A systematic review of analyzing the vibration modes of the cylindrical shell in the MRI machine to investigate the sound noise attenuation solutions
Subject Areas : Journal of New Applied and Computational Findings in Mechanical Systems
1 -
Keywords: MRI. Vibrational modes. Cylindrical Shell. MPP.,
Abstract :
Magnetic resonance imaging (MRI) is one of the non-invasive medical imaging methods based on magnetic fields and radio waves. This study focuses on reducing the acoustic noise inside the cylindrical shell of the scanner where the patient is placed. These modes are excited by eddy currents created in the cylindrical shell by gradient magnetic fields. In addition, the wall of the scanner half-tunnel is usually connected to the gradient spiral cylinder, which causes some vibrations to be transmitted to the wall, resulting in the generation of sound waves. The present study deals with the methods of managing the noise from the half-tunnel wall of the scanner and the transmission noise from the spiral gradient cylinder through the wall. This research shows that one of the best noise management methods is the design of a Micro-Perforated Panel (MPP) between the gradient cylinder and the wall of the cylindrical shell of the scanner. Numerical analysis of gradient cycles provides solutions that can reduce vibration and noise levels based on acoustic analysis.
References:
1. Livanov K. Axisymmetric vibrations of simply supported cylindrical shells. Journal of Applied Mathematics and Mechanics. 1961;25(4):1095-101.
2. Rinehart S, Wang J. Vibration of simply supported cylindrical shells with longitudinal stiffeners. Journal of Sound and Vibration. 1972;24(2):151-63.
3. Beskos D, Oates J. Dynamic analysis of ring-stiffened circular cylindrical shells. Journal of Sound and Vibration. 1981;75(1):1-15.
4. Mustafa B, Ali R. An energy method for free vibration analysis of stiffened circular cylindrical shells. Computers & structures. 1989;32(2):355-63.
5. Soedel W. On the vibration of shells with Timoshenko-Mindlin type shear deflections and rotatory inertia. Journal of Sound and Vibration. 1982;83(1):67-79.
6. Suzuki K, Leissa A. Exact solutions for the free vibrations of open cylindrical shells with circumferentially varying curvature and thickness. Journal of sound and vibration. 1986;107(1):1-15.
7. Sivadas K, Ganesan N. Free vibration of circular cylindrical shells with axially varying thickness. Journal of sound and vibration. 1991;147(1):73-85.
8. Zhang L, Xiang Y. Exact solutions for vibration of stepped circular cylindrical shells. Journal of sound and vibration. 2007;299(4-5):948-64.
9. Bhangale RK, Ganesan N. Free vibration studies of simply supported non-homogeneous functionally graded magneto-electro-elastic finite cylindrical shells. Journal of Sound and Vibration. 2005;288(1-2):412-22.
10. Kadoli R, Ganesan N. Buckling and free vibration analysis of functionally graded cylindrical shells subjected to a temperature-specified boundary condition. Journal of sound and vibration. 2006;289(3):450-80.
11. Paliwal D, Bhalla V. Large amplitude free vibrations of cylindrical shell on Pasternak foundations. International journal of pressure vessels and piping. 1993;54(3):387-98.
12. Chen W-q, Ding H-j, Xu R-q. On exact analysis of free vibrations of embedded transversely isotropic cylindrical shells. International journal of pressure vessels and piping. 1998;75(13):961-6.
13. Pellicano F. Vibrations of circular cylindrical shells: theory and experiments. Journal of sound and vibration. 2007;303(1-2):154-70.
14. Xuebin L. Study on free vibration analysis of circular cylindrical shells using wave propagation. Journal of sound and vibration. 2008;311(3-5):667-82.
15. Lin C-W, Bell FL. On the non-symmetric vibrations of thin cylindrical shells with clamped-clamped edges. Nuclear Engineering and Design. 1968;7(3):194-200.
16. Tottenham H, Shimizu K. Analysis of the free vibration of cantilever cylindrical thin elastic shells by the matrix progression method. International Journal of Mechanical Sciences. 1972;14(5):293-310.
17. Askari E, Daneshmand F. Coupled vibrations of cantilever cylindrical shells partially submerged in fluids with continuous, simply connected and non-convex domain. Journal of Sound and Vibration. 2010;329(17):3520-36.
