Journal of Computational Applied Mechanics

Surrogate-Assisted Peak-Slope Optimization of Dynamic Vibration Absorbers

Document Type : Research Paper

Authors

1 Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, P.O. Box 87317-53153, Kashan, Iran

2 China Medical University Hospital, China Medical University, Taichung, Taiwan

Abstract

mechanical systems by shifting the associated response peaks. However, optimizing their performance is computationally demanding, especially in systems with many degrees of freedom or numerous components, such as inerter-based DVAs. This study proposes a computationally efficient, surrogate-assisted optimization framework that leverages a novel Peak-Slope (PS) performance metric. As a reinterpretation of the classical H_∞ approach, the PS metric evaluates the effectiveness of vibration absorbers by measuring the secant slope between adjacent resonance peaks in the frequency response function. A well-tuned DVA yields a PS value approaching zero, indicating minimal variation between peaks and thus optimal mitigation of resonance. To reduce complexity, the structural parameters are held constant, and the influence of absorber parameters on the PS metric is isolated. The optimization space is simplified using surrogate models constructed via quartic polynomial regression. A novel decoupling algorithm introduced in this study enables efficient estimation of the PS metric as the Decoupled Peak-Slope (DPS) by expressing it as a sum of independent surrogate functions, each dependent on a single DVA parameter. Optimization is then performed by minimizing this total sum. A fully coupled 1DOF–1DOF system, incorporating masses, springs, dampers, and inerters, is used as the benchmark to validate the method. The DPS approach is compared against traditional genetic algorithm (GA)-based optimization, demonstrating substantial gains in both speed and accuracy. Further validation is conducted using reduced-order systems from the literature, confirming the true decoupling capability of the framework. For four distinct structural configurations, the decoupled surrogate equations are generated and summarized, forming a catalogue of precomputed polynomial functions that enables rapid evaluation of optimal DVA parameters across a range of systems. The results show strong agreement with analytical solutions and superior performance over GA-based methods. This positions the DPS framework as a fast, accurate tool for future semi-active DVA systems, enabling real-time tuning via precomputed surrogate functions.

