Journal of Vibration and Sound

Journal of Vibration and Sound

Dynamic response control of buried piezoelectric cylindrical shell under dynamic loading effect

Document Type : research article

Authors
S. Mahmoud HashemiNejad 1
Hanyeh Naeimi 2
1 عضو هیات علمی
2 Faculty of Mechanics, Iran University of Science and Technology
Abstract
In this research, the dynamic response and vibration control of a sandwich piezoelectric cylindrical shell buried in an elastic medium under the effect of a moving ring load has been investigated. First, the dynamic equations of the shell are obtained based on Love's thin-walled shell theory, and then they are coupled with the governing equations of the surrounding elastic medium. Then, the resulting differential equations are solved using the Fourier transform, and after using Gauss's numerical integral for the inverse Fourier transform, the steady state dynamic response of the system is obtained. To reduce the vibrations caused by the moving load, a PID controller with optimized constants has been used. With extensive research done, the innovation presented in this research is the active reduction of the level of vibrations of a smart buried shell (pipe, tunnel) under the effect of a moving applied load. In a way, this innovation is at the same time being buried in the unlimited elastic environment and the piezoelectricity of the shell. The results show that the implemented controller is able to reduce the displacement range and stress in the system. Also, the operation of the piezoelectric active layer based on the appropriate controller reduces the sensitivity of the system to parameter changes.
Keywords
Dynamic response active control
buried piezoelectric cylindrical shell
moving ring load
PID controller
Subjects
[1]  Shell theory. Springer, European Mathematical Society,2014. Encyclopedia of Mathematics. [accessed 23 February 2024] Available from:    http://encyclopediaofmath.org/index.php?title=Shell_theory&oldid=33309.
[2]  Naghdi, P., On the theory of thin elastic shells. Quarterly of applied Mathematics, 1957, 14(4): pp.369-380.
[3]  Love, Augustus Edward Hough. "XVI. The small free vibrations and deformation of a thin elastic shell." Philosophical Transactions of the Royal Society of London. (A.) 179, 1888, pp.491-546.
[4]  Payton, R., Dynamic membrane stresses in a circular elastic shell. 1961.
[5]  Ruzzene, M. and A.M. Baz. Dynamic stability of periodic shells with moving loads. in Smart Structures and Materials 2001: Smart Structures and Integrated Systems. 2001. SPIE.
[6]  Zhang, J.D., B. Zhen, and X. Li, The Critical Velocity for an Infinite Cylindrical Shell under a Moving Load. Applied Mechanics and Materials, 2014, 441: pp.461-464.
[7]  Lee, S. and J. Seok, Dynamic analysis of a hollow cylinder subject to a dual traveling force imposed on its inner surface. Journal of Sound and Vibration, 2015, 340: pp.283-302.
[8]  Arazm, M., H. Eipakchi, and M. Ghannad, Vibrational behavior investigation of axially functionally graded cylindrical shells under moving pressure. Acta Mechanica, 2019, 230: pp.3221-3234.
[9]  Eipakchi, H., F.M. Nasrekani, and S. Ahmadi, An analytical approach for the vibration behavior of viscoelastic cylindrical shells under internal moving pressure. Acta Mechanica, 2020, 231: pp.3405-3418.
[10] Huo, H., et al., Exact benchmark solutions of random vibration responses for thin-walled orthotropic cylindrical shells. International Journal of Mechanical Sciences, 2021, 207: pp.106644.
[11] Saeedi, Soheil, Mohsen Kholdi, Abbas Loghman, Hossein Ashrafi, and Mohammad Arefi. "Thermo-elasto-plastic analysis of thick-walled cylinder made of functionally graded materials using successive approximation method." International Journal of Pressure Vessels and Piping”, 194, 2021, 104481.
[12] Gao, X.-L., Critical velocities of a two-layer composite tube under a moving internal pressure. Acta Mechanica, 2023, 234(5): pp.2021-2043.