18. Lee J, Leissa A, Wang A. Vibrations of cantilevered circular cylindrical shells: shallow versus deep shell theory. International Journal of Mechanical Sciences. 1983;25(5):361-83.
19. Leissa A, Lee J, Wang A. Vibrations of cantilevered doubly-curved shallow shells. International Journal of Solids and Structures. 1983;19(5):411-24.
20. Ganesan N, Sivadas K. Free vibration of cantilever circular cylindrical shells with variable thickness. Computers & structures. 1990;34(4):669-77.
21. Annigeri A, Ganesan N, Swarnamani S. Free vibrations of clamped–clamped magneto-electro-elastic cylindrical shells. Journal of Sound and Vibration. 2006;292(1-2):300-14.
22. Wong S, Bush W. Axisymmetric vibrations of a clamped cylindrical shell using matched asymptotic expansions. Journal of sound and vibration. 1993;160(3):523-31.
23. Leissa AW. Vibration of plates: Scientific and Technical Information Division, National Aeronautics and …; 1969.
24. Leissa AW. Vibration of shells: Scientific and Technical Information Office, National Aeronautics and Space …; 1973.
25. Dowell E, Ventres C. Modal equations for the nonlinear flexural vibrations of a cylindrical shell. International Journal of Solids and Structures. 1968;4(10):975-91.
26. Atluri S. A perturbation analysis of non-linear free flexural vibrations of a circular cylindrical shell. International Journal of Solids and Structures. 1972;8(4):549-69.
27. Birman V, Bert CW. Non-linear beam-type vibrations of long cylindrical shells. International journal of non-linear mechanics. 1987;22(4):327-34.
28. Chiba M. Non-linear hydroelastic vibration of a cantilever cylindrical tank—I. Experiment (empty case). International journal of non-linear mechanics. 1993;28(5):591-9.
29. Amabili M, Pellicano F, Paidoussis M. Nonlinear vibrations of simply supported, circular cylindrical shells, coupled to quiescent fluid. Journal of Fluids and Structures. 1998;12(7):883-918.
30. Amabili M, Pellicano F, Païdoussis M. Non-linear dynamics and stability of circular cylindrical shells containing flowing fluid. Part III: truncation effect without flow and experiments. Journal of Sound and Vibration. 2000;237(4):617-40.
31. Amabili M, Karagiozis K, Païdoussis M. Effect of geometric imperfections on non-linear stability of circular cylindrical shells conveying fluid. International Journal of Non-Linear Mechanics. 2009;44(3):276-89.
32. Karagiozis K, Amabili M, Païdoussis M. Nonlinear dynamics of harmonically excited circular cylindrical shells containing fluid flow. Journal of Sound and Vibration. 2010;329(18):3813-34.
33. Sun S, Liu L. Parametric study and stability analysis on nonlinear traveling wave vibrations of rotating thin cylindrical shells. Archive of Applied Mechanics. 2021;91:2833-51.
34. Pellicano F, Amabili M, Paıdoussis M. Effect of the geometry on the non-linear vibration of circular cylindrical shells. International Journal of Non-Linear Mechanics. 2002;37(7):1181-98.
35. Gonçalves P, Silva F, Del Prado Z. Low-dimensional models for the nonlinear vibration analysis of cylindrical shells based on a perturbation procedure and proper orthogonal decomposition. Journal of Sound and Vibration. 2008;315(3):641-63.
36. Amabili M, Sarkar A, Paıdoussis M. Reduced-order models for nonlinear vibrations of cylindrical shells via the proper orthogonal decomposition method. Journal of Fluids and Structures. 2003;18(2):227-50.
37. Amabili M. Nonlinear vibrations of laminated circular cylindrical shells: Comparison of different shell theories. Composite Structures. 2011;94(1):207-20.
38. Kurylov Y, Amabili M. Nonlinear vibrations of clamped-free circular cylindrical shells. Journal of sound and vibration. 2011;330(22):5363-81.
39. Jansen E. A comparison of analytical–numerical models for nonlinear vibrations of cylindrical shells. Computers & structures. 2004;82(31-32):2647-58.
40. Jansen E. A perturbation method for nonlinear vibrations of imperfect structures: application to cylindrical shell vibrations. International Journal of Solids and Structures. 2008;45(3-4):1124-45.
41. Popov A. The application of Hamiltonian dynamics and averaging to nonlinear shell vibration. Computers & structures. 2004;82(31-32):2659-70.
