Graphical Abstract Figure
Abstract
This study investigates the theoretical and experimental aspects of the vibro-acoustic characteristics of cylindrical shells with internal substructures. On the theoretical side, a hybrid calculation method is proposed, which combines the condensed transfer function method with the direct stiffness method and the precise transfer matrix method. The cylindrical shell with internal substructures is decoupled, and the governing equations for the cylindrical shell substructure and the internal substructure are separately established. Furthermore, the coupling forces between the cylindrical shell substructure and the plate substructure are solved based on the condensed transfer function method. These coupling forces are then incorporated into the overall transfer equation of the cylindrical shell to obtain the vibro-acoustic response of the coupled structure. Compared with the finite element calculation results, the validity of the calculation method in this paper is verified. In terms of experiments, the natural frequency, mode, and vibration acoustic response of the model were tested and compared with the theoretical results, which was in good agreement. The study demonstrates that the proposed hybrid calculation method based on the condensed transfer function is effective in predicting the vibro-acoustic characteristics of cylindrical shells with internal substructures.
References
1.
Leissa
, A. W.
, and Nordgren
, R. P.
, 1993
, “Vibration of Shells
,” ASME J. Appl. Mech.
, 41
(2
), p. 544
. 2.
Qatu
, M. S.
, 2002
, “Recent Research Advances in the Dynamic Behavior of Shells: 1989–2000, Part 1: Laminated Composite Shells
,” ASME Appl. Mech. Rev.
, 55
(4
), pp. 325
–350
. 3.
Qatu
, M. S.
, 2002
, “Recent Research Advances in the Dynamic Behavior of Shells: 1989–2000, Part 2: Homogeneous Shells
,” ASME Appl. Mech. Rev.
, 55
(5
) pp. 415
–434
. 4.
Peterson
, M. R.
, and Boyd
, D. E.
, 1978
, “Free Vibrations of Circular Cylinders With Longitudinal Interior Partitions
,” J. Sound Vib.
, 60
(1
), pp. 45
–62
. 5.
Guo
, Y. P.
, 1996
, “Acoustic Scattering From Cylindrical Shells With Deck-Type Internal Plate at Oblique Incidence
,” J. Acoust. Soc. Am.
, 99
(5
), pp. 2701
–2713
. 6.
Guo
, Y. P.
, 1992
, “Sound Scattering From an Internally Loaded Cylindrical Shell
,” J. Acoust. Soc. Am.
, 91
(2
), pp. 926
–938
. 7.
Guo
, Y. P.
, 1994
, “Sound Scattering by Bulkheads in Cylindrical Shells
,” J. Acoust. Soc. Am.
, 95
(5
), pp. 2550
–2559
. 8.
Tso
, Y. K.
, and Hansen
, C. H.
, 1995
, “Wave Propagation Through Cylinder/Plate Junctions
,” J. Sound Vib.
, 186
(3
), pp. 447
–461
. 9.
Lee
, Y. S.
, Choi
, M. H.
, and Kim
, J. H.
, 2003
, “Free Vibrations of Laminated Composite Cylindrical Shells With an Interior Rectangular Plate
,” J. Sound Vib.
, 265
(4
), pp. 795
–817
. 10.
Haft
, E. E.
, and Smith
, B. L.
, 2012
, “Vibration of a Circular Cylindrical Shell Closed by an Elastic Plate
,” AIAA J.
, 5
(11
), pp. 2080
–2082
. 11.
Maxit
, L.
, and Ginoux
, J. M.
, 2010
, “Prediction of the Vibro-Acoustic Behavior of a Submerged Shell Non Periodically Stiffened by Internal Frames
,” J. Acoust. Soc. Am.
, 128
(1
), pp. 137
–151
. 12.
Takahashi
, S.
, and Hirano
, Y.
, 2008
, “Vibration of a Combination of Circular Plates and Cylindrical Shells: 1st Report, A Cylindrical Shell With Circular Plates at Ends
,” Bull. JSME
, 35
(274
), pp. 1215
–1222
. 13.
Huang
, D. T.
, and Soedel
, W.
, 1993
, “Study of the Forced Vibration of Shell-Plate Combinations Using the Receptance Method
,” J. Sound Vib.
, 166
(2
), pp. 341
–369
. 14.
Missaoui
, J.
, and Cheng
, L.
, 1999
, “Vibroacoustic Analysis of a Finite Cylindrical Shell With Internal Floor Partition
,” J. Sound Vib.
