Nonlinear combined resonance of axially moving conical shells under interaction between transverse and parametric modes. (English) Zbl 1534.74033
Summary: The purpose of present paper is to establish a conical shell model for exploring combined resonance response of axially moving graphene platelets reinforced metal foams (GPLRMF) conical shells subjected to coupled external and parametric excitations in thermal environments. The Reddy’s higher order shear deformation theory (HSDT) is applied to derive the stress-strain relationship, and the governing equations of the shell structure are obtained using Hamilton’s principle. The displacements and boundary conditions are characterized by a set of displacement shape functions with orthogonal properties. Then, the combined resonant for the conical shell are solved, where the method of varying amplitude (MVA) is adopted for discretizing and formulating the nonlinear governing motion equations. The correctness of the steady-state approximate solutions is verified by conducting comparative analysis, where the existing valuable literature is served as reference. In addition, the effects of initial phase angle, damping interference, material property, axially moving velocity, temperature change, coning angle as well as external excitation amplitude on the vibrational mechanism are analyzed, and the jumping phenomenon, bifurcation behavior, and chaotic characteristics are discussed in detail.
MSC:
| 74H45 | Vibrations in dynamical problems in solid mechanics |
| 74H60 | Dynamical bifurcation of solutions to dynamical problems in solid mechanics |
| 74H65 | Chaotic behavior of solutions to dynamical problems in solid mechanics |
| 74K25 | Shells |
| 74E30 | Composite and mixture properties |
| 74H15 | Numerical approximation of solutions of dynamical problems in solid mechanics |
Keywords:
Reddy higher-order shear deformation theory; Hamilton principle; graphene platelet; reinforced metal foam; bifurcation; chaotic behavior; method of varying amplitudesReferences:
| [1] | Banerjee, R.; Rout, M.; Karmakar, A.; Bose, D., Low-velocity impact response of hybrid CNTs reinforced conical shell under hygrothermal conditions, Fiber Polym, 24, 8, 2849-2866, (2023) |
| [2] | Wang, C. G.; Song, X. Y.; Zang, J.; Zhang, Y. W., Experimental and theoretical investigation on vibration of laminated composite conical-cylindrical-combining shells with elastic foundation in hygrothermal environment, Compos Struct, 323, Article 117470 pp., (2023) |
| [3] | Zhu, Z. Y.; Zhang, Y. F.; Xu, R. K.; Zhao, L.; Wang, G.; Liu, Q. S., Analysis of thermal-vibration coupling modeling of combined conical-cylindrical shell under complex boundary conditions, J Vib Control, Article 10775463231193254 pp., (2023) |
| [4] | Karimiasl, M.; Alibeigloo, A., Nonlinear vibration characteristic of FGM sandwich cylindrical panel with auxetic core subjected to the temperature gradient, Commun Nonlinear Sci, 123, Article 107267 pp., (2023) · Zbl 1518.35587 |
| [5] | Hao, Y. X.; Li, H.; Zhang, W.; Gu, X. J.; Yang, S. W., Nonlinear vibration of porous truncated conical shell under unified boundary condition and mechanical load, Thin Wall Struct, 195, Article 111355 pp., (2023) |
| [6] | Li, H.; Hao, Y. X.; Zhang, W.; Liu, L. T.; Yang, S. W.; Cao, Y. T., Natural vibration of an elastically supported porous truncated joined conical-conical shells using artificial spring technology and generalized differential quadrature method, Aerosp Sci Technol, 121, Article 107385 pp., (2022) |
| [7] | Huang, Q. Y.; Gao, Y.; Hua, F. F.; Fu, W. B.; You, Q. Q.; Gao, J.; Zhou, X. Q., Free vibration analysis of carbon-fiber plain woven reinforced composite conical-cylindrical shell under thermal environment with general boundary conditions, Compos Struct, 322, Article 117340 pp., (2023) |
| [8] | Dastjerdi, S.; Malikan, M.; Akgöz, B., On analysis of nanocomposite conical structures, Int J Eng Sci, 191, Article 103918 pp., (2023) · Zbl 07729808 |
| [9] | Wu, J. H.; Sun, Y. D.; Duan, Y., Exact solutions for free and forced vibrations of cross-ply composite laminated combined conical-cylindrical shells with arbitrary boundary conditions, Ocean Eng, 285, 1, Article 115371 pp., (2023) |