[13] Chonan, S., Dynamic response of a cylindrical shell imperfectly bonded to a surrounding continuum of infinite extent. Journal of Sound and Vibration, 1981, 78(2): pp.257-267.
[14] Dwivedi, J., V. Singh, and P. Upadhyay, Nonaxisymmetric dynamic response of imperfectly bonded buried fluid-filled orthotropic cylindrical shells. 1996.
[15] Hasheminejad, S.M. and M. Komeili, Effect of imperfect bonding on axisymmetric elastodynamic response of a lined circular tunnel in poroelastic soil due to a moving ring load. International Journal of Solids and Structures, 2009, 46(2): pp.398-411.
[16] Yuan, Z., et al., Dynamic response of a tunnel buried in a saturated poroelastic soil layer to a moving point load. Soil Dynamics and Earthquake Engineering, 2015, 77: pp.348-359.
[17] Alzabeebee, S.I.A., Enhanced design approaches for rigid and flexible buried pipes using advanced numerical modelling. 2017, University of Birmingham.
[18] Akbarov, S., M. Mehdiyev, and M. Ozisik, Three-dimensional dynamics of the moving load acting on the interior of the hollow cylinder surrounded by the elastic medium. Structural Engineering and Mechanics, 2018, 67(2): pp.185-206.
[19] Akbarov, S.D. and M.A. Mehdiyev, 3D dynamics of the oscillating-moving load acting in the interior of the hollow cylinder surrounded with elastic medium. Structural Engineering and Mechanics, 2019, 71(6): pp.713-738.
[20] Tong, L., et al., Dynamic effect of a moving ring load on a cylindrical structure embedded in poroelastic space based on nonlocal Biot theory. Soil Dynamics and Earthquake Engineering, 2020, 128: p.105897.
[21] Liu, Y., Z. Qin, and F. Chu, Nonlinear dynamic responses of sandwich functionally graded porous cylindrical shells embedded in elastic media under 1: 1 internal resonance. Applied Mathematics and Mechanics, 2021, 42(6): pp.805-818.
[22] Alibeigloo, A., M. Talebitooti, Three-dimensional transient coupled thermoelasticity analysis of FGM cylindrical panel embedded in piezoelectric layers. Mechanics of Smart Structures, 2021.
[23] Girnis, S., et al. Action of Moving Load on a Two-Layer Shell in Elastic Medium. in International Scientific Conference on Agricultural Machinery Industry “Interagromash"”. 2022. Springer.
[24] Singh, V., P. Upadhyay, and B. Kishor, On the dynamic response of buried orthotropic cylindrical shells under moving load. International journal of mechanical sciences, 1988, 30(6): pp.397-406.
[25] Saviz, M., M. Shakeri, and M. Yas, Three-dimensional elasticity analysis of a laminated cylindrical shell with piezoelectric layer under dynamic loads. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2007, 221(12): pp.1507-1519.
[26] Zhang, Y., S. Xie, and X. Zhang, Vibration control of a simply supported cylindrical shell using a laminated piezoelectric actuator. Acta Mechanica, 2008, 196(1): pp.87-101.
[27] Sheng, G. and X. Wang, Response and control of functionally graded laminated piezoelectric shells under thermal shock and moving loadings. Composite Structures, 2010, 93(1): pp.132-141.
[28] Zhang, S., R. Schmidt, and X. Qin, Active vibration control of piezoelectric bonded smart structures using PID algorithm. Chinese journal of aeronautics, 2015, 28(1): pp.305-313.
[29] Arefi, M., R. Karroubi, and M. Irani-Rahaghi, Free vibration analysis of functionally graded laminated sandwich cylindrical shells integrated with piezoelectric layer. Applied Mathematics and Mechanics, 2016, 37: pp.821-834.
[30] Zhou, Y., J. Zhu, and D. Liu, Dynamic analysis of laminated piezoelectric cylindrical shells. Engineering Structures, 2020, 209: p. 109945.
