Dynamics of a rotating ring-stiffened sandwich conical shell with an auxetic honeycomb core

doi:10.1007/s10483-024-3124-7

Abstract

Abstract:

The free vibration analysis of a rotating sandwich conical shell with a re-entrant auxetic honeycomb core and homogenous isotropic face layers reinforced with a ring support is studied. The shell is modeled utilizing the first-order shear deformation theory (FSDT) incorporating the relative, centripetal, and Coriolis accelerations alongside the initial hoop tension created by the rotation. The governing equations, compatibility conditions, and boundary conditions are attained using Hamilton's principle. Utilizing trigonometric functions, an analytical solution is derived in the circumferential direction, and a numerical one is presented in the meridional direction via the differential quadrature method (DQM). The effects of various factors on the critical rotational speeds and forward and backward frequencies of the shell are studied. The present work is the first theoretical work regarding the dynamic analysis of a rotating sandwich conical shell with an auxetic honeycomb core strengthened with a ring support.

Key words: free vibration, conical shell, rotating shell, ring support, auxetic honeycomb

2010 MSC Number:

74H60
74H65

S. JAHANGIRI, A. GHORBANPOUR ARANI, Z. KHODDAMI MARAGHI. Dynamics of a rotating ring-stiffened sandwich conical shell with an auxetic honeycomb core. Applied Mathematics and Mechanics (English Edition), 2024, 45(6): 963-982.