42. Bakhtiari-Nejad F, Bideleh SMM. Nonlinear free vibration analysis of prestressed circular cylindrical shells on the Winkler/Pasternak foundation. Thin-Walled Structures. 2012;53:26-39.
43. Leizerovich G, Seregin S. Free vibrations of circular cylindrical shells with a small added concentrated mass. Journal of Applied Mechanics and Technical Physics. 2016;57:841-6.
44. Chakravorty D, Bandyopadhyay J. Effects of release of boundary constraints on the natural frequencies of clamped, thin, cylindrical shells. Computers & structures. 1994;52(3):489-93.
45. Kovtunov V. Dynamic stability and nonlinear parametric vibration of cylindrical shells. Computers & structures. 1993;46(1):149-56.
46. Amabili M, Paı¨ doussis MP. Review of studies on geometrically nonlinear vibrations and dynamics of circular cylindrical shells and panels, with and without fluid-structure interaction. Appl Mech Rev. 2003;56(4):349-81.
47. Amabili M. Nonlinear vibrations and stability of shells and plates: Cambridge University Press; 2008.
48. Soldatos K. A comparison of some shell theories used for the dynamic analysis of cross-ply laminated circular cylindrical panels. Journal of sound and vibration. 1984;97(2):305-19.
49. Chandrashekhara K, Kumar DP. Static response of composite circular cylindrical shells studied by different theories. Meccanica. 1998;33:11-27.
50. Messina A, Soldatos KP. Vibration of completely free composite plates and cylindrical shell panels by a higher-order theory. International Journal of Mechanical Sciences. 1999;41(8):891-918.
51. Soldatos KP, Messina A. The influence of boundary conditions and transverse shear on the vibration of angle-ply laminated plates, circular cylinders and cylindrical panels. Computer methods in applied mechanics and engineering. 2001;190(18-19):2385-409.
52. Soedel W, Qatu MS. Vibrations of shells and plates. Acoustical Society of America; 2005.
53. Taracila V, Edelstein WA, Kidane TK, Eagan TP, Baig TN, Brown RW. Analytical calculation of cylindrical shell modes: Implications for MRI acoustic noise. Concepts in Magnetic Resonance Part B: Magnetic Resonance Engineering: An Educational Journal. 2005;25(1):60-4.
54. Shao W, Mechefske CK. Analysis of the sound field in finite length infinite baffled cylindrical ducts with vibrating walls of finite impedance. The Journal of the Acoustical Society of America. 2005;117(4):1728-36.
55. Li G, Mechefske CK. Structural-acoustic modal analysis of cylindrical shells: application to MRI scanner systems. Magma. 2009;22(6):353.
56. Mechefske CK, Wang F. Theoretical, numerical, and experimental modal analysis of a single-winding gradient coil insert cylinder. Magnetic Resonance Materials in Physics, Biology and Medicine. 2006;19:152-66.
57. Edelstein WA, Hedeen RA, Mallozzi RP, El-Hamamsy S-A, Ackermann RA, Havens TJ. Making MRI quieter. Magnetic Resonance Imaging. 2002;20(2):155-63.
58. Mechefske CK, Wu Y, Rutt BK. MRI gradient coil cylinder sound field simulation and measurement. J Biomech Eng. 2002;124(4):450-5.
59. Yao G, Mechefske C, Rutt B. Characterization of vibration and acoustic noise in a gradient-coil insert. Magnetic Resonance Materials in Physics, Biology and Medicine. 2004;17:12-27.
60. Wang Y, Liu F, Crozier S. Simulation study of noise reduction methods for a split MRI system using a finite element method. Medical Physics. 2015;42(12):7122-31.
61. Wang Y, Liu F, Weber E, Tang F, Jin J, Tesiram Y, et al. Acoustic analysis for a split MRI system using FE method. Concepts in Magnetic Resonance Part B: Magnetic Resonance Engineering. 2015;45(2):85-96.
62. Winkler SA, Alejski A, Wade T, McKenzie CA, Rutt BK. On the accurate analysis of vibroacoustics in head insert gradient coils. Magnetic resonance in medicine. 2017;78(4):1635-45.
63. Sakhr J, Chronik BA. Vibrational response of a MRI gradient coil cylinder to time-harmonic Lorentz-force excitations: An exact linear elastodynamic model for shielded longitudinal gradient coils. Applied Mathematical Modelling. 2019;74:350-72.