, 226
(1
), pp. 101
–123
. 15.
Missaoui
, J.
, Cheng
, L.
, and Richard
, M. J.
, 1996
, “Free and Forced Vibration of a Cylindrical Shell With a Floor Partition
,” J. Sound Vib.
, 190
(1
), pp. 21
–40
. 16.
Danial
, A. N.
, and Doyle
, J. F.
, 1995
, “Dynamic Analysis of Folded Plate Structures on a Massively Parallel Computer
,” Comput. Struct.
, 54
(3
), pp. 521
–529
. 17.
Casimir
, J. B.
, Kevorkian
, S.
, and Vinh
, T.
, 2005
, “The Dynamic Stiffness Matrix of Two-Dimensional Elements: Application to Kirchhoff’s Plate Continuous Elements
,” J. Sound Vib.
, 287
(3
), pp. 571
–589
. 18.
Li
, H.
, Yin
, X.
, and Wu
, W.
, 2016
, “Dynamic Stiffness Formulation for In-Plane and Bending Vibrations of Plates With Two Opposite Edges Simply Supported
,” J. Vib. Control
, 24
(9
), pp. 1652
–1669
. 19.
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
. 20.
Wang
, X.
, Jiang
, Q.
, Xiong
, Y.
, and Gu
, X.
, 2020
, “Experimental Studies on the Vibro-Acoustic Behavior of a Stiffened Submerged Conical-Cylindrical Shell Subjected to Force and Acoustic Excitation
,” J. Low Freq. Noise Vib. Act. Control
, 39
(2
), pp. 280
–296
. 21.
Wang
, X.
, Chen
, L.
, Li
, N.
, Xia
, Y.
, and Xiong
, Y.
, 2020
, “An Experimental and Modeling Study on Vibro-Acoustic Response of Double-Walled Steel Cylindrical Shells
,” Int. J. Steel Struct.
, 20
(4
), pp. 1081
–1099
. 22.
Jiammeepreecha
, W.
, and Chucheepsakul
, S.
, 2017
, “Nonlinear Axisymmetric Free Vibration Analysis of Liquid-Filled Spherical Shell With Volume Constraint
,” ASME J. Vib. Acoust.
, 139
(5
), p. 051016
. 23.
Zhang
, Q.
, Mao
, Y.
, and Qi
, D.
, 2018
, “Analytical Modeling of the Vibro-Acoustic Response of a Double-Walled Cylindrical Shell With Microperforation Excited by Turbulent Boundary Layer Pressure Fluctuations
,” ASME J. Vib. Acoust.
, 140
(2
), p. 021012
. 24.
Gao
, H.
, Shuai
, C.
, Ma
, J.
, and Xu
, G.
, 2022
, “Free Vibration of Rubber Matrix Cord-Reinforced Combined Shells of Revolution Under Hydrostatic Pressure
,” ASME J. Vib. Acoust.
, 144
(1
), p. 011002
. 25.
Meyer
, V.
, Maxit
, L.
, Guyader
, J. L.
, Leissing
, T.
, and Audoly
, C.
, 2015
, “A Condensed Transfer Function Method as a Tool for Solving Vibroacoustic Problems
,” Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci.
, 230
(6
), pp. 928
–938
. 26.
Meyer
, V.
, Maxit
, L.
, Guyader
J. L.
, and Leissing
, T.
, 2016
, “Prediction of the Vibroacoustic Behavior of a Submerged Shell With Non-Axisymmetric Internal Substructures by a Condensed Transfer Function Method
,” J. Sound Vib.
, 360
, pp. 260
–276
. 27.
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
, p. 111960
. 28.
Jia
, W.
, Chen
, M.
, Xie
, K.
, and Zhou
, Z.
, 2023
, “Theoretical and Experimental Studies of Effects of Non-Axisymmetric Inner Structures on Vibration Signatures of Axisymmetric Submarine Hulls
,” Appl. Math. Model.
, 120
, pp. 485
–512
. 29.
Li
, Z.
, Jin
, G.
, Ye
, T.
, Yang
, T. J.
, Tang
, T.
, Zhong
, S.
, and Tian
, L.
, 2023
, “A Unified Vibration Modeling of Open Cylindrical Shell-Rectangular Plate Coupling Structures Based on the Dynamic Stiffness Method
,” J. Sound Vib.
, 563
, p. 117870
. 30.
Su
, J.
, Lei
, Z.
, Qu
, Y.
, and Hua
, 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
. 