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References 45

1	YOUSEFI, A. H., MEMARZADEH, P., AFSHARI, H., and HOSSEINI, S. J. Agglomeration effects on free vibration characteristics of three-phase CNT/polymer/fiber laminated truncated conical shells. Thin-Walled Structures, 157, 107077 (2020)
2	HU, S., WANG, Q., ZHONG, R., PENG, Q., and QIN, B. A dynamic stiffness formulation for the vibration analysis of rotating cross-ply laminated coupled conical-cylindrical-conical shells. Thin-Walled Structures, 182, 110230 (2023)
3	AMIRABADI, H., AFSHARI, H., SARAFRAZ, M., and RAHMANI, S. Effects of non-uniformity in thickness and volume fraction of agglomerated CNTs on the dynamics of a spinning CNT-reinforced nanocomposite truncated conical shell. Noise & Vibration Worldwide, 55, 167- 185 (2024)
4	ZHUO, X., XU, P. Y., LI, H., CHU, C., SUN, P. Y., GU, D. W., SHI, D. S., LI, H., HAN, Q. K., and WEN, B. C. The analysis of nonlinear vibration characteristics of fiber-reinforced composite thin wall truncated conical shell: theoretical and experimental investigation. European Journal of Mechanics-A/Solids, 105, 105268 (2024)
5	LI, X., ZHAO, S., QIU, S., WANG, D., CHEN, J., ZHANG, C., and QU, Y. Theoretical analysis for free vibration of submerged conical motor stator. Applied Ocean Research, 142, 103809 (2024)
6	HE, H., CHEN, X. Q., JIANG, F., and AFSHARI, H. Dynamics of a spinning three-phase polymer/fiber/GNP laminated nanocomposite conical shell with non-uniform thickness. International Journal of Structural Stability and Dynamics, (2024) doi: 10.1142/S0219455424501189
7	PAL, S., ROUT, M., SINGHA, T. O., and KARMAKAR, A. Thermoelastic free vibration of rotating pretwisted porous p-FGM, e-FGM, and s-FGM conical shells in nonlinear temperature distribution. Journal of Vibration and Control, (2024) doi: 10.1177/10775463241240625
8	MOHAMMADLOU, V., KHODDAMI MARAGHI, Z., and GHORBANPOUR ARANI, A. Thermoelastic analysis of axisymmetric conical shells: investigating stress-strain response under uniform heat flow with semi-coupled approach. Numerical Heat Transfer, Part A: Applications, (2024) doi: 10.1080/10407782.2024.2326943
9	KHODDAMI MARAGHI, Z., AMIR, S., and ARSHID, E. On the natural frequencies of smart circular plates with magnetorheological fluid core embedded between magnetostrictive patches on Kerr elastic substance. Mechanics Based Design of Structures and Machines, 52 (3), 1651- 1668 (2024)
10	GHORBANPOUR-ARANI, A., KHODDAMI MARAGHI, Z., and GHORBANPOUR ARANI, A. The frequency response of intelligent composite sandwich plate under biaxial in-plane forces. Journal of Solid Mechanics, 15 (1), 1- 18 (2023)
11	EIPAKCHI, H., and NASREKANI, F. M. A closed-form solution for asymmetric free vibration analysis of composite cylindrical shells with metamaterial honeycomb core layer based on shear deformation theory. Mechanics Based Design of Structures and Machines, 51 (11), 6513- 6531 (2023)
12	SOLEIMANI-JAVID, Z., AMIR, S., and KHODDAMI MARAGHI, Z. Vibration analysis of sandwich beam with honeycomb core and piezoelectric facesheets affected by PD controller. Smart Structures and Systems, 28 (2), 195- 212 (2021)
13	GIBSON, L. J., ASHBY, M. F., SCHAJER, G., and ROBERTSON, C. The mechanics of two-dimensional cellular materials. Mathematical and Physical Sciences, 382 (1782), 25- 42 (1982)
14	QI, C., REMENNIKOV, A., PEI, L. Z., YANG, S., YU, Z. H., and NGO, T. D. Impact and close-in blast response of auxetic honeycomb-cored sandwich panels: experimental tests and numerical simulations. Composite Structures, 180, 161- 178 (2017)
15	DUC, N. D., EOCK, K. S., CONG, P. H., ANH, N. T., and KHOA, N. D. Dynamic response and vibration of composite double curved shallow shells with negative Poisson's ratio in auxetic honeycombs core layer on elastic foundations subjected to blast and damping loads. International Journal of Mechanical Sciences, 133, 504- 512 (2017)
16	ZHU, X., ZHANG, J., ZHANG, W., and CHEN, J. Vibration frequencies and energies of an auxetic honeycomb sandwich plate. Mechanics of Advanced Materials and Structures, 26 (23), 1951- 1957 (2019)
17	EIPAKCHI, H., and NASREKANI, F. M. Vibrational behavior of composite cylindrical shells with auxetic honeycombs core layer subjected to a moving pressure. Composite Structures, 254, 112847 (2020)
18	NGUYEN, N. V., NGUYEN-XUAN, H., NGUYEN, T. N., KANG, J., and LEE, J. A comprehensive analysis of auxetic honeycomb sandwich plates with graphene nanoplatelets reinforcement. Composite Structures, 259, 113213 (2021)
19	QUYEN, N. V., TANH, N. V., QUAN, T. Q., and DUC, N. D. Nonlinear forced vibration of sandwich cylindrical panel with negative Poisson's ratio auxetic honeycombs core and CNTRC face sheets. Thin-Walled Structures, 162, 107571 (2021)
20	XU, F., YU, K., and HUA, L. In-plane dynamic response and multi-objective optimization of negative Poisson's ratio (NPR) honeycomb structures with sinusoidal curve. Composite Structures, 269, 114018 (2021)
21	XIAO, P., ZHANG, Y. F., JIE, S., and ZHENG, S. Global buckling analysis of composite honeycomb sandwich plate with negative Poisson's ratio (CHSP-NPR) using variational asymptotic equivalent model. Composite Structures, 264, 113721 (2021)
