Abstract
In this paper, vibration analysis of rotating combined thin-walled shells with multiple conical segments has been carried out. Considering the centrifugal force, Coriolis force, and initial hoop tension due to rotation, the elastic strain energy and kinetic energy of a single rotating conical shell are expressed based on Love’s first approximation theory. The artificial springs are introduced to simulate the connections of adjacent conical shells and the boundaries of the rotating combined thin-walled shells. Taking characteristic orthogonal polynomial series as the admissible functions, the Rayleigh–Ritz method is employed to derive the frequency equations of the combined shell and corresponding vibration characteristics are then obtained. Given that the cylindrical shell and annular plates can be regarded as conical shells with semi-vertex angles of 0 deg and 90 deg, respectively, the solution given is also available for the vibration analysis of rotating combined thin-walled shells comprised of any segments of cylindrical, conical shell, and annular plate. As examples of rotating combined thin-walled shells with two and five segments, vibrations of rotating conical–conical joined shell and cylindrical–conical–cylindrical–conical–cylindrical joined shell are investigated in the paper. Traveling wave frequencies and corresponding mode shapes are shown, and the effects of rotating speed, circumferential wave number, spring stiffness, and semi-vertex angles on the vibration behavior are given in detail.
Issue Section:
Research Papers
References
1.
Talebitooti
, M.
, 2016
, “Thermal Effect on Free Vibration of Ring-Stiffened Rotating Functionally Graded Conical Shell With Clamped Ends
,” Mech. Adv. Mater. Struc.
, 25
(2
), pp. 155
–165
. 2.
Daneshjou
, K.
, Talebitooti
, M.
, and Talebitooti
, R.
, 2013
, “Free Vibration and Critical Speed of Moderately Thick Rotating Laminated Composite Conical Shell Using Generalized Differential Quadrature Method
,” Appl. Math. Mech.-Engl. Ed.
, 34
(4
), pp. 437
–456
. 3.
Sun
, S.
, Cao
, D.
, and Han
, Q.
, 2013
, “Vibration Studies of Rotating Cylindrical Shells With Arbitrary Edges Using Characteristic Orthogonal Polynomials in the Rayleigh–Ritz Method
,” Int. J. Mech. Sci.
, 68
, pp. 180
–189
. 4.
Zhang
, X. M.
, Liu
, G. R.
, and Lam
, K. Y.
, 2001
, “Frequency Analysis of Cylindrical Panels Using a Wave Propagation Approach
,” Appl. Acoust.
, 62
(5
), pp. 527
–543
. 5.
Chen
, Y. H.
, Jin
, G. Y.
, and Liu
, Z. G.
, 2013
, “Free Vibration Analysis of Circular Cylindrical Shell With Non-Uniform Elastic Boundary Constraints
,” Int. J. Mech. Sci.
, 74
, pp. 120
–132
. 6.
Irie
, T.
, Yamada
, G.
, and Muramoto
, Y.
, 1984
, “Free Vibration of Joined Conical-Cylindrical Shells
,” J. Sound Vib.
, 95
(1
), pp. 31
–39
. 7.
Caresta
, M.
, and Kessissoglou
, N. J.
, 2010
, “Free Vibrational Characteristics of Isotropic Coupled Cylindrical-Conical Shells
,” J. Sound Vib.
, 329
(6
), pp. 733
–751
. 8.
Kang
, J. H.
, 2012
, “Three-Dimensional Vibration Analysis of Joined Thick Conical-Cylindrical Shells of Revolution With Variable Thickness
,” J. Sound Vib.
, 331
(18
), pp. 4187
–4198
. 9.
Qu
, Y. G.
, Chen
, Y.
, Long
, X. H.
, Hua
, H. X.
, and Meng
, G.
, 2013
, “A Variational Method for Free Vibration Analysis of Joined Cylindrical-Conical Shells
,” J. Vib. Control
, 19
(16
), pp. 2319
–2334
. 10.
Ma
, X. L.
, Jin
, G. Y.
, Xiong
, Y. P.
, and Liu
, Z. G.
, 2014
, “Free and Forced Vibration Analysis of Coupled Conical-Cylindrical Shells With Arbitrary Boundary Conditions
,” Int. J. Mech. Sci.
, 88
, pp. 122
–137
. 11.
Pang
, F. Z.
, Wu
, C.
, Song
, H. B.
, and Li
, H. C.