Keywords

Main Subjects

[1]          Z. Liu, K. Zhou, L. Wang, T. Jiang, H. Dai, Dynamical stability of cantilevered pipe conveying fluid in the presence of linear dynamic vibration absorber, Journal of Computational Applied Mechanics, Vol. 50, No. 1, pp. 182-190, 2019.
[2]          F. Freddi, C. Galasso, G. Cremen, A. Dall’Asta, L. Di Sarno, A. Giaralis, F. Gutiérrez-Urzúa, C. Málaga-Chuquitaype, S. A. Mitoulis, C. Petrone, Innovations in earthquake risk reduction for resilience: Recent advances and challenges, International Journal of Disaster Risk Reduction, Vol. 60, pp. 102267, 2021.
[3]          T. E. Saaed, G. Nikolakopoulos, J.-E. Jonasson, H. Hedlund, A state-of-the-art review of structural control systems, Journal of Vibration and Control, Vol. 21, No. 5, pp. 919-937, 2015.
[4]          X. Song, J. Liu, M. Xia, Advanced Vibration-Based Fault Diagnosis and Vibration Control Methods, 18, MDPI, 2023, pp. 7704.
[5]          M. Jafari, M. Mohammadimehr, Forced vibration control of Timoshenko’s micro sandwich beam with CNT/GPL/CNR reinforced composites integrated by piezoelectric on Kerr’s elastic foundation using MCST, Journal of Computational Applied Mechanics, Vol. 56, No. 1, pp. 15-42, 2025.
[6]          A. M. Zenkour, H. D. El-Shahrany, Forced vibration of a magnetoelastic laminated composite beam on Pasternak’s foundation, Journal of Computational Applied Mechanics, Vol. 52, No. 3, pp. 478-497, 2021.
[7]          H. Frahm, Device for damping vibrations of bodies, 1911.
[8]          J. Ormondroyd, J. P. Den Hartog, The theory of the dynamic vibration absorber, Journal of Fluids Engineering, Vol. 49, No. 2, 1928.
[9]          J. P. Den Hartog, 1985, Mechanical vibrations, Courier Corporation,
[10]        R. E. D. Bishop, D. B. Welbourn, The problem of the dynamic vibration absorber, Engineering, London, Vol. 174, pp. 769, 1952.
[11]        J. E. Brock, A note on the damped vibration absorber, 1946.
[12]        W.-H. L. M. R. Roohollah Talebitooti, Concurrent energy harvesting and vibration suppression utilizing PZT-based dynamic vibration absorber, Archive of Applied Mechanics, pp. 1-20, 2022.
[13]        S. Mehdi Mohammadimehr Saeid, Vibration analysis of rotating fully-bonded and delaminated sandwich beam with CNTRC face sheets and AL-foam flexible core in thermal and moisture environments, Mechanics Based Design of Structures and Machines, Vol. 48, No. 5, pp. 584-614, 2020.
[14]        F. L. M. B. M. V. S. M. Antonio Argentino, SMA-based adaptive tuned mass dampers: Analysis and comparison, Mechanical Systems and Signal Processing, Vol. 186, pp. 109883, 2023.
[15]        N. Duy Chinh, Vibration control of a rotating shaft by passive mass-spring-disc dynamic vibration absorber, Archive of Mechanical Engineering, Vol. 67, No. 3, pp. 279-297, 2020.
[16]        M. M. M. Mohammadimehr, Stability and free vibration analyses of double-bonded micro composite sandwich cylindrical shells conveying fluid flow, Applied Mathematical Modelling, Vol. 47, pp. 685-709, 2017.
[17]        B. R. N. M. M. S Javad Atifeh, Stress and free vibration analysis of piezoelectric hollow circular FG-SWBNNTs reinforced nanocomposite plate based on modified couple stress theory subjected to thermo-mechanical loadings, Journal of Vibration and Control, Vol. 24, No. 15, pp. 3471-3486, 2018.
[18]        R. R. M. Mohammadimehr, Bending and vibration analyses of a rotating sandwich cylindrical shell considering nanocomposite core and piezoelectric layers subjected to thermal and magnetic fields, Applied Mathematics and Mechanics, Vol. 39, No. 2, pp. 219-240, 2018.
[19]        M. M. A. A. Monajemi, Stability analysis of a spinning soft-core sandwich beam with CNTs reinforced metal matrix nanocomposite skins subjected to residual stress, Mechanics Based Design of Structures and Machines, Vol. 52, No. 1, pp. 338-358, 2024.
[20]        S.-B. Choi, Y.-M. Han, 2016, Piezoelectric actuators: control applications of smart materials, CRC Press,
[21]        Z. Deng, M. J. Dapino, Review of magnetostrictive materials for structural vibration control, Smart Materials and Structures, Vol. 27, No. 11, pp. 113001, 2018.