22	SARAFRAZ, M., SEIDI, H., KAKAVAND, F., and VILIANI, N. S. Free vibration and buckling analyses of a rectangular sandwich plate with an auxetic honeycomb core and laminated three-phase polymer/GNP/fiber face sheets. Thin-Walled Structures, 183, 110331 (2023)
23	SARAFRAZ, M., SEIDI, H., KAKAVAND, F., and VILIANI, N. S. Flutter characteristics of a rectangular sandwich plate with laminated three-phase polymer/GNP/fiber face sheets and an auxetic honeycomb core in yawed supersonic fluid flow. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 45 (4), 197 (2023)
24	RAHMANI, S., SEIDI, H., KAKAVAND, F., and SOLTANI, E. Flutter analysis of a cantilever trapezoidal sandwich plate with an auxetic honeycomb core and three-phase nanocomposite face sheets subjected to yawed supersonic gas flow. International Journal of Structural Stability and Dynamics, (2023) doi: 10.1142/S0219455424501797
25	RAHMANI, S., SEIDI, H., KAKAVAND, F., and SOLTANI, E. Free vibration analysis of a cantilever trapezoidal sandwich plate with an auxetic reentrant honeycomb core and laminated nanocomposite polymer/CNT/fiber face sheets. Mechanics Based Design of Structures and Machines, (2023) doi: 10.1080/15397734.2023.2288663
26	AMIRABADI, H., MOTTAGHI, A., SARAFRAZ, M., and AFSHARI, H. Free vibrational behavior of a conical sandwich shell with a functionally graded auxetic honeycomb core. Journal of Vibration and Control, (2024) doi: 10.1177/10775463241240215
27	AFSHARI, H., ARIASERESHT, Y., KOLOOR, S. S. R., AMIRABADI, H., and BIDGOLI, M. O. Supersonic flutter behavior of a polymeric truncated conical shell reinforced with agglomerated CNTs. Waves in Random and Complex Media, (2022) doi: 10.1080/17455030.2022.2082581
28	YANG, S. W., HAO, Y. X., ZHANG, W., YANG, L., and LIU, L. T. Nonlinear vibration of functionally graded graphene platelet-reinforced composite truncated conical shell using first-order shear deformation theory. Applied Mathematics and Mechanics (Englis Edition), 42 (7), 981- 998 (2021) doi: 10.1007/s10483-021-2747-9
29	AFSHARI, H. Free vibration analysis of GNP-reinforced truncated conical shells with different boundary conditions. Australian Journal of Mechanical Engineering, 20 (5), 1363- 1378 (2022)
30	REDDY, J. N. Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, CRC Press, Florida (2003)
31	KANEKO, T. On Timoshenko's correction for shear in vibrating beams. Journal of Physics D: Applied Physics, 8 (16), 1927 (1975)
32	AFSHARI, H., and AMIRABADI, H. Vibration characteristics of rotating truncated conical shells reinforced with agglomerated carbon nanotubes. Journal of Vibration and Control, 28 (15-16), 1894- 1914 (2022)
33	DANESHJOU, K., TALEBITOOTI, M., and TALEBITOOTI, R. Free vibration and critical speed of moderately thick rotating laminated composite conical shell using generalized differential quadrature method. Applied Mathematics and Mechanics (English Edition), 34 (4), 437- 456 (2013) doi: 10.1007/s10483-013-1682-8
34	REDDY, J. N. Energy Principles and Variational Methods in Applied Mechanics, John Wiley & Sons, New York (2017)
35	QINKAI, H., and FULEI, C. Parametric instability of a rotating truncated conical shell subjected to periodic axial loads. Mechanics Research Communications, 53, 63- 74 (2013)
36	DONG, Y., LI, Y., CHEN, D., and YANG, J. Vibration characteristics of functionally graded graphene reinforced porous nanocomposite cylindrical shells with spinning motion. Composites Part B: Engineering, 145, 1- 13 (2018)
37	DONG, Y., ZHU, B., WANG, Y., LI, Y., and YANG, J. Nonlinear free vibration of graded graphene reinforced cylindrical shells: effects of spinning motion and axial load. Journal of Sound and Vibration, 437, 79- 96 (2018)
38	LI, H., LAM, K. Y., and NG, T. Y. Rotating Shell Dynamics, Elsevier, Amsterdam (2005)
39	AMABILI, M. Non-linearities in rotation and thickness deformation in a new third-order thickness deformation theory for static and dynamic analysis of isotropic and laminated doubly curved shells. International Journal of Non-Linear Mechanics, 69, 109- 128 (2015)
40	BELLMAN, R., KASHEF, B., and CASTI, J. Differential quadrature: a technique for the rapid solution of nonlinear partial differential equations. Journal of Computational Physics, 10 (1), 40- 52 (1972)
41	BERT, C. W., and MALEKI, M. Differential quadrature method in computational mechanics: a review. Applied Mechanics Reviews, 49 (1), 1- 28 (1996)
42	GENTA, G. Dynamics of Rotating Systems, Springer Science & Business Media, Berlin (2005)
43	BAGHERI, H., KIANI, Y., and ESLAMI, M. Free vibration of conical shells with intermediate ring support. Aerospace Science and Technology, 69, 321- 332 (2017)
44	DAI, Q., CAO, Q., and CHEN, Y. Frequency analysis of rotating truncated conical shells using the Haar wavelet method. Applied Mathematical Modelling, 57, 603- 613 (2018)
45	ADAB, N., AREFI, M., and AMABILI, M. A comprehensive vibration analysis of rotating truncated sandwich conical microshells including porous core and GPL-reinforced face-sheets. Composite Structures, 279, 114761 (2022)

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