Reliability analysis of the hysteretic nonlinear energy sink in shock mitigation considering uncertainties
Abstract
The reliability of the hysteretic nonlinear energy sink in shock mitigation is investigated herein. The hysteretic nonlinear energy sink is a passive vibration control device which is coupled to a primary linear oscillator. Apart from its small mass and a nonlinear elastic spring of the Duffing oscillator, it also comprises a purely hysteretic and a linear elastic spring of potentially negative stiffness. The Bouc–Wen model is used to describe the force produced by both the purely hysteretic and linear elastic springs. The hysteretic nonlinear energy sink protects the primary system through the energy pumping mechanism which transfers energy from the primary system and dissipates it in the hysteretic nonlinear energy sink. Three nonlinear equations of motion describe the resulting two-degree-of-freedom system response. The parameters of the system to be considered as uncertain are the natural frequency of the primary system and the hysteretic nonlinear energy sink linear elastic spring, which follow a normal distribution. A reliability analysis is then performed to evaluate the robustness of the coupled system in the presence of uncertainty. Specifically, the reliability index is calculated based on first passage probabilities of distinct dissipation energy level crossings using the Monte Carlo method. Several examples are examined considering various levels of initial input energy, and useful conclusions are drawn concerning the influence of uncertainty in the system robustness.
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The classical Type I NES with purely cubic stiffness was found performing better compared with the hysteretic NES at some energy levels and uncertain natural frequency of the primary system.
“Nevertheless, the classical Type I NES with purely cubic stiffness was found performing better compared with the HNES at some energy levels and uncertain natural frequency of the primary system.”
From A review on nonlinear energy sinks: designs, analysis and applications of impact and rotary types (2023) · cites this paper as [156]
Incorporating a negative linear stiffness in the hysteretic NES enhanced the robustness of performance for broadband energy levels.
“Moreover, it was found that incorporating a negative linear stiffness in the HNES enhanced the robustness of performance for broadband energy levels.”
From A review on nonlinear energy sinks: designs, analysis and applications of impact and rotary types (2023) · cites this paper as [156]
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- Authors
- Tsiatas, G. C., & Karatzia, D. A.
- Affiliations
- University of Patras (GR)
- Department of Mathematics, University of Patras, Greece
- Corresponding author
- Tsiatas, George C
- ORCID
- Tsiatas, George C
- Venue
- Journal of Vibration and Control
- Publisher
- SAGE Publications
- Published
- 2020-04-05
- Volume
- 26
- Issue
- 23-24
- Pages
- 2261-2273
- ISSN
- 1077-5463 (ISSN-L)
- 1741-2986
- OpenAlex
- W3014706381
- Cited by
- 23
- References
- 25
- Citations by year
- 2026: 2 · 2025: 1 · 2024: 4 · 2023: 7 · 2022: 5 · 2021: 3 · 2020: 1
- FWCI
- 2.34
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of Vibration and Control (publishedVersion)
- Funders
- Greece and the European Union (2018-050-0502-15364)
- Topics
- Physical Sciences › Engineering › Civil and Structural Engineering › Vibration Control and Rheological Fluids
- Social Sciences › Decision Sciences › Statistics, Probability and Uncertainty › Probabilistic and Robust Engineering Design
- Physical Sciences › Engineering › Control and Systems Engineering › Vibration and Dynamic Analysis
- Keywords
- shock mitigation, passive vibration control, reliability analysis, Bouc-Wen model, Duffing oscillator, negative stiffness, energy pumping, first-passage probability, parameter uncertainty, two-degree-of-freedom system, Monte Carlo simulation
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