Improving Wilson-θ and Newmark-β Methods for Quasi-Periodic Solutions of Nonlinear Dynamical Systems

Guang, Liu; Lv, Z. R.; Chen, Y. M.

doi:10.4236/jamp.2018.68138

Cited by 9 publications

(6 citation statements)

References 14 publications

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“…The negative characteristic of this method is reflected in the numerical extension of the period. It is described in more detail in (Bathe, 2014;Newmark, 1959;Jin et al, 2004;Liu et al, 2018;Wilson, 2001;Anahory Simoes et al, 2023;Karimi et al, 2018;Hassan, 2019). Solving system oscillation equations using the Newmark method by direct integration is shown by Algorithm 3.…”

Section: Newmark Methodsmentioning

confidence: 99%

“…Numerical methods are processed in numerous papers and books, see (Hoffman, 2001;Rao, 2001;Wilson, 2001;Bathe, 2014;Subbaraj & Dokainish, 1989;Newmark, 1959;Noh & Bathe, 2019;Jin et al, 2004;Liu et al, 2018). Wilson in the ref.…”

Section: Introductionmentioning

confidence: 99%

“…(2001) investigated dynamics of structures using numerical integration. The paper of Liu et al (2018) gives an improvement of the Wilson-θ and Newmark-β methods for quasi-periodic solutions of nonlinear dynamical systems.…”

Section: Introductionmentioning

confidence: 99%

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Numerical methods and their application in dynamics of structures

Vasiljević¹

2023

Vojnotehnički glasnik

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Introduction/purpose: The aim of this paper is to analyse the numerical methods for solving differential equations of dynamic equilibrium in technical problems. Methods: The paper gives an overview of the following numerical methods: the method of central difference, the method of linear acceleration, the Newmark method, and the Wilson th method. Results: Various problems in applying numerical methods in dynamics of structures have been solved. Conclusion: It has been shown that the application of numerical methods has a fundamental importance in dynamics of structures.

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Section: Newmark Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Numerical methods and their application in dynamics of structures

Vasiljević¹

2023

Vojnotehnički glasnik

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“…The interaction between the wheel and road surface and the interaction between the bus body and the human body are achieved through the contact points. That is, the displacement compatibility condition and the force equilibrium condition are used in the process of solving the differential equation of vibration [18]. It is noteworthy that only the vertical displacement and force are transmitted between the bus wheel and the road surface, which is the same for the interaction between the human body and the bus body.…”

Section: Differential Equations Of Human-bus-road Coupled Vibrationmentioning

confidence: 99%

Study on Passenger Comfort Based on Human–Bus–Road Coupled Vibration

2020

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Nowadays, the comfort of drivers and passengers is drawing more and more attention. The interaction between vehicles and the asphalt road can cause coupled vibration and reduce the comfort of passengers. Therefore, the research on human–vehicle–road coupled vibration and the comfort of passengers is of great importance. In this paper, the three-dimensional human–bus–road coupled vibration system is established, including the bus model, the parallel biomechanical human model with 2 degrees-of-freedom (DOF), and road surface roughness condition. The proposed coupled model was then used to study the dynamic response of the system and the comfort evaluation of the human body. In the comfort evaluation, the annoyance rate based method was proposