Abstract
Although frequency-domain optimization approaches are commonly used for noise control, ubiquitous transient behaviors indicate that time-domain approaches cannot be ignored. Thus, this paper minimizes the transient noise radiated from the vibration system with constant gain velocity feedback (GGVF) control by combining topology optimization and parameter optimization. Based on the solid isotropic material with penalization (SIMP) model, the pseudo density is introduced to characterize the presence or absence of piezoelectric material. To satisfy engineering requirements, constraints on the usage amount of piezoelectric material, consumable energy, and maximum transient voltage are considered. Transient sound radiation is predicted by using a finite element/time-domain boundary element method (FEM/TDBEM). Sensitivity formulae of objective function to pseudo density and feedback gain are derived using a combination scheme. Namely, a direct method is applied to obtain the vibration sensitivity information at all boundary nodes, the results of which are input into the sensitivity calculation of transient sound radiation addressed by an adjoint variable method. This scheme integrates the advantages of the direct method which can calculate the vibration sensitivity of all nodes at once and of the adjoint variable method which has high computational efficiency. The gradient-based method of moving asymptotes (MMA) is employed to solve for optimised solutions. Numerical examples demonstrate the accuracy of the sensitivity formulae and the effectiveness of the concurrent optimization strategy.
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References
AkhavanAlavi SM, Mohammadimehr M, Edjtahed SH (2019) Active control of micro Reddy beam integrated with functionally graded nanocomposite sensor and actuator based on linear quadratic regulator method. Eur J Mech A-Solids 74:449–461. https://doi.org/10.1016/j.euromechsol.2018.12.008
Alkhatib R, Golnaraghi MF (2003) Active structural vibration control: a review. Shock Vib Dig 35:367–383. https://doi.org/10.1177/05831024030355002
Araújo AL, Madeira JFA (2020) Multiobjective optimization solutions for noise reduction in composite sandwich panels using active control. Compos Struct 247:112440. https://doi.org/10.1016/j.compstruct.2020.112440
Aridogan U, Basdogan I (2015) A review of active vibration and noise suppression of plate-like structures with piezoelectric transducers. J Intell Mater Syst Struct 26:1455–1476. https://doi.org/10.1177/1045389X15585896
Bendsøe MP (1989) Optimal shape design as a material distribution problem. Struct Optim 1:193–202
Bendsøe MP, Sigmund O (2004) Topology optimization: theory, methods, and applications. Springer, Berlin
Choi S-B (2006) Active structural acoustic control of a smart plate featuring piezoelectric actuators. J Sound Vib 294:421–429. https://doi.org/10.1016/j.jsv.2006.01.040
Dong YH, Li YH, Li XY, Yang J (2020) Active control of dynamic behaviors of graded graphene reinforced cylindrical shells with piezoelectric actuator/sensor layers. Appl Math Model 82:252–270. https://doi.org/10.1016/j.apm.2020.01.054
Du JB, Olhoff N (2010) Topological design of vibrating structures with respect to optimum sound pressure characteristics in a surrounding acoustic medium. Struct Multidisc Optim 42:43–54. https://doi.org/10.1007/s00158-009-0477-y
Dutta R, Ganguli R, Mani V (2011) Swarm intelligence algorithms for integrated optimization of piezoelectric actuator and sensor placement and feedback gains. Smart Mater Struct. https://doi.org/10.1088/0964-1726/20/10/105018
Fonseca P, Sas P, Brussel H (1999) A comparative study of methods for optimising sensor and actuator locations in active control applications. J Sound Vib 221:651–679. https://doi.org/10.1006/jsvi.1998.2026
Geng L, Zhang XZ, Bi CX (2015) Reconstruction of transient vibration and sound radiation of an impacted plate using time domain plane wave superposition method. J Sound Vib 344:114–125. https://doi.org/10.1016/j.jsv.2015.01.046
Guo H, Wang YS, Yang C et al (2019) Vehicle interior noise active control based on piezoelectric ceramic materials and improved fuzzy control algorithm. Appl Acoust 150:216–226. https://doi.org/10.1016/j.apacoust.2019.02.018
Hasheminejad SM, Keshavarzpour H (2013) Active sound radiation control of a thick piezolaminated smart rectangular plate. J Sound Vib 332:4798–4816. https://doi.org/10.1016/j.jsv.2013.04.028
Hasheminejad SM, Oveisi A (2016) Active vibration control of an arbitrary thick smart cylindrical panel with optimally placed piezoelectric sensor/actuator pairs. Int J Mech Mater Des 12:1–16. https://doi.org/10.1007/s10999-015-9293-2