| [10] | Song, X. Y.; Wang, C. G.; Wang, S.; Zhang, Y. W., Vibration evolution of laminated composite conical shell with arbitrary foundation in hygrothermal environment: experimental and theoretical investigation, Mech Syst Signal Pr, 200, Article 110565 pp., (2023) |
| [11] | Wang, Y. Q.; Chai, Q. D.; Xing, W. C., Vibrations of joined conical-cylindrical shells with bolt connections: theory and experiment, J Sound Vib, 554, Article 117695 pp., (2023) |
| [12] | Sun, Y. H.; Song, Z. G., A method for dynamic analysis and design of joined conical-cylindrical shells based on the model condensation, Appl Math Model, 119, 354-372, (2023) |
| [13] | Zhu, Z. Y.; Wang, G.; Xuan, Z. H.; Xu, R. K.; Zhang, Y. F.; He, Y. J.; Liu, Q. S., Vibration analysis of the combined conical-cylindrical shells coupled with annular plates in thermal environment, Thin Wall Struct, 185, Article 110640 pp., (2023) |
| [14] | Peng, Q.; Wang, Q. S.; Chen, Z. X.; Zhong, R.; Liu, T.; Qin, B., Dynamic stiffness formulation for free vibration analysis of rotating cross-ply laminated combined elliptical-cylindrical-conical shell, Ocean Eng, 269, Article 113486 pp., (2023) |
| [15] | Yang, S. W.; Hao, Y. X.; Zhang, W.; Yang, L.; Liu, L. T., Nonlinear vibration of functionally graded graphene platelet-reinforced composite truncated conical shell using first-order shear deformation theory, Appl Math Mech-Engl, 42, 7, 981-998, (2021) · Zbl 1481.74331 |
| [16] | Wang, Z. Q.; Yang, S. W.; Hao, Y. X.; Zhang, W.; Ma, W. S.; Zhang, X. D., Modeling and free vibration analysis of variable stiffness system for sandwich conical shell structures with variable thickness, Int J Struct Stab Dyn, 23, 15, (2023) · Zbl 1537.74141 |
| [17] | Yang, S. W.; Zhang, W.; Hao, Y. X.; Niu, Y., Nonlinear vibrations of FGM truncated conical shell under aerodynamics and in-plane force along meridian near internal resonances, Thin Wall Struct, 142, 369-391, (2019) |
| [18] | Hao, Y.; Li, H.; Zhang, W.; Ge, X.; Yang, S.; Cao, Y., Active vibration control of smart porous conical shell with elastic boundary under impact loadings using GDQM and IQM, Thin Wall Struct, 175, Article 109232 pp., (2022) |
| [19] | Li, H.; Hao, Y. X.; Zhang, W.; Liu, L. T.; Yang, S. W.; Wang, D. M., Vibration analysis of porous metal foam truncated conical shells with general boundary conditions using GDQ, Compos Struct, 269, Article 114036 pp., (2021) |
| [20] | Sahoo, P. K.; Chatterjee, S., Vibrational control and resonance of a nonlinear tilted cantilever beam under multi-harmonic low and high-frequency excitations, Commun Nonlinear Sci, 125, Article 107386 pp., (2023) · Zbl 1536.74078 |
| [21] | Wei, M. K.; Han, X. J.; Bi, Q. S., Route to mixed-mode oscillations via step-shaped sharp transition of equilibria in a nonlinear gyroscope oscillator, Commun Nonlinear Sci, 127, Article 107545 pp., (2023) |
| [22] | Yuan, Q.; Kang, H. J.; Zhao, Y. B.; Cong, Y. Y.; Su, X. Y., Parametric resonance of multi-frequency excited MEMS based on homotopy analysis method, Commun Nonlinear Sci, 125, Article 107351 pp., (2023) · Zbl 1538.74069 |
| [23] | Ding, H. X.; She, G. L., Nonlinear primary resonance behavior of graphene platelet-reinforced metal foams conical shells under axial motion, Nonlinear Dyn, 111, 15, 13723-13752, (2023) |
| [24] | Ghayesh, M. H.; Farajpour, A.; Farokhi, H., Viscoelastically coupled mechanics of fluid-conveying microtubes, Internat J Engrg Sci, 145, Article 103139 pp., (2019) · Zbl 1476.74028 |
| [25] | Ghayesh, M. H.; Farokhi, H.; Farajpour, A., Viscoelastically coupled in-plane and transverse dynamics of imperfect microplates, Thin Walled Struct, 150, Article 106117 pp., (2020) |
| [26] | Sun, S.; Liu, L., Multiple internal resonances in nonlinear vibrations of rotating thin-walled cylindrical shells, J Sound Vib, 510, Article 116313 pp., (2021) |
| [27] | Jahangiri, R.; Rezaee, M.; Manafi, H., Nonlinear and chaotic vibrations of FG double curved sandwich shallow shells resting on visco-elastic nonlinear hetenyi foundation under combined resonances, Compos Struct, 295, Article 115721 pp., (2022) |
| [28] | Wang, D.; Bai, C.; Zhang, H., Nonlinear vibrations of fluidconveying FG cylindrical shells with piezoelectric actuator layer and subjected to external and piezoelectric parametric excitations, Compos Struct, 248, Article 112437 pp., (2020) |
| [29] | Demsic, M.; Urosˇ, M.; Lazarevic, A. J.; Lazarevic, D., Resonance regions due to interaction of forced and parametric vibration of a parabolic cable, J Sound Vib, 447, 78-104, (2019) |
| [30] | Mao, X. Y.; Ding, H.; Chen, L. Q., Dynamics of a supercritically axially moving beam with parametric and forced resonance, Nonlinear Dyn, 89, 2, 1475-1487, (2017) |
| [31] | Latalski, J.; Warminski, J., Primary and combined multi-frequency parametric resonances of a rotating thin-walled composite beam under harmonic base excitation, J Sound Vib, 523, Article 116680 pp., (2022) |
| [32] | Takahashi, K., Dynamic stability of cables subjected to an axial periodic load, J Sound Vib, 144, 2, 323-330, (1991) |
| [33] | Lilien, Jl; Dacosta, Ap, Vibration amplitudes caused by parametric excitation of cable stayed structures, J Sound Vib, 174, 1, 69-90, (1994) · Zbl 1147.74344 |
| [34] | Chen, H. Y.; Wang, Y. C.; Wang, D.; Xie, K., Effect of axial load and thermal heating on dynamic characteristics of axially moving Timoshenko beam, Int J Struct Stab Dyn, Article 2350191 pp., (2023) · Zbl 1532.74027 |
| [35] | Wang, Y. B.; Fang, X. R.; Ding, H.; Chen, L. Q., Quasi-periodic vibration of an axially moving beam under conveying harmonic varying mass, Appl Math Model, 123, 644-658, (2023) |
| [36] | Raj, S. K.; Sahoo, B.; Nayak, A. R.; Panda, L. N., Parametric analysis of an axially moving beam with time-dependent velocity, longitudinally varying tension and subjected to internal resonance, Arch Appl Mech, 94, 1-20, (2024) |
| [37] | Hu, Y. D.; Xie, M. X., Magnetoelastic simultaneous resonance of axially moving plate strip under a line load in stationary magnetic field, Thin Walled Struct, 185, Article 110607 pp., (2023) |
| [38] | Hu, Y.; Cao, T., Magnetoelastic primary resonance of an axially moving ferromagnetic plate in an air gap field, Appl Math Model, 118, 370-392, (2023) · Zbl 1510.74079 |
| [39] | Qiao, Y.; Yao, G., Stability and nonlinear vibration of an axially moving plate interacting with magnetic field and subsonic airflow in a narrow gap, Nonlinear Dyn, 110, 4, 3187-3208, (2022) |
| [40] | Cao, T. X.; Hu, Y. D., Magnetoelastic primary resonance and bifurcation of an axially moving ferromagnetic plate under harmonic magnetic force, Commun Nonlinear Sci, 117, Article 106974 pp., (2023) · Zbl 1506.74132 |
| [41] | Oveissi, S.; Ghassemi, A.; Salehi, M.; Eftekhari, S. A.; Ziaei-Rad, S., Hydro-Hygro-Thermo-Magneto-Electro elastic wave propagation of axially moving nano-cylindrical shells conveying various magnetic-nano-fluids resting on the electromagnetic-visco-Pasternak medium, Thin Wall Struct, 173, Article 108926 pp., (2022) |
| [42] | Mohamadi, A.; Ghasemi, F. A.; Shahgholi, M., Nonlinear vibration, stability, and bifurcation analysis of axially moving and spinning cylindrical shells, Mech Des Struct, 51, 7, 4032-4062, (2023) |
| [43] | Li, M.; Li, Y. Q.; Liu, X. H.; Dai, F. H.; Yu, D., Forced vibration of an axially moving laminated composite cylindrical shallow shell, Meccanica, (2023) · Zbl 1532.74046 |
| [44] | Yang, S. W.; Hao, Y. X.; Zhang, W.; Ma, W. S.; Wu, M. Q., Nonlinear frequency and bifurcation of carbon fiber-reinforced polymer truncated laminated conical shell, J Vib Eng Technol, (2023) |
| [45] | Cho, J. R., Large amplitude vibration of FG-GPL reinforced conical shell panels on elastic foundation, Materials (Basel), 16, 17, (2023) |
| [46] | Banijamali, S. M.; Jafari, A. A., length Vibration analysis and critical speeds of a rotating functionally graded conical shell stiffened with Anisogrid lattice structure based on FSDT, Thin Wall Struct, 188, Article 110841 pp., (2023) |
| [47] | Xia, L. Q.; Wang, R. Q.; Chen, G.; Asemi, K.; Tounsi, A., The finite element method for dynamics of FG porous truncated conical panels reinforced with graphene platelets based on the 3-D elasticity, Adv Nano Res, 14, 4, 375-389, (2023) |