[22]        M. S. K. Jacob, Damping of Smart Systems by Shape Memory Alloys (SMAs).
[23]        M. Arabzadeh-Ziari, M. Mohammadimehr, E. Arabzadeh-Ziari, M. Asgari, Deflection, buckling and vibration analyses for a sandwich nanocomposite structure with foam core reinforced with GPLs and SMAs based on TSDBT, Journal of Computational Applied Mechanics, Vol. 55, No. 2, pp. 289-321, 2024.
[24]        Z. K. Maraghi, S. A. Mirhaj, Ö. Civalek, Instability and vibration behaviour of sandwich plate on Kerr foundation, Engineering Structures, Vol. 341, pp. 120876, 2025.
[25]        M. A. Mohammadimehr, A. Loghman, S. Amir, M. Mohammadimehr, E. Arshid, Ö. Civalek, Magneto-electro vibration analysis of a moderately thick double-curved sandwich panel with porous core and GPLRC using FSDT, Journal of Computational Applied Mechanics, Vol. 56, No. 3, pp. 673-693, 2025.
[26]        F. Ghasemi, A. Salari, E. Salari, A. Rastgoo, Machine learning-assisted investigation on nonlinear vibration analysis of bio-inspired auxetic tubes, International Journal of Structural Integrity, 2025.
[27]        H. Ezzati, S. Pashalou, A. Rastgoo, F. Ebrahimi, Vibration analysis of multilayer graphene origami-enabled metamaterial plates, Acta Mechanica, Vol. 235, No. 12, pp. 7623-7640, 2024.
[28]        E. Haghparast, A. G. Arani, A. H. S. Arani, Vibration of axially moving sandwich plate with honeycomb core and nanocomposite face sheets, Steel and Composite Structures, Vol. 55, No. 5, pp. 433, 2025.
[29]        S. Givi, A. Ghorbanpour Arani, Z. Khoddami Maraghi, E. Arshid, Free vibration and supersonic flutter analyses of a sandwich cylindrical shell with CNT-reinforced honeycomb core integrated with piezoelectric layers, Mechanics Based Design of Structures and Machines, Vol. 53, No. 5, pp. 3225-3253, 2025.
[30]        W. J. Carter, F. C. Liu, Steady-state behavior of nonlinear dynamic vibration absorber, 1961.
[31]        A. G. Thompson, Optimum tuning and damping of a dynamic vibration absorber applied to a force excited and damped primary system, Journal of Sound and Vibration, Vol. 77, No. 3, pp. 403-415, 1981.
[32]        O. Nishihara, T. Asami, Closed-form solutions to the exact optimizations of dynamic vibration absorbers (minimizations of the maximum amplitude magnification factors), J. Vib. Acoust., Vol. 124, No. 4, pp. 576-582, 2002.
[33]        T. Asami, O. Nishihara, H 2 optimization of the three-element type dynamic vibration absorbers, J. Vib. Acoust., Vol. 124, No. 4, pp. 583-592, 2002.
[34]        T. Asami, O. Nishihara, A. M. Baz, Analytical solutions to H∞ and H 2 optimization of dynamic vibration absorbers attached to damped linear systems, J. Vib. Acoust., Vol. 124, No. 2, pp. 284-295, 2002.
[35]        H. Yamaguchi, Damping of transient vibration by a dynamic absorber, Trans. Jpn. Soc. Mech. Eng., Vol. 54, No. 499, pp. 561, 1988.
[36]        O. Nishihara, H. Matsuhisa, others, Design of a dynamic vibration absorber for minimization of maximum amplitude magnification factor (derivation of algebraic exact solution), Japanese Society of Mechanical Engineering, Vol. 63, pp. 3438-3445, 1997.
[37]        F. Sadek, B. Mohraz, A. W. Taylor, R. M. Chung, A method of estimating the parameters of tuned mass dampers for seismic applications, Earthquake Engineering \& Structural Dynamics, Vol. 26, No. 6, pp. 617-635, 1997.
[38]        H.-C. Tsai, G.-C. Lin, Optimum tuned-mass dampers for minimizing steady-state response of support-excited and damped systems, Earthquake engineering \& structural dynamics, Vol. 22, No. 11, pp. 957-973, 1993.
[39]        J. H. Ruoyu Zhang, Hybrid Analytical Optimal Approach and Comparative Analyses for Tuned Viscous Mass Damper with Negative Stiffness (TVMDNS), Journal of Vibration Engineering \& Technologies, pp. 1-18, 2024.
[40]        T. Igusa, K. Xu, Vibration control using multiple tuned mass dampers, Journal of sound and vibration, Vol. 175, No. 4, pp. 491-503, 1994.
[41]        A. J. Clark, others, Multiple passive tuned mass dampers for reducing earthquake induced building motion, in Proceeding of, 779-784.
[42]        H. Anthony Frederick, Multi-degree of freedom passive and active vibration absorbers for the control of structural vibration,  Thesis, 2003.
[43]        J. C. S. J. J. Yong, Geometrical design method of multi-degree-of-freedom dynamic vibration absorbers, Journal of Sound and Vibration, Vol. 303, No. 1-2, pp. 343-356, 2007.
[44]        D. G. T. Y. Q. W. Y. S. Jinsong Zhou, Multi-degree of Freedom Dynamic Vibration Absorber of the Carbody of High-Speed Trains, in Proceeding of, 3-7.
[45]        D. G. Y. J. Y. S. Jinsong Zhou, Study on multi-degree of freedom dynamic vibration absorber of the car body of high-speed trains, Mechanical Sciences, Vol. 13, No. 1, pp. 239-256, 2022.
[46]        R. B. B. A. K. W. A. K. S. Rj Alkhoury, Ride dynamic analysis of a hybrid discrete and continuous vehicle model,  pp. 2008.
[47]        F. Mariano, Optimal parameters and characteristics of a three degree of freedom dynamic vibration absorber, 2012.
[48]        S.-P. Y. G.-S. G. Y.-J. S. Lin Wang, Nonlinear dynamical analysis and parameters optimization of four semi-active on-off dynamic vibration absorbers, Journal of Vibration and Control, Vol. 19, No. 1, pp. 143-160, 2013.
[49]        T. Szolc, Medium frequency dynamic investigation of the railway wheelset-track system using a discrete-continuous model, Archive of Applied Mechanics, Vol. 68, pp. 30-45, 1998.
[50]        A. F. B. Noori, Optimum design of dynamic vibration absorbers for a beam, based on H∞ and H 2 Optimization, Archive of Applied Mechanics, Vol. 83, pp. 1773-1787, 2013.
[51]        W. Chia-Man Chang Yi-Ren, Elastic beam with nonlinear suspension and a dynamic vibration absorber at the free end, Transactions of the Canadian Society for Mechanical Engineering, Vol. 38, No. 1, pp. 107-137, 2014.
[52]        H. D. H. P. P Frank Pai, Acoustic multi-stopband metamaterial plates design for broadband elastic wave absorption and vibration suppression, International journal of mechanical sciences, Vol. 103, pp. 104-114, 2015.
[53]        C. Tianxing Wu Rong, Vibration control of base system using distributed dynamic vibration absorbers, Journal of Vibration and Control, Vol. 20, No. 10, pp. 1589-1600, 2014.
[54]        L. C. C. Y. Deyu Li, Dynamic vibration absorbers for vibration control within a frequency band, Journal of Sound and Vibration, Vol. 330, No. 8, pp. 1582-1598, 2011.
[55]        C. A. C. C. Gregorio Toscano Pulido, Multiobjective structural optimization using a microgenetic algorithm, Structural and Multidisciplinary Optimization, Vol. 30, pp. 388-403, 2005.
[56]        A. C. G. L. J. H. G. Z. Zheng-Dong Ma, Design optimization of a runflat structure based on multi-objective genetic algorithm, Structural and Multidisciplinary Optimization, Vol. 51, pp. 1363-1371, 2015.
[57]        Y. X. J. B. N. S. Zhaoqing Chen, Hybrid analytical H-norm optimization approach for dynamic vibration absorbers, International Journal of Mechanical Sciences, Vol. 264, pp. 108796, 2024.
[58]        R. Gaetan Kerschen Ghislain, $H_\infty$ optimization of multiple tuned mass dampers for multimodal vibration control, Computers \& Structures, Vol. 248, pp. 106485, 2021.
[59]        A. Toshihiko, Calculation of the $H_\infty$ optimized design of a single-mass dynamic vibration absorber attached to a damped primary system, Mechanical Engineering Journal, Vol. 7, No. 5, pp. 20-00250, 2020.
[60]        K. Y. T. A. Yoshito Mizukawa, Optimal design of a hysteretically damped dynamic vibration absorber, Mechanical Engineering Journal, Vol. 7, No. 2, pp. 19-00482, 2020.
[61]        A. K.-J. Marcial Baduidana, Parameters optimization of three-element dynamic vibration absorber with inerter and grounded stiffness, Journal of Vibration and Control, Vol. 30, No. 7-8, pp. 1548-1565, 2024.
[62]        J. C. J. M. A. A. F.-H. M. A.-M. E. B. Jg Mendoza Larios, A novel high-performance passive non-traditional inerter-based dynamic vibration absorber, Journal of Sound and Vibration, Vol. 485, pp. 115583, 2020.
Journal of Computational Applied Mechanics
Volume 56, Issue 4
October 2025
Pages 838-862
  • Receive Date: 17 July 2025
  • Revise Date: 28 July 2025
  • Accept Date: 31 July 2025