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NAAS Journal 2026

International Journal Of Chemistry, Mathematics And Physics(IJCMP)

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  3. Vol-10,Issue-3, July - September 2026
  4. Mathematical Modelling and Multi-Objective Optimization of an Inerter-Based Dynamic Vibration Absorber

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Mathematical Modelling and Multi-Objective Optimization of an Inerter-Based Dynamic Vibration Absorber

Sultan Mahamdnur Ibrahim


International Journal of Chemistry, Mathematics And Physics(IJCMP), Vol-10,Issue-3, July - September 2026, Pages 1-15 , 10.22161/ijcmp.10.3.1

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Article Info: Received: 30 May 2026; Received in revised form: 28 June 2026; Accepted: 01 July 2026; Available online: 08 July 2026

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This study presents the mathematical modelling and multi-objective optimization of a passive inerter-based dynamic vibration absorber for suppressing vibration in a lightly damped primary structure. A two-degree-of-freedom model is formulated in which a grounded inerter augments the apparent inertia of the absorber without introducing an equivalent increase in physical mass. Analytical frequency-response functions and a state-space representation are derived to evaluate both steady-state and transient behaviour. The absorber tuning ratio, damping ratio, and inertance ratio are optimized using the Non-dominated Sorting Genetic Algorithm II (NSGA-II). Two competing objectives are considered: minimization of the worst-case primary-mass displacement transmissibility and minimization of the normalized absorber stroke. The resulting Pareto front is used to identify a balanced compromise design through knee-point, equal-weight, and minimum-distance-to-utopia criteria. For the selected design, the optimized tuning, damping, and inertance ratios are 1.50, 0.465, and 0.108, respectively. The inerter increases the apparent absorber inertia to approximately 3.2 times its physical mass. Compared with the uncontrolled structure, the optimized inerter-based absorber reduces the peak transmissibility from 25.0 to 3.45, corresponding to an 86.2% reduction. It also outperforms an equal-mass conventional dynamic vibration absorber, which produces a peak transmissibility of 5.27 and a normalized peak stroke of 17.5, whereas the inerter-based design limits the corresponding stroke to 6.54. Time-domain simulations confirm improved harmonic and impulsive responses, while sensitivity analysis demonstrates substantially greater tolerance to primary-frequency mistuning. The results show that an appropriately optimized inerter-based absorber can simultaneously provide stronger vibration attenuation, reduced travel demand, and improved robustness compared with a conventional equal-mass absorber.

Dynamic vibration absorber, Inerter, Multi-objective optimization, NSGA-II, Vibration suppression.

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