| [48] | Ding H.X., She G.L. Nonlinear combined resonances of axially moving graphene platelets reinforced metal foams cylindrical shells under forced vibrations. Nonlinear Dyn 2023. 10.1007/s11071-023-09059-5. |
| [49] | Zhang, Y. W.; She, G. L., Combined resonance of graphene platelets reinforced metal foams cylindrical shells with spinning motion under nonlinear forced vibration, Eng Struct, 300, Article 117177 pp., (2024) |
| [50] | Zhang, Y. W.; She, G. L., Nonlinear transient response of graphene platelets reinforced metal foams annular plate considering rotating motion and initial geometric imperfection, Aerosp Sci Technol, 142, Article 108693 pp., (2023) |
| [51] | Gibson, I. J.; Ashby, M. F., The mechanics of three-dimensional cellular materials, Proc R Soc Lond A, 382, 1782, 43-59, (1982) |
| [52] | Choi, J.; Lakes, R., Analysis of elastic modulus of conventional foams and of re-entrant foam materials with a negative poisson’s ratio, Int J Mech Sci, 37, 51-59, (1995) · Zbl 0819.73002 |
| [53] | Ashby, M. F.; Evans, T.; Fleck, N. A.; Hutchinson, J.; Wadley, H.; Gibson, L., Metal foams: a design guide, (2000), Butterworth-Heinemann |
| [54] | Halpin, J. C.; Kardos, J. L., The Halpin-Tsai equations: a review, Polym Eng Sci, 16, 344-352, (1976) |
| [55] | de Villoria, R. G.; Miravete, A., Mechanical model to evaluate the effect of the dispersion in nanocomposites, Acta Mater, 55, 3025-3031, (2007) |
| [56] | Rafiee, M. A.; Rafiee, J.; Wang, Z.; Song, H. H.; Yu, Z. Z.; Koratkar, N., Enhanced mechanical properties of nanocomposites at low graphene content, ACS Nano, 3, 12, 3884-3890, (2009) |
| [57] | Ke, L. L.; Yang, J.; Kitipornchai, S., Nonlinear free vibration of functionally graded carbon nanotube-reinforced composite beams, Compos Struct, 92, 676-683, (2010) |
| [58] | Reddy, J. N., A simple higher-order theory for laminated composite plates, J Appl Mech-T Asme, 51, 4, 745-752, (1984) · Zbl 0549.73062 |
| [59] | Akbari, M.; Kiani, Y.; Aghdam, M. M.; Eslami, M. R., Free vibration of FGM Lévy conical panels, Compos Struct, 116, 732-746, (2014) |
| [60] | Aghamohammadi, M.; Sorokin, V.; Mace, B., Dynamic analysis of the response of Duffing-type oscillators subject to interacting parametric and external excitations, Nonlinear Dyn, 107, 1, 99-120, (2021) |
| [61] | Nayfeh, A.; Mook, D., Nonlinear oscillations, (1979), Wiley: Wiley New York · Zbl 0418.70001 |
| [62] | Dong, Y. H.; Li, X. Y.; Gao, K.; Li, Y. H.; Yang, J., Harmonic resonances of graphene-reinforced nonlinear cylindrical shells: effects of spinning motion and thermal environment, Nonlinear Dyn, 99, 981-1000, (2019) · Zbl 1459.74118 |
| [63] | Li, X., Parametric resonances of rotating composite laminated nonlinear cylindrical shells under periodic axial loads and hygrothermal environment, Compos Struct, 255, Article 112887 pp., (2020) |
| [64] | Irie, T.; Yamada, G.; Tanaka, K., Natural frequencies of truncated conical shells, J Sound Vib, 92, 447-453, (1984) |
| [65] | Tong, L., Effect of axial load on free vibration of orthotropic conical shells, J Vib Acoust, 118, 164-168, (1996) |
| [66] | Liew, K. M.; Ng, T. Y.; Zhao, X., Free vibration analysis of conical shells via the element-free kp-Ritz method, J Sound Vib, 281, 3-5, 627-645, (2005) |
| [67] | Li, F. M.; Kishimoto, K.; Huang, W. H., The calculations of natural frequencies and forced vibration responses of conical shell using the Rayleigh-Ritz method, Mech Res Commun, 36, 595-602, (2009) · Zbl 1258.74106 |
| [68] | Kerboua, Y.; Lakis, A. A.; Hmila, M., Vibration analysis of truncated conical shells subjected to flowing fluid, Appl Math Model, 34, 791-809, (2010) · Zbl 1185.74050 |
| [69] | Sofiyev, A. H., The non-linear vibration of FGM truncated conical shells, Compos Struct, 94, 7, 2237-2245, (2012) |
| [70] | Reddy, J. N.; Chin, C. D., Thermomechanical analysis of functionally graded cylinders and plates, J Therm Stresses, 21, 6, 593-626, (1998) |
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