Article
Mechanics
Siu-Siu Guo, Qingxuan Shi, Zhao-Dong Xu
Summary: This paper investigates hysteretic systems under non-stationary excitations and proposes a method to solve these systems. The non-stationary response of the system is analyzed through indicators such as hysteretic energy and probability density function. The influence of different degradation levels on the response is also discussed.
Article
Engineering, Civil
Jianhua Xian, Cheng Su, Ziqi Wang
Summary: In this study, an explicit time-domain method (ETDM) is proposed to determine the higher-order response statistics of linear systems subjected to non-stationary non-Gaussian random excitations. The method directly formulates the first four orders of cumulants of dynamic responses based on the cumulant operation rule. Furthermore, an equivalent linearization - explicit time-domain method (EL-ETDM) is developed to solve the non-stationary non-Gaussian random vibration problems of Duffing systems, which allows for the analysis of higher-order cumulants of the linearized system.
Article
Multidisciplinary Sciences
Huan Huang, Yuyu Li, Wenxiong Li, Guihe Tang, Yanmei Lv
Summary: A novel approach is developed for random vibration analysis of nonlinear frame structures under seismic random excitations. The method integrates the plastic hinge model and auxiliary differential equations, and proposes an explicit iteration scheme for solving the equations, resulting in non-stationary random responses.
SCIENTIFIC REPORTS
(2022)
Article
Automation & Control Systems
Jorge M. Monsalve, Anton Melnikov, Bert Kaiser, David Schuffenhauer, Michael Stolz, Lutz Ehrig, Hermann A. G. Schenk, Holger Conrad, Harald Schenk
Summary: This article introduces a circuit model that captures the full nonlinear behavior of an asymmetric electrostatic transducer, showing good simulation performance for MEMS loudspeakers or microphones. The fitted parameters of the model agree well with experimental data, and additional complex behaviors can be introduced if needed.
IEEE-ASME TRANSACTIONS ON MECHATRONICS
(2022)
Article
Automation & Control Systems
Jorge M. Monsalve, Anton Melnikov, Bert Kaiser, David Schuffenhauer, Michael Stolz, Lutz Ehrig, Hermann A. G. Schenk, Holger Conrad, Harald Schenk
Summary: This article presents a circuit model that accurately captures the nonlinear behavior of an electrostatic transducer, validating its simulation results with experimental measurements. The model can be further extended to analyze additional complex behaviors.
IEEE-ASME TRANSACTIONS ON MECHATRONICS
(2022)
Article
Physics, Mathematical
Kajal Krishna Dey, Golam Ali Sekh
Summary: In the case of fixed stiffness, strong correlated random excitations distort the Poincare map, making it purely random, while random response competes with chaotic motion to enhance system stability. In the case of periodically modulated stiffness, random fields can change the system's state from transient to stable.
JOURNAL OF STATISTICAL PHYSICS
(2021)
Article
Mathematics, Applied
Martin Bresar, Pavle Boskoski, Martin Horvat
Summary: In this study, the direction of coupling in coupled Duffing oscillator systems in different dynamical regimes was successfully inferred by observing the conditional mutual information (CMI) based on Shannon entropy. It was also shown that in the weak coupling limit, the values of CMI can be used to infer the coupling parameters through information susceptibility.
Article
Mathematics, Applied
Homero G. Diaz-Marin, Osvaldo Osuna
Summary: In this paper, we investigate the existence and stability conditions of quasi-periodic solutions for a Duffing-type oscillator with constant damping, a unique odd nonlinearity, and time-dependent coefficients which are quasi-periodic. We extend some previous results for periodic coefficients and quintic nonlinearity. By using the classical theory of perturbations, we provide numerical examples for the quintic case to illustrate our findings.
REVISTA DE LA UNION MATEMATICA ARGENTINA
(2023)
Article
Mechanics
Nguyen V. Manh, Nguyen N. Linh, Anh. T. Nguyen, N. D. Anh
Summary: This study focuses on the harvesting of energy from mono-stable Duffing oscillators with piezoelectric coupling under white noise excitation. The higher-order averaging procedure is extended for the first time to find approximate stationary joint probability density functions of amplitude and full phase. The mean-square electric voltage and mean output power are derived through the approximate relation between the electric voltage and the mechanical states. The results are verified by Monte Carlo simulation, and the effects of system parameters on displacement and power are discussed.