, 2017
, “The Free Vibration Characteristics of Isotropic Coupled Conical-Cylindrical Shells Based on the Precise Integration Transfer Matrix Method
,” Curved Layer. Struct.
, 4
(1
), pp. 272
–287
. 12.
Lee
, J.
, 2018
, “Free Vibration Analysis of Joined Conical-Cylindrical Shells by Matched Fourier-Chebyshev Collocation Method
,” J. Mech. Sci. Technol.
, 32
(10
), pp. 4601
–4612
. 13.
Zarei
, M.
, Rahimi
, G. H.
, and Hemmatnezhad
, M.
, 2021
, “On the Free Vibrations of Joined Grid-Stiffened Composite Conical-Cylindrical Shells
,” Thin Walled Struct.
, 161
, p. 107465
. 14.
Kouchakzadeh
, M. A.
, and Shakouri
, M.
, 2014
, “Free Vibration Analysis of Joined Cross-Ply Laminated Conical Shells
,” Int. J. Mech. Sci.
, 78
, pp. 118
–125
. 15.
Sarkheil
, S.
, Foumani
, M. S.
, and Navazi
, H. M.
, 2016
, “Theoretical and Experimental Analysis of the Free Vibrations of a Shell Made of N Cone Segments Joined Together
,” Thin Walled Struct.
, 108
, pp. 416
–427
. 16.
Bagheri
, H.
, Kiani
, Y.
, and Eslami
, M. R.
, 2017
, “Free Vibration of Joined Conical-Conical Shells
,” Thin Walled Struct.
, 120
, pp. 446
–457
.17.
Izadi
, M. H.
, Hosseini-Hashemi
, S.
, and Korayem
, M. H.
, 2018
, “Analytical and FEM Solutions for Free Vibration of Joined Cross-Ply Laminated Thick Conical Shells Using Shear Deformation Theory
,” Arch. Appl. Mech.
, 88
(12
), pp. 2231
–2246
. 18.
Soureshjani
, A. H.
, Talebitooti
, R.
, and Talebitooti
, M.
, 2020
, “Thermal Effects on the Free Vibration of Joined FG-CNTRC Conical-Conical Shells
,” Thin Walled Struct.
, 156
, p. 106960
. 19.
Fu
, T.
, Wu
, X.
, Xiao
, Z. M.
, Chen
, Z. B.
, and Li
, B.
, 2021
, “Analysis of Vibration Characteristics of FGM Sandwich Joined Conical-Conical Shells Surrounded by Elastic Foundations
,” Thin Walled Struct.
, 165
, p. 107979
. 20.
Damercheloo
, A. R.
, Khorshidvand
, A. R.
, Khorsandijou
, S. M.
, and Jabbari
, M.
, 2021
, “Free Vibrational Characteristics of GNP-Reinforced Joined Conical-Conical Shells With Different Boundary Conditions
,” Thin Walled Struct.
, 169
, p. 108287
. 21.
Cheng
, L.
, and Nicolas
, J.
, 1992
, “Free Vibration Analysis of a Cylindrical Shell-Circular Plate System With General Coupling and Various Boundary Conditions
,” J. Sound Vib.
, 155
(2
), pp. 231
–247
. 22.
Lee
, Y. S.
, Yang
, M. S.
, and Kim
, H. S.
, 2002
, “A Study on the Free Vibration of The Joined Cylindrical-Spherical Shell Structures
,” Comput. Civil Struct. Eng.
, 80
(27–30
), pp. 2405
–2414
.23.
Liang
, S.
, and Chen
, H. L.
, 2006
, “The Natural Vibration of a Conical Shell With an Annular End Plate
,” J. Sound Vib.
, 294
(4–5
), pp. 927
–943
. 24.
Wu
, S. H.
, Qu
, Y. G.
, and Hua
, H. X.
, 2013
, “Vibrations Characteristics of Joined Cylindrical-Spherical Shell With Elastic-Support Boundary Conditions
,” J. Mech. Sci. Technol.
, 27
(5
), pp. 1265
–1272
. 25.
Lee
, J.
, 2017
, “Free Vibration Analysis of Joined Spherical-Cylindrical Shells by Matched Fourier-Chebyshev Expansions
,” Int. J. Mech. Sci.
, 122
, pp. 53
–62
. 26.
Tang
, Q. S.
, Li
, C. F.
, She
, H. X.
, and Wen
, B. C.
