The optimal design of dynamic systems with negative stiffness inertial amplifier tuned mass dampers

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This paper introduces the inertial amplifier viscoelastic tuned mass dampers (IAVTMD). The viscoelastic materials are implanted inside the core material of the inertial amplifier tuned mass dampers. The standard linear solid models are applied mathematically to formulate the viscoelastic material. H2 and H ∞ optimization mechanisms apply to derive the exact mathematical closed-form formulations for optimal design parameters for novel inertial amplifier viscoelastic tuned mass dampers. The optimum IAVTMD installs at the top of the structures to mitigate the dynamic responses, determining the dynamic responses analytically through transfer function formation. At first, IAVTMD’s dynamic response reduction capacity compares with the conventional tuned mass damper’s (CTMD) dynamic response reduction capacity. As a result, H2 optimized IAVTMD’s dynamic response reduction capacity is significantly 20.87% and 26.47% superior to two well-established H2 optimized conventional tuned mass damper’s dynamic response reduction capacity. In addition, H ∞ optimized IAVTMD has 15.48% more dynamic response reduction capacity than H ∞ conventional tuned mass damper. H2 and H ∞ optimized tuned mass damper inerters with optimal closed-form solutions are introduced in this paper. A higher damper mass ratio and a lower inerter mass ratio are recommended to produce H2 and H ∞ optimized tuned mass damper inerter (TMDI) with a lower frequency and damping ratio in an affordable range. Accordingly, H2 and H ∞ optimized IAVTMD’s dynamic response reduction capacities are significantly 6.94% and 23.29% superior to H2 and H ∞ optimized TMDI’s dynamic response reduction capacity. The closed-form expressions for optimal design parameters of inertial amplifier viscoelastic tuned mass dampers and tuned mass damper inerters are mathematically correct and effective for practical applications.

“…Equation (60) substitutes in equation (59) and the optimal closed-form solution for the damping ratio of TMDI derives as (Chowdhury et al, 2023a)…”

Section: Comparison Of Dynamic Responsesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The optimum enhanced viscoelastic tuned mass dampers: Exact closed-form expressions

Chowdhury

Banerjee

Adhikari

2023

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“…Accordingly, to solve problem (12) analytically, the fixed point theory (Den Hartog, 1947) is used here due to its high accuracy and efficiency, which makes it possible to obtain the optimal parameters of the proposed IGS-TEDVA. This FPT of Den Hartog has been previously used for the optimization of dynamic systems with negative stiffness inertial amplifier tuned mass dampers (Chowdhury et al, 2022).…”

Section: The Vibration Absorber Suggestedmentioning

confidence: 99%

Parameters optimization of three-element dynamic vibration absorber with inerter and grounded stiffness

Baduidana

Kenfack-Jiotsa

2023

Improving the control performance of dynamic vibration absorbers has recently been effective by introducing a grounded negative stiffness device. However, the negative stiffness structure is unstable and difficult to achieve in engineering practice , and its major drawback is that it amplif ies the vibration response of the primary system at low frequency region. Meanwhile, some mechanical devices can be combined to make the DVA work even better with a grounded positive stiffness. For this purpose, this paper combines for the first time the control effect of the inerter device and grounded positive stiffness into a three-element DVA model in order to better improve vibration reduction of an undamped primary system under excitation. First, the dynamic equation of motion of the system is written according to Newton ’s second law. Then, the steady-state displacement response of the primary system under harmonic excitation is calculated. In order to minimize the resonant response of the primary system around its natural frequency, the extended fixed point theory is applied. Thus, the optimized parameters such as the tuning frequency ratio, the stiffness ratio , and the approximate damping ratio are determined as a function of mass ratio and inerter – mass ratio. From the results analysis, it was found that the inerter – mass ratio has a better working range to guarantee the stability of the coupled system. Then , study on the effect of inerter – mass ratio on the primary system response is carried out. It can be seen that increasing the inerter – mass ratio in the optimal working range can reduce the response of the primary system beyond its uncontrolled static response. However, it is necessary to avoid the situation where the inerter – mass ratio is very large because it can lead to unrealistic optimal parameters. Finally, comparison with other DVA models is show n under harmonic and random excitation of the primary system. It is found that the proposed DVA model in this paper has high control performance and can be used in many engineering practice s .

“…In the field of metamaterials, analogous combinations of negative stiffness with inertial amplifiers have also been acknowledged [Banerjee et al (2021); Dwivedi et al (2020); Yuksel and Yilmaz (2020)]. On the other hand, tuned mass dampers [Tsai (1995)], tuned mass damper inerters [De Domenico and Ricciardi (2018)], negative stiffness inertial amplifier tuned mass dampers Chowdhury et al (2022b), and tuned inerter dampers [De Domenico et al (2018)] are generally utilized in hybrid mode at the structural level to improve the performance of the base isolators [Adhikari and Banerjee (2021); Banerjee et al (2019); Chowdhury et al (2021); Chowdhury et al (2022a), (2022c)]. However, state-of-the-art on the base-isolation system may not incorporate neither the use of an enhanced inerter at the base isolator level to improve overall vibration reduction capability nor provided rigorous explicit analytical closed-form equations for optimal design parameters for its design.…”

Section: Introductionmentioning

confidence: 99%

The exact closed-form equations for optimal design parameters of enhanced inerter-based isolation systems

Chowdhury

Banerjee

2022

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This paper introduces the enhanced inerter-based isolation system (EIBI) to improve broadband vibration control. Using the H2 optimization method, the exact closed-form expressions for the optimal design parameters of the EIBI, such as the frequency and viscous damping ratio, have been derived analytically. The optimal frequency and viscous damping ratios of EIBI decrease as the mass ratio of the EIBI increases. For optimal design purposes, the optimal viscous damping ratio of EIBI lies between 0.20 < ζ b < 0.30, which is practically affordable and precise to implement. The exact closed-form expressions for optimal design parameters for traditional base isolators (TBI) have also been derived using the H2 method to make a fair comparison with EIBI. When the base mass ratio of TBI increases, its optimal frequency and viscous damping ratios decrease. The response reduction capacity of each optimized novel isolator was compared to the response reduction capacity of each optimized TBI. Analysis of the frequency domain demonstrates that the response reduction capacity of the proposed EIBI is significantly 2.77% and 17.46% greater than that of the TBI subjected to harmonic and random white-noise base excitations. To verify the accuracy of the optimal closed-form expressions derived for each isolator using near-field earthquake base excitations, a numerical study employing the Newmark-beta method has been conducted. Hence, the time-history analysis reveals that the displacement and acceleration reduction capacities of EIBI are significantly superior to that of the TBI subjected to near-field earthquake base excitations by 12.86% and 24.61%, respectively. The EIBI systems are cost-effective and have greater vibration reduction capacities than TBIs.