MECHANICS RESEARCH COMMUNICATIONS
(2023)
Article
Mathematics, Applied
Fan Kong, Huimin Zhang, Yixin Zhang, Panpan Chao, Wei He
Summary: This article proposes a statistical linearization method for determining the response moment of multi-degree-of-freedom nonlinear systems with fractional elements and subjected to combined stochastic and periodic excitation. The method decomposes the response into periodic and stochastic components and solves the resulting coupled differential equations using the harmonic balance and statistical linearization methods. Numerical examples demonstrate the accuracy of the proposed method.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2022)
Article
Mathematics, Interdisciplinary Applications
M. Shamsul Alam, M. Ashraful Huq, M. Kamrul Hasan, M. Saifur Rahman
Summary: A new technique for solving strong nonlinear oscillatory problems is presented, which is independent of trigonometric functions and involves simple determination of unknown coefficients. The method is illustrated with examples, showing good agreement with numerical solutions for large amplitude oscillations of some nonlinear oscillators.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Materials Science, Multidisciplinary
Konstantinos Tsaltas
Summary: This paper proposes an improved method for approximating the frequency of the cubic-quintic Duffing oscillator by using a weighted average amplitude-frequency relation.
RESULTS IN PHYSICS
(2023)
Article
Acoustics
Luigi Miniero, Georg A. Mensah, Claire Bourquard, Nicolas Noiray
Summary: The ingestion of hot gas in the resonant cavity of Helmholtz dampers can affect the damper's resonance frequency and prevent the control of thermoacoustic feedback in gas turbines. This study presents experimental and theoretical investigations on this issue and develops a physics-based model for dampers. The results can be used to design acoustic dampers that are robust against the risk of hot gas ingestion.
JOURNAL OF SOUND AND VIBRATION
(2023)
Article
Engineering, Civil
Ziqi Wang
Summary: This study addresses the fundamental limitation of equivalent linearization methods in nonlinear random vibration analysis, proposing a method to construct an estimator that converges on the nonlinear system solution using a limited number of nonlinear system simulations and optimizing the equivalent linear system to approach the nonlinear system solution quickly, especially for rare event probabilities.
Article
Mathematics, Applied
Minjuan Yuan, Liang Wang, Yiyu Jiao, Wei Xu
Summary: In this paper, an improved cell mapping method based on dimension-extension is proposed to study the global dynamics of fractional systems, which successfully describes one-step mappings using Markov chains, avoiding memory losses. Simulations demonstrate the high accuracy and efficiency of the method, revealing abundant global dynamics behaviors in fractional smooth and discontinuous oscillators.
Article
Engineering, Mechanical
R. Allahvirdizadeh, A. Andersson, R. Karoumi
Summary: The operational safety of high-speed trains on ballasted bridges relies on preventing ballast destabilization. This study explores the impact of epistemic uncertainties on the system using ISRA. Neglecting these uncertainties can lead to overestimation of permissible train speeds and reduced system safety.
PROBABILISTIC ENGINEERING MECHANICS
(2024)
Article
Engineering, Mechanical
Lujie Shi, Leila Khalij, Christophe Gautrelet, Chen Shi, Denis Benasciutti
Summary: This study proposes an innovative Two-phase method based on the Langlie method and the D-optimality criterion to overcome the intrinsic shortcomings of the staircase method used in estimating the fatigue limit distribution. Through simulation-based study, it is demonstrated that the proposed method improves the estimation performance for the mean and standard deviation of the fatigue limit distribution.
PROBABILISTIC ENGINEERING MECHANICS
(2024)
Article
Engineering, Mechanical
Axay Thapa, Atin Roy, Subrata Chakraborty
Summary: This article compares different metamodeling approaches for reliability analysis of tunnels to evaluate their performance. The study found that Kriging and support vector regression models perform well in estimating the reliability of underground tunnels.
PROBABILISTIC ENGINEERING MECHANICS
(2024)
Article
Engineering, Mechanical
Jiaqi Wang, Zhenzhou Lu, Lu Wang
Summary: This paper proposes an efficient method to estimate the FP-GS using reliability updating, avoiding the time-consuming double-loop structure analysis. By utilizing the likelihood function and adaptive Kriging model, the unconditional FP and all conditional FPs can be estimated simultaneously.
PROBABILISTIC ENGINEERING MECHANICS
(2024)
Article
Engineering, Mechanical
Jiaxu Li, Ming Liu, Xu Yan, Qianting Yang
Summary: Wind pressure is essential for architectural design, and this study found that using different probabilistic distribution models can improve the accuracy of reference wind pressure calculation. In the research conducted in Liaoning Province, the extreme value type III model and moment method achieved the best fit. Additionally, probability density functions for wind speed and wind direction were established for further analysis of wind pressure.
PROBABILISTIC ENGINEERING MECHANICS
(2024)
Article
Engineering, Mechanical
Yufan Cheng, Xinchen Zhuang, Tianxiang Yu
Summary: This paper proposes a time-dependent kinematic reliability analysis method that takes into account the truncated random variables and joint clearances, effectively addressing the issues of dimension variables and correlation between joint clearance variables. The proposed method transforms time-dependent reliability into time-independent reliability, greatly reducing computational complexity and obtaining upper and lower bounds of failure probability.
PROBABILISTIC ENGINEERING MECHANICS
(2024)