64. Sakhr J, Chronik BA. Parametric modeling of steady-state gradient coil vibration: Resonance dynamics under variations in cylinder geometry. Magnetic Resonance Imaging. 2021;82:91-103.
65. McJury M. Acoustic noise levels generated during high field MR imaging. Clinical Radiology. 1995;50(5):331-4.
66. McJury MJ. Acoustic noise and magnetic resonance imaging: a narrative/descriptive review. Journal of Magnetic Resonance Imaging. 2022;55(2):337-46.
67. McJury PhD M, Shellock PhD FG. Auditory noise associated with MR procedures: a review. Journal of Magnetic Resonance Imaging. 2000;12(1):37-45.
68. Cho Z, Park S, Kim J, Chung S, Chung S, Chung J, et al. Analysis of acoustic noise in MRI. Magnetic resonance imaging. 1997;15(7):815-22.
69. Mechefske CK, Geris R, Gati JS, Rutt BK. Acoustic noise reduction in a 4 T MRI scanner. Magnetic Resonance Materials in Physics, Biology and Medicine. 2001;13:172-6.
70. Cho Z, Chung S, Chung J, Park S, Kim J, Moon C, et al. A new silent magnetic resonance imaging using a rotating DC gradient. Magnetic resonance in medicine. 1998;39(2):317-21.
71. Crémillieux Y, Wheeler‐Kingshott CA, Briguet A, Doran SJ. STEAM‐Burst: a single‐shot, multi‐slice imaging sequence without rapid gradient switching. Magnetic resonance in medicine. 1997;38(4):645-52.
72. Goldman A, Gossman W, Friedlander P. Reduction of sound levels with antinoise in MR imaging. Radiology. 1989;173(2):549-50.
73. McJury M, Stewart R, Crawford D, Toma E. The use of active noise control (ANC) to reduce acoustic noise generated during MRI scanning: some initial results. Magnetic resonance imaging. 1997;15(3):319-22.
74. Chen CK, Chiueh T-D, Chen J-H. Active cancellation system of acoustic noise in MR imaging. IEEE transactions on biomedical engineering. 1999;46(2):186-91.
75. Li M, Lim TC, Lee J-H. Simulation study on active noise control for a 4-T MRI scanner. Magnetic resonance imaging. 2008;26(3):393-400.
76. Li M, Rudd B, Lim TC, Lee JH. In situ active control of noise in a 4 T MRI scanner. Journal of Magnetic Resonance Imaging. 2011;34(3):662-9.
77. Chambers J, Bullock D, Kahana Y, Kots A, Palmer A. Developments in active noise control sound systems for magnetic resonance imaging. Applied Acoustics. 2007;68(3):281-95.
78. Mansfield P, Glover P, Bowtell R. Active acoustic screening: design principles for quiet gradient coils in MRI. Measurement Science and Technology. 1994;5(8):1021.
79. Mansfield P, Chapman BL, Bowtell R, Glover P, Coxon R, Harvey PR. Active acoustic screening: reduction of noise in gradient coils by Lorentz force balancing. Magnetic resonance in medicine. 1995;33(2):276-81.
80. Bowtell RW, Mansfield P. Quite transverse gradiant coils: Lorentz force balanced designs using geometrical similitude. Magnetic resonance in medicine. 1995;34(3):494-7.
81. Mansfield P, Haywood B. Principles of active acoustic control in gradient coil design. Magnetic Resonance Materials in Physics, Biology and Medicine. 2000;10:147-51.
82. Mansfield P, Haywood B, Coxon R. Active acoustic control in gradient coils for MRI. Magnetic Resonance in Medicine: An Official Journal of the International Society for Magnetic Resonance in Medicine. 2001;46(4):807-18.
83. Edelstein WA, Kidane TK, Taracila V, Baig TN, Eagan TP, Cheng YCN, et al. Active‐passive gradient shielding for MRI acoustic noise reduction. Magnetic Resonance in Medicine: An Official Journal of the International Society for Magnetic Resonance in Medicine. 2005;53(5):1013-7.
84. Roozen N, Koevoets A, Den Hamer A. Active vibration control of gradient coils to reduce acoustic noise of MRI systems. IEEE/ASME Transactions on mechatronics. 2008;13(3):325-34.