[31] Liu, J., et al., Deformation of laminated and sandwich cylindrical shell with covered or embedded piezoelectric layers under compression and electrical loading. Composite Structures, 2020, 240: p. 112041.
[32] Lee, S.-L., Active vibration suppression of wind turbine blades integrated with piezoelectric sensors. Science and Engineering of Composite Materials, 2021, 28(1): pp.402-414.
[33] Li, C., P. Li, and X. Miao, Research on nonlinear vibration control of laminated cylindrical shells with discontinuous piezoelectric layer. Nonlinear Dynamics, 2021, 104(4), pp.3247-3267.
[34] Acharya, R., et al., Structural response of a low-fill box culvert under static and traffic loading. Journal of Performance of Constructed Facilities, 2016, 30(1): p. 04014184.
[35] Forrest, J. and H. Hunt, A three-dimensional tunnel model for calculation of train-induced ground vibration. Journal of sound and vibration, 2006, 294(4-5): pp.678-705.
[36] Rahimi, G., M. Arefi, and M. Khoshgoftar, Application and analysis of functionally graded piezoelectrical rotating cylinder as mechanical sensor subjected to pressure and thermal loads. Applied Mathematics and Mechanics, 2011, 32: pp.997-1008.
[37] Mohammadi, M., et al., Higher-order thermo-elastic analysis of FG-CNTRC cylindrical vessels surrounded by a Pasternak foundation. Nanomaterials, 2019, 9(1): p. 79.
[38] Visioli, Antonio. Practical PID control. Springer Science & Business Media, 2006.
[39] Sathe, M.P., et al., Speed Control of DC Motor using PID Controller-A Review, 2019.
[40] Dubey, V., H. Goud, and P.C. Sharma, Role of PID control techniques in process control system: a review. Data Engineering for Smart Systems: Proceedings of SSIC 2021, 2022: pp.659-670.
[41] Abdennour, A. and F.A. Alturki, A Comparative Study of PI/PID Classical and Intelligent Tuning Methods. Journal of Engineering and Computer Sciences, 2008, 1(1): pp.29-42.
[42] Hasheminejad, S.M. and A. Jamalpoor, Control of sound transmission into a hybrid double-wall sandwich cylindrical shell. Journal of Vibration and Control, 2022, 28(5-6): pp.689-706.
[43] Ke, L., Y. Wang, and J. Reddy, Thermo-electro-mechanical vibration of size-dependent piezoelectric cylindrical nanoshells under various boundary conditions. Composite Structures, 2014, 116: pp.626-636.
[44] Lu, J.-F., et al., Response of a circular tunnel embedded in saturated soil to a series of equidistant moving loads. Acta Mechanica, 2017. 228: pp.3675-3693.
[45] Steele, C., Beams and shells with moving loads. International Journal of Solids and Structures, 1971, 7(9): pp.1171-1198.
[46] Lu, Jian-Fei, and Dong-Sheng Jeng. "Dynamic response of a circular tunnel embedded in a saturated poroelastic medium due to a moving load." 2006, pp.750-756.
[47] Hwang, W.-S., H.C. Park, and W. Hwang, Vibration control of a laminated plate with piezoelectric sensor/actuator: finite element formulation and modal analysis. Journal of Intelligent Material Systems and Structures, 1993, 4(3): pp.317-329.
[48] Kheibari, Forough, and Yaghoub Tadi Beni. "Size dependent electro-mechanical vibration of single-walled piezoelectric nanotubes using thin shell model." Materials & Design, 114, 2017, pp.572-583.
[49] Wang, Y.Q., Y.F. Liu, and J.W. Zu, Analytical treatment of nonlocal vibration of multilayer functionally graded piezoelectric nanoscale shells incorporating thermal and electrical effect. The European Physical Journal Plus, 134, 2019, pp.1-15.