He XQ, Ng TY, Sivashanker S, Liew KM (2001) Active control of FGM plates with integrated piezoelectric sensors and actuators. Int J Solids Struct 38:1641–1655. https://doi.org/10.1016/S0020-7683(00)00050-0
Hu J, Kang Z (2019) Topological design of piezoelectric actuator layer for linear quadratic regulator control of thin-shell structures under transient excitation. Smart Mater Struct. https://doi.org/10.1088/1361-665X/ab1e96
Hu KM, Li H (2018) Multi-parameter optimization of piezoelectric actuators for multi-mode active vibration control of cylindrical shells. J Sound Vib 426:166–185. https://doi.org/10.1016/j.jsv.2018.04.021
Hwang WS, Park HC (1993) Finite element modeling of piezoelectric sensors and actuators. AIAA J 31:930–937. https://doi.org/10.2514/3.11707
Kapuria S, Yasin MY (2013) Active vibration control of smart plates using directional actuation and sensing capability of piezoelectric composites. Acta Mech 224:1185–1199. https://doi.org/10.1007/s00707-013-0864-8
Kögl M, Silva ECN (2005) Topology optimization of smart structures: Design of piezoelectric plate and shell actuators. Smart Mater Struct 14:387–399. https://doi.org/10.1088/0964-1726/14/2/013
Lee CY, Kim JH (2021) Active flutter suppression of smart-skin antenna structures with piezoelectric sensors and actuators. Aerospace 8:257. https://doi.org/10.3390/aerospace8090257
Li CF, Li PY, Miao XY (2021) Research on nonlinear vibration control of laminated cylindrical shells with discontinuous piezoelectric layer. Nonlinear Dyn 104:3247–3267. https://doi.org/10.1007/s11071-021-06497-x
Loghmani A, Danesh M, Kwak MK, Keshmiri M (2016) Active control of radiated sound power of a smart cylindrical shell based on radiation modes. Appl Acoust 114:218–229. https://doi.org/10.1016/j.apacoust.2016.07.027
Lu YF, Shao Q, Yang F et al (2020) Optimal vibration control of membrane structures with in-plane polyvinylidene fluoride actuators. Int J Struct Stab Dyn 20:2050095. https://doi.org/10.1142/S0219455420500959
Long K, Yang XY, Saeed N, Tian RH, Wen P, Wang X (2021) Topology optimization of transient problem with maximum dynamic response constraint using SOAR scheme. Front Mech Eng 16:593–606. https://doi.org/10.1007/s11465-021-0636-4
Madeira JFA, Araujo AL (2020) Optimal distribution of active piezoelectric elements for noise attenuation in sandwich panels. Int J Smart Nano Mater 11:400–416. https://doi.org/10.1080/19475411.2020.1829159
Mansur WJ, Brebbia CA (1982a) Formulation of the boundary element method for transient problems governed by the scalar wave equation. Appl Math Model 6:307–311. https://doi.org/10.1016/S0307-904X(82)80039-5
Mansur WJ, Brebbia CA (1982b) Numerical implementation of the boundary element method for two dimensional transient scalar wave propagation problems. Appl Math Model 6:299–306. https://doi.org/10.1016/S0307-904X(82)80038-3
Moita JMS, Correia IFP, Soares CMM, Soares CAM (2004) Active control of adaptive laminated structures with bonded piezoelectric sensors and actuators. Comput Struct 82:1349–1358. https://doi.org/10.1016/j.compstruc.2004.03.030
Moretti M, Silva ECN, Reddy JN (2019) Topology optimization of flextensional piezoelectric actuators with active control law. Smart Mater Struct. https://doi.org/10.1088/1361-665X/aafd56
Ou DY, Mak CM (2013) Transient vibration and sound radiation of a stiffened plate. J Vib Control 19:1378–1385. https://doi.org/10.1177/1077546312450731
Qu YG, Peng ZK, Zhang WM, Meng G (2019a) Nonlinear vibro-acoustic behaviors of coupled sandwich cylindrical shell and spring-mass-damper systems. Mech Syst Signal Process 124:254–274. https://doi.org/10.1016/j.ymssp.2019.01.048
Qu YG, Zhang WM, Peng ZK, Meng G (2019b) Time-domain structural-acoustic analysis of composite plates subjected to moving dynamic loads. Compos Struct 208:574–584. https://doi.org/10.1016/j.compstruct.2018.09.103
Ripamonti F, Giampà A, Giona R (2022) Numerical and experimental study of an active control logic for modifying the acoustic performance of single-layer panels. J Sound Vib 520:1–18. https://doi.org/10.1016/j.jsv.2021.116608
Shang LY, Zhao GZ, Zhai JJ (2017) Topology optimization for coupled acoustic-structural systems under random excitation. Struct Multidisc Optim 56:809–822. https://doi.org/10.1007/s00158-017-1687-3
Silva ECN, Kikuchi N (1999) Design of piezoelectric transducers using topology optimization. Smart Mater Struct 8:350–364. https://doi.org/10.1088/0964-1726/8/3/307