85. Wang Y, Liu F, Li Y, Tang F, Crozier S. Asymmetric gradient coil design for use in a short, open bore magnetic resonance imaging scanner. Journal of Magnetic Resonance. 2016;269:203-12.
86. Li G, Mechefske CK. A comprehensive experimental study of micro-perforated panel acoustic absorbers in MRI scanners. Magnetic Resonance Materials in Physics, Biology and Medicine. 2010;23(3):177-85.
87. Nan J, Zong N, Chen Q, Zhang L, Zheng Q, Xia Y. A Structure Design Method for Reduction of MRI Acoustic Noise. Computational and Mathematical Methods in Medicine. 2017;2017:6253428.
1. Livanov K. Axisymmetric vibrations of simply supported cylindrical shells. Journal of Applied Mathematics and Mechanics. 1961;25(4):1095-101.
2. Rinehart S, Wang J. Vibration of simply supported cylindrical shells with longitudinal stiffeners. Journal of Sound and Vibration. 1972;24(2):151-63.
3. Beskos D, Oates J. Dynamic analysis of ring-stiffened circular cylindrical shells. Journal of Sound and Vibration. 1981;75(1):1-15.
4. Mustafa B, Ali R. An energy method for free vibration analysis of stiffened circular cylindrical shells. Computers & structures. 1989;32(2):355-63.
5. Soedel W. On the vibration of shells with Timoshenko-Mindlin type shear deflections and rotatory inertia. Journal of Sound and Vibration. 1982;83(1):67-79.
6. Suzuki K, Leissa A. Exact solutions for the free vibrations of open cylindrical shells with circumferentially varying curvature and thickness. Journal of sound and vibration. 1986;107(1):1-15.
7. Sivadas K, Ganesan N. Free vibration of circular cylindrical shells with axially varying thickness. Journal of sound and vibration. 1991;147(1):73-85.
8. Zhang L, Xiang Y. Exact solutions for vibration of stepped circular cylindrical shells. Journal of sound and vibration. 2007;299(4-5):948-64.
9. Bhangale RK, Ganesan N. Free vibration studies of simply supported non-homogeneous functionally graded magneto-electro-elastic finite cylindrical shells. Journal of Sound and Vibration. 2005;288(1-2):412-22.
10. Kadoli R, Ganesan N. Buckling and free vibration analysis of functionally graded cylindrical shells subjected to a temperature-specified boundary condition. Journal of sound and vibration. 2006;289(3):450-80.
11. Paliwal D, Bhalla V. Large amplitude free vibrations of cylindrical shell on Pasternak foundations. International journal of pressure vessels and piping. 1993;54(3):387-98.
12. Chen W-q, Ding H-j, Xu R-q. On exact analysis of free vibrations of embedded transversely isotropic cylindrical shells. International journal of pressure vessels and piping. 1998;75(13):961-6.
13. Pellicano F. Vibrations of circular cylindrical shells: theory and experiments. Journal of sound and vibration. 2007;303(1-2):154-70.
14. Xuebin L. Study on free vibration analysis of circular cylindrical shells using wave propagation. Journal of sound and vibration. 2008;311(3-5):667-82.
15. Lin C-W, Bell FL. On the non-symmetric vibrations of thin cylindrical shells with clamped-clamped edges. Nuclear Engineering and Design. 1968;7(3):194-200.
16. Tottenham H, Shimizu K. Analysis of the free vibration of cantilever cylindrical thin elastic shells by the matrix progression method. International Journal of Mechanical Sciences. 1972;14(5):293-310.
17. Askari E, Daneshmand F. Coupled vibrations of cantilever cylindrical shells partially submerged in fluids with continuous, simply connected and non-convex domain. Journal of Sound and Vibration. 2010;329(17):3520-36.
18. Lee J, Leissa A, Wang A. Vibrations of cantilevered circular cylindrical shells: shallow versus deep shell theory. International Journal of Mechanical Sciences. 1983;25(5):361-83.
19. Leissa A, Lee J, Wang A. Vibrations of cantilevered doubly-curved shallow shells. International Journal of Solids and Structures. 1983;19(5):411-24.
20. Ganesan N, Sivadas K. Free vibration of cantilever circular cylindrical shells with variable thickness. Computers & structures. 1990;34(4):669-77.
21. Annigeri A, Ganesan N, Swarnamani S. Free vibrations of clamped–clamped magneto-electro-elastic cylindrical shells. Journal of Sound and Vibration. 2006;292(1-2):300-14.
