Karagiozis, K.N., Amabili, M., Paidoussis, M.P. and Misra A.K., 2005. Nonlinear vibrations of fluid-filled clamped circular cylindrical shells. Journal of Fluids and Structures, 21, pp. 579–595. doi.org/10.1016/j.jfluidstructs.2005.07.020 28. Oliazadeh, P., Farshidianfar, A. and Crocker, M.J., 2019. Study of sound transmission through single-and double-walled plates with absorbing material: Experimental and analytical investigation. Applied Acoustics, 145, pp. 7-24. doi.org/10.1016/j.apacoust.2018.09.014