Tzou HS, Tseng CI (1991) Distributed vibration control and identification of coupled elastic/piezoelectric systems: finite element formulation and applications. Mech Syst Signal Process 5:215–231. https://doi.org/10.1016/0888-3270(91)90044-6
Wang SY, Quek ST, Ang KK (2001) Vibration control of smart piezoelectric composite plates. Smart Mater Struct 10:637–644. https://doi.org/10.1088/0964-1726/10/4/306
Wang Y, Kang Z, Zhang X (2023) A velocity field level set method for topology optimization of piezoelectric layer on the plate with active vibration control. Mech Adv Mater Struct 30:1326–1339. https://doi.org/10.1080/15376494.2022.2030444
Wrona S, Pawelczyk M, Cheer J (2021) Acoustic radiation-based optimization of the placement of actuators for active control of noise transmitted through plates. Mech Syst Signal Process 147:107009. https://doi.org/10.1016/j.ymssp.2020.107009
Wu TW (2000) Boundary element acoustics: fundamentals and computer codes (advances in boundary elements). Southampton, UK
Zargham S, Ward TA, Ramli R, Badruddin IA (2016) Topology optimization: a review for structural designs under vibration problems. Struct Multidisc Optim 53:1157–1177. https://doi.org/10.1007/s00158-015-1370-5
Zhai JJ, Shang LY, Zhao GZ (2020) Simultaneous optimization of control parameters and placements of piezoelectric patches for active structural acoustic control of shell structures under random excitation. J Intell Mater Syst Struct 31:1204–1219. https://doi.org/10.1177/1045389X20916799
Zhai JJ, Zhao GZ, Shang LY (2017) Integrated design optimization of structural size and control system of piezoelectric curved shells with respect to sound radiation. Struct Multidisc Optim 56:1287–1304. https://doi.org/10.1007/s00158-017-1721-5
Zhai JJ, Zhao GZ, Shang LY (2016) Integrated design optimization of structure and vibration control with piezoelectric curved shell actuators. J Intell Mater Syst Struct 27:2672–2691. https://doi.org/10.1177/1045389X16641203
Zhang H, Xie X, Jiang JQ, Yamashita M (2015) Assessment on transient sound radiation of a vibrating steel bridge due to traffic loading. J Sound Vib 336:132–149. https://doi.org/10.1016/j.jsv.2014.10.006
Zhang X, Kang Z, Li M (2014) Topology optimization of electrode coverage of piezoelectric thin-walled structures with CGVF control for minimizing sound radiation. Struct Multidisc Optim 50:799–814. https://doi.org/10.1007/s00158-014-1082-2
Zhang XP, Kang Z (2014) Dynamic topology optimization of piezoelectric structures with active control for reducing transient response. Comput Methods Appl Mech Eng 281:200–219. https://doi.org/10.1016/j.cma.2014.08.011
Zhang Y, Zhang XZ, Bi CX, Zhang YB (2017) An inverse direct time domain boundary element method for the reconstruction of transient acoustic field. J Vib Acoust Trans ASME 139:021013. https://doi.org/10.1115/1.4035381
Zhang CW, Long K, Yang XY, Chen Z, Saeed N, Wang X (2022) A transient topology optimization with time-varying deformation restriction via augmented Lagrange method. Int J Mech Mater Des 18:683–700. https://doi.org/10.1007/s10999-022-09598-6
Zhao W, Chen L, Chen H, Marburg S (2019) Topology optimization of exterior acoustic-structure interaction systems using the coupled FEM-BEM method. Int J Numer Methods Eng 119:404–431. https://doi.org/10.1002/nme.6055
Zheng H, Zhang S, Zhao G (2021) Integrated design optimization of actuator layout and structural ply parameters for the dynamic shape control of piezoelectric laminated curved shell structures. Struct Multidisc Optim 63:2375–2398. https://doi.org/10.1007/s00158-020-02818-7
Zorić ND, Tomović AM, Obradović AM (2019) Active vibration control of smart composite plates using optimized self-tuning fuzzy logic controller with optimization of placement, sizing and orientation of PFRC actuators. J Sound Vib 456:173–198. https://doi.org/10.1016/j.jsv.2019.05.035
Acknowledgements
This research project is supported by the National Key Research and Development Program of China (2020YFB1709403) and the National Natural Science Foundation of China (U1508209, 11072049, 12102076). The authors would like to acknowledge the support of these funds.
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Zheng, H., Zhao, G., Han, W. et al. Concurrent optimization of actuator/sensor layout and control parameter on piezoelectric curved shells with active vibration control for minimizing transient noise. Struct Multidisc Optim 67, 1 (2024). https://doi.org/10.1007/s00158-023-03707-5
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DOI: https://doi.org/10.1007/s00158-023-03707-5