22. Wong S, Bush W. Axisymmetric vibrations of a clamped cylindrical shell using matched asymptotic expansions. Journal of sound and vibration. 1993;160(3):523-31.
23. Leissa AW. Vibration of plates: Scientific and Technical Information Division, National Aeronautics and …; 1969.
24. Leissa AW. Vibration of shells: Scientific and Technical Information Office, National Aeronautics and Space …; 1973.
25. Dowell E, Ventres C. Modal equations for the nonlinear flexural vibrations of a cylindrical shell. International Journal of Solids and Structures. 1968;4(10):975-91.
26. Atluri S. A perturbation analysis of non-linear free flexural vibrations of a circular cylindrical shell. International Journal of Solids and Structures. 1972;8(4):549-69.
27. Birman V, Bert CW. Non-linear beam-type vibrations of long cylindrical shells. International journal of non-linear mechanics. 1987;22(4):327-34.
28. Chiba M. Non-linear hydroelastic vibration of a cantilever cylindrical tank—I. Experiment (empty case). International journal of non-linear mechanics. 1993;28(5):591-9.
29. Amabili M, Pellicano F, Paidoussis M. Nonlinear vibrations of simply supported, circular cylindrical shells, coupled to quiescent fluid. Journal of Fluids and Structures. 1998;12(7):883-918.
30. Amabili M, Pellicano F, Païdoussis M. Non-linear dynamics and stability of circular cylindrical shells containing flowing fluid. Part III: truncation effect without flow and experiments. Journal of Sound and Vibration. 2000;237(4):617-40.
31. Amabili M, Karagiozis K, Païdoussis M. Effect of geometric imperfections on non-linear stability of circular cylindrical shells conveying fluid. International Journal of Non-Linear Mechanics. 2009;44(3):276-89.
32. Karagiozis K, Amabili M, Païdoussis M. Nonlinear dynamics of harmonically excited circular cylindrical shells containing fluid flow. Journal of Sound and Vibration. 2010;329(18):3813-34.
33. Sun S, Liu L. Parametric study and stability analysis on nonlinear traveling wave vibrations of rotating thin cylindrical shells. Archive of Applied Mechanics. 2021;91:2833-51.
34. Pellicano F, Amabili M, Paıdoussis M. Effect of the geometry on the non-linear vibration of circular cylindrical shells. International Journal of Non-Linear Mechanics. 2002;37(7):1181-98.
35. Gonçalves P, Silva F, Del Prado Z. Low-dimensional models for the nonlinear vibration analysis of cylindrical shells based on a perturbation procedure and proper orthogonal decomposition. Journal of Sound and Vibration. 2008;315(3):641-63.
36. Amabili M, Sarkar A, Paıdoussis M. Reduced-order models for nonlinear vibrations of cylindrical shells via the proper orthogonal decomposition method. Journal of Fluids and Structures. 2003;18(2):227-50.
37. Amabili M. Nonlinear vibrations of laminated circular cylindrical shells: Comparison of different shell theories. Composite Structures. 2011;94(1):207-20.
38. Kurylov Y, Amabili M. Nonlinear vibrations of clamped-free circular cylindrical shells. Journal of sound and vibration. 2011;330(22):5363-81.
39. Jansen E. A comparison of analytical–numerical models for nonlinear vibrations of cylindrical shells. Computers & structures. 2004;82(31-32):2647-58.
40. Jansen E. A perturbation method for nonlinear vibrations of imperfect structures: application to cylindrical shell vibrations. International Journal of Solids and Structures. 2008;45(3-4):1124-45.
41. Popov A. The application of Hamiltonian dynamics and averaging to nonlinear shell vibration. Computers & structures. 2004;82(31-32):2659-70.
42. Bakhtiari-Nejad F, Bideleh SMM. Nonlinear free vibration analysis of prestressed circular cylindrical shells on the Winkler/Pasternak foundation. Thin-Walled Structures. 2012;53:26-39.
43. Leizerovich G, Seregin S. Free vibrations of circular cylindrical shells with a small added concentrated mass. Journal of Applied Mechanics and Technical Physics. 2016;57:841-6.
44. Chakravorty D, Bandyopadhyay J. Effects of release of boundary constraints on the natural frequencies of clamped, thin, cylindrical shells. Computers & structures. 1994;52(3):489-93.