, 2018
, “Vibration Analysis of Bolted Joined Cylindrical-Cylindrical Shell Structure Under General Connection Condition
,” Appl. Acoust.
, 140
, pp. 236
–247
. 27.
Bagheri
, H.
, Kiani
, Y.
, Bagheri
, N.
, and Eslami
, M. R.
, 2020
, “Free Vibration of Joined Cylindrical-Hemispherical FGM Shells
,” Arch. Appl. Mech.
, 90
(10
), pp. 2185
–2199
. 28.
He
, Q.
, Dai
, H. L.
, Gui
, Q. F.
, and Li
, J. J.
, 2020
, “Analysis of Vibration Characteristics of Joined Cylindrical-Spherical Shells
,” Eng. Struct.
, 218
, p. 110767
. 29.
Ma
, X. L.
, Jin
, G. Y.
, Shi
, S. X.
, Ye
, T. G.
, and Liu
, Z. G.
, 2017
, “An Analytical Method for Vibration Analysis of Cylindrical Shells Coupled With Annular Plate Under General Elastic Boundary and Coupling Conditions
,” J. Vib. Control
, 23
(2
), pp. 305
–328
. 30.
Wu
, S. H.
, Qu
, Y. G.
, and Hua
, H. X.
, 2013
, “Vibration Characteristics of a Spherical-Cylindrical-Spherical Shell by a Domain Decomposition Method
,” Mech. Res. Commun.
, 49
, pp. 17
–26
. 31.
Xie
, K.
, Chen
, M.
, and Li
, Z.
, 2017
, “Free and Forced Vibration Analysis of Ring-Stiffened Conical–Cylindrical–Spherical Shells Through a Semi-Analytic Method
,” ASME J. Vib. Acoust.
, 139
(3
), p. 031001
. 32.
Bagheri
, H.
, Kiani
, Y.
, and Eslami
, M. R.
, 2018
, “Free Vibration of Joined Conical-Cylindrical-Conical Shells
,” Acta Mech.
, 229
(7
), pp. 2751
–2764
. 33.
Sobhani
, E.
, Arbabian
, A.
, Civalek
, O.
, and Avcar
, M.
, 2021
, “The Free Vibration Analysis of Hybrid Porous Nanocomposite Joined Hemispherical-Cylindrical-Conical Shells
,” Eng. Comput.
, pp. 1
–28
.34.
Ninh
, D. G.
, Minh
, V. T.
, Van Tuan
, N.
, Hung
, N. C.
, and Van Phong
, D.
, 2021
, “Novel Numerical Approach for Free Vibration of Nanocomposite Joined Conical-Cylindrical-Conical Shells
,” AIAA J.
, 59
(1
), pp. 366
–378
. 35.
Sobhani
, E.
, Masoodi
, A. R.
, and Ahmadi-Pari
, A. R.
, 2021
, “Vibration of FG-CNT and FG-GNP Sandwich Composite Coupled Conical-Cylindrical-Conical Shell
,” Compos. Struct.
, 273
, p. 114281
. 36.
Sarkheil
, S.
, and Foumani
, M. S.
, 2016
, “Free Vibrational Characteristics of Rotating Joined Cylindrical-Conical Shells
,” Thin Walled Struct.
, 107
, pp. 657
–670
. 37.
Sarkheil
, S.
, Foumani
, M. S.
, and Navazi
, H. M.
, 2017
, “Free Vibrations of a Rotating Shell Made of P Joined Cones
,” Int. J. Mech. Sci.
, 124
, pp. 83
–94
. 38.
Qin
, Z. Y.
, Yang
, Z. B.
, Zu
, J.
, and Chu
, F. L.
, 2018
, “Free Vibration Analysis of Rotating Cylindrical Shells Coupled With Moderately Thick Annular Plates
,” Int. J. Mech. Sci.
, 142
, pp. 127
–139
. 39.
Chai
, Q. D.
, and Wang
, Y. Q.
, 2021
, “A General Approach for Free Vibration Analysis of Spinning Joined Conical-Cylindrical Shells With Arbitrary Boundary Conditions
,” Thin Walled Struct.
, 168
, p. 108243
. 40.
Leissa
, A. W.
, 1993
, Vibration of Shell
, Acoustical Society of America
, New York
.41.
Magrab
, E. B.
, 2000
, An Engineer’s Guide to MATLAB
, Prentice Hall
, Hoboken, NJ
.Copyright © 2022 by ASME
You do not currently have access to this content.
