Implementasi HarmonicBalance.jl untuk Menentukan Performansi Isolator Getaran Nonlinear Quasi-Zero Stiffness
DOI:
https://doi.org/10.37859/jst.v12i2.10574
Abstract
Isolasi getaran merupakan sebuah teknik pengendalian getaran untuk mereduksi transmisi getaran dari sumber gangguan ke objek yang diisolasi. Kajian ini menyajikan penentuan performa suatu isolator nonlinier pada komponen gaya pemulih dan gaya peredamannya berdasarkan variasi redaman nonlinier dan amplitudo eksitasi. Selanjutnya, eksitasi harmonik dikenakan ke isolator dan jawab steady-state dalam ranah frekuensi ditentukan melalui penerapan metode harmonic balance (HB). Berdasarkan penerapan metode ini diperoleh transmisibilitas isolator yang digunakan sebagai metrik untuk menentukan performanya. Metode HB ini digunakan melalui implementasi paket program Julia yang bernama HarmonicBalance.jl. Berdasarkan simulasi yang telah dilakukan diketahui bahwa redaman nonlinier memberikan dampak yang signifikan bagi isolator untuk mereduksi transmisibilitas terutama ketika amplitudo eksitasi besar.
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Liu C, Zhang W, Yu K, Liu T, Zheng Y. Quasi-zero-stiffness vibration isolation: Designs, improvements and applications. Eng Struct 2024;301:117282. https://doi.org/10.1016/j.engstruct.2023.117282.
Li H, Li Y, Li J. Negative stiffness devices for vibration isolation applications: A review. Adv Struct Eng 2020;23:1739–55. https://doi.org/10.1177/1369433219900311.
Ibrahim RA. Recent advances in nonlinear passive vibration isolators. J Sound Vib 2008;314:371–452. https://doi.org/10.1016/j.jsv.2008.01.014.
Ma Z, Zhou R, Yang Q. Recent Advances in Quasi-Zero Stiffness Vibration Isolation Systems: An Overview and Future Possibilities. Machines 2022;10. https://doi.org/10.3390/machines10090813.
Balaji PS, Karthik SelvaKumar K. Applications of Nonlinearity in Passive Vibration Control: A Review. vol. 9. Springer Singapore; 2021. https://doi.org/10.1007/s42417-020-00216-3.
Carrella A, Brennan MJ, Waters TP. Static analysis of a passive vibration isolator with quasi-zero-stiffness characteristic. J Sound Vib 2007;301:678–89. https://doi.org/10.1016/j.jsv.2006.10.011.
Carrella A, Brennan MJ, Waters TP. Optimization of a quasi-zero-stiffness isolator. J Mech Sci Technol 2007;21:946–9. https://doi.org/10.1007/BF03027074.
Carrella A, Brennan MJ, Kovacic I, Waters TP. On the force transmissibility of a vibration isolator with quasi-zero-stiffness. J Sound Vib 2009;322:707–17. https://doi.org/https://doi.org/10.1016/j.jsv.2008.11.034.
Cheng C, Ma R, Hu Y. Beneficial performance of a quasi-zero stiffness vibration isolator with generalized geometric nonlinear damping. Noise Vib Worldw 2021;52:59–71. https://doi.org/10.1177/0957456520972385.
Yilmaz C, Kikuchi N. Analysis and design of passive band-stop filter-type vibration isolators for low-frequency applications. J Sound Vib 2006;291:1004–28. https://doi.org/https://doi.org/10.1016/j.jsv.2005.07.019.
Yan G, Zou HX, Wang S, Zhao LC, Wu ZY, Zhang WM. Bio-inspired vibration isolation: Methodology and design. Appl Mech Rev 2021;73:1–21. https://doi.org/10.1115/1.4049946.
Yan Z, Dai H, Wang Q, Atluri SN. Harmonic Balance Methods: A Review and Recent Developments. C - Comput Model Eng Sci 2023;137:1419–59. https://doi.org/10.32604/cmes.2023.028198.
Wu W, Tang B. The Elliptic Harmonic Balance Method for the Performance Analysis of a Two-Stage Vibration Isolation System with Geometric Nonlinearity. Shock Vib 2021:1–13. https://doi.org/10.1155/2021/6690686.
Li YL, Huang JL, Zhu WD. An enhanced incremental harmonic balance method to improve the computational efficiency and convergence for systems with non-polynomial nonlinearities. Nonlinear Dyn 2025;113:8265–94. https://doi.org/10.1007/s11071-024-10739-z.
Li YL, Huang JL, Zhu WD. A generalized incremental harmonic balance method by combining a data-driven framework for initial value selection of strongly nonlinear dynamic systems. Int J Non Linear Mech 2025;169:1–22. https://doi.org/10.1016/j.ijnonlinmec.2024.104951.
Krack M, Gross J. Harmonic Balance for Nonlinear Vibration Problems. Springer Cham; 2019. https://doi.org/10.1007/978-3-030-14023-6.
Košata J, del Pino J, Heugel TL, Zilberberg O. HarmonicBalance.jl: A Julia suite for nonlinear dynamics using harmonic balance. SciPost Phys Codebases 2022;6:1–28. https://doi.org/10.21468/scipostphyscodeb.6.
Martins TS, Trainotti F, Zwölfer A, Afonso F. A Python Implementation of a Robust Multi-Harmonic Balance With Numerical Continuation and Automatic Differentiation for Structural Dynamics. J Comput Nonlinear Dyn 2023;18:1–12. https://doi.org/10.1115/1.4062424.
Bezanson J, Edelman A, Karpinski S, Shah VB. Julia: A fresh approach to numerical computing. SIAM Rev 2017;59:65–98. https://doi.org/10.1137/141000671.
Gowda S, Ma Y, Cheli A, Gwóźzdź M, Shah VB, Edelman A, et al. High-performance symbolic-numerics via multiple dispatch. ACM Commun Comput Algebr 2022;55:92–96. https://doi.org/10.1145/3511528.3511535.
Breiding P, Timme S. HomotopyContinuation.jl: A Package for Homotopy Continuation in Julia. In: Davenport JH, Kauers M, Labahn G, Urban J, editors. Lect. Notes Comput. Sci. (Conference Int. Congr. Math. Software), Cham: Springer International Publishing; 2018, p. 458–65.
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