45. Kovtunov V. Dynamic stability and nonlinear parametric vibration of cylindrical shells. Computers & structures. 1993;46(1):149-56.
46. Amabili M, Paı¨ doussis MP. Review of studies on geometrically nonlinear vibrations and dynamics of circular cylindrical shells and panels, with and without fluid-structure interaction. Appl Mech Rev. 2003;56(4):349-81.
47. Amabili M. Nonlinear vibrations and stability of shells and plates: Cambridge University Press; 2008.
48. Soldatos K. A comparison of some shell theories used for the dynamic analysis of cross-ply laminated circular cylindrical panels. Journal of sound and vibration. 1984;97(2):305-19.
49. Chandrashekhara K, Kumar DP. Static response of composite circular cylindrical shells studied by different theories. Meccanica. 1998;33:11-27.
50. Messina A, Soldatos KP. Vibration of completely free composite plates and cylindrical shell panels by a higher-order theory. International Journal of Mechanical Sciences. 1999;41(8):891-918.
51. Soldatos KP, Messina A. The influence of boundary conditions and transverse shear on the vibration of angle-ply laminated plates, circular cylinders and cylindrical panels. Computer methods in applied mechanics and engineering. 2001;190(18-19):2385-409.
52. Soedel W, Qatu MS. Vibrations of shells and plates. Acoustical Society of America; 2005.
53. Taracila V, Edelstein WA, Kidane TK, Eagan TP, Baig TN, Brown RW. Analytical calculation of cylindrical shell modes: Implications for MRI acoustic noise. Concepts in Magnetic Resonance Part B: Magnetic Resonance Engineering: An Educational Journal. 2005;25(1):60-4.
54. Shao W, Mechefske CK. Analysis of the sound field in finite length infinite baffled cylindrical ducts with vibrating walls of finite impedance. The Journal of the Acoustical Society of America. 2005;117(4):1728-36.
55. Li G, Mechefske CK. Structural-acoustic modal analysis of cylindrical shells: application to MRI scanner systems. Magma. 2009;22(6):353.
56. Mechefske CK, Wang F. Theoretical, numerical, and experimental modal analysis of a single-winding gradient coil insert cylinder. Magnetic Resonance Materials in Physics, Biology and Medicine. 2006;19:152-66.
57. Edelstein WA, Hedeen RA, Mallozzi RP, El-Hamamsy S-A, Ackermann RA, Havens TJ. Making MRI quieter. Magnetic Resonance Imaging. 2002;20(2):155-63.
58. Mechefske CK, Wu Y, Rutt BK. MRI gradient coil cylinder sound field simulation and measurement. J Biomech Eng. 2002;124(4):450-5.
59. Yao G, Mechefske C, Rutt B. Characterization of vibration and acoustic noise in a gradient-coil insert. Magnetic Resonance Materials in Physics, Biology and Medicine. 2004;17:12-27.
60. Wang Y, Liu F, Crozier S. Simulation study of noise reduction methods for a split MRI system using a finite element method. Medical Physics. 2015;42(12):7122-31.
61. Wang Y, Liu F, Weber E, Tang F, Jin J, Tesiram Y, et al. Acoustic analysis for a split MRI system using FE method. Concepts in Magnetic Resonance Part B: Magnetic Resonance Engineering. 2015;45(2):85-96.
62. Winkler SA, Alejski A, Wade T, McKenzie CA, Rutt BK. On the accurate analysis of vibroacoustics in head insert gradient coils. Magnetic resonance in medicine. 2017;78(4):1635-45.
63. Sakhr J, Chronik BA. Vibrational response of a MRI gradient coil cylinder to time-harmonic Lorentz-force excitations: An exact linear elastodynamic model for shielded longitudinal gradient coils. Applied Mathematical Modelling. 2019;74:350-72.
64. Sakhr J, Chronik BA. Parametric modeling of steady-state gradient coil vibration: Resonance dynamics under variations in cylinder geometry. Magnetic Resonance Imaging. 2021;82:91-103.
65. McJury M. Acoustic noise levels generated during high field MR imaging. Clinical Radiology. 1995;50(5):331-4.
66. McJury MJ. Acoustic noise and magnetic resonance imaging: a narrative/descriptive review. Journal of Magnetic Resonance Imaging. 2022;55(2):337-46.
67. McJury PhD M, Shellock PhD FG. Auditory noise associated with MR procedures: a review. Journal of Magnetic Resonance Imaging. 2000;12(1):37-45.
68. Cho Z, Park S, Kim J, Chung S, Chung S, Chung J, et al. Analysis of acoustic noise in MRI. Magnetic resonance imaging. 1997;15(7):815-22.
69. Mechefske CK, Geris R, Gati JS, Rutt BK. Acoustic noise reduction in a 4 T MRI scanner. Magnetic Resonance Materials in Physics, Biology and Medicine. 2001;13:172-6.
70. Cho Z, Chung S, Chung J, Park S, Kim J, Moon C, et al. A new silent magnetic resonance imaging using a rotating DC gradient. Magnetic resonance in medicine. 1998;39(2):317-21.
71. Crémillieux Y, Wheeler‐Kingshott CA, Briguet A, Doran SJ. STEAM‐Burst: a single‐shot, multi‐slice imaging sequence without rapid gradient switching. Magnetic resonance in medicine. 1997;38(4):645-52.
72. Goldman A, Gossman W, Friedlander P. Reduction of sound levels with antinoise in MR imaging. Radiology. 1989;173(2):549-50.
73. McJury M, Stewart R, Crawford D, Toma E. The use of active noise control (ANC) to reduce acoustic noise generated during MRI scanning: some initial results. Magnetic resonance imaging. 1997;15(3):319-22.
74. Chen CK, Chiueh T-D, Chen J-H. Active cancellation system of acoustic noise in MR imaging. IEEE transactions on biomedical engineering. 1999;46(2):186-91.
75. Li M, Lim TC, Lee J-H. Simulation study on active noise control for a 4-T MRI scanner. Magnetic resonance imaging. 2008;26(3):393-400.
76. Li M, Rudd B, Lim TC, Lee JH. In situ active control of noise in a 4 T MRI scanner. Journal of Magnetic Resonance Imaging. 2011;34(3):662-9.
77. Chambers J, Bullock D, Kahana Y, Kots A, Palmer A. Developments in active noise control sound systems for magnetic resonance imaging. Applied Acoustics. 2007;68(3):281-95.
78. Mansfield P, Glover P, Bowtell R. Active acoustic screening: design principles for quiet gradient coils in MRI. Measurement Science and Technology. 1994;5(8):1021.
79. Mansfield P, Chapman BL, Bowtell R, Glover P, Coxon R, Harvey PR. Active acoustic screening: reduction of noise in gradient coils by Lorentz force balancing. Magnetic resonance in medicine. 1995;33(2):276-81.
80. Bowtell RW, Mansfield P. Quite transverse gradiant coils: Lorentz force balanced designs using geometrical similitude. Magnetic resonance in medicine. 1995;34(3):494-7.
81. Mansfield P, Haywood B. Principles of active acoustic control in gradient coil design. Magnetic Resonance Materials in Physics, Biology and Medicine. 2000;10:147-51.
82. Mansfield P, Haywood B, Coxon R. Active acoustic control in gradient coils for MRI. Magnetic Resonance in Medicine: An Official Journal of the International Society for Magnetic Resonance in Medicine. 2001;46(4):807-18.
83. Edelstein WA, Kidane TK, Taracila V, Baig TN, Eagan TP, Cheng YCN, et al. Active‐passive gradient shielding for MRI acoustic noise reduction. Magnetic Resonance in Medicine: An Official Journal of the International Society for Magnetic Resonance in Medicine. 2005;53(5):1013-7.
84. Roozen N, Koevoets A, Den Hamer A. Active vibration control of gradient coils to reduce acoustic noise of MRI systems. IEEE/ASME Transactions on mechatronics. 2008;13(3):325-34.
85. Wang Y, Liu F, Li Y, Tang F, Crozier S. Asymmetric gradient coil design for use in a short, open bore magnetic resonance imaging scanner. Journal of Magnetic Resonance. 2016;269:203-12.
86. Li G, Mechefske CK. A comprehensive experimental study of micro-perforated panel acoustic absorbers in MRI scanners. Magnetic Resonance Materials in Physics, Biology and Medicine. 2010;23(3):177-85.
87. Nan J, Zong N, Chen Q, Zhang L, Zheng Q, Xia Y. A Structure Design Method for Reduction of MRI Acoustic Noise. Computational and Mathematical Methods in Medicine. 2017;2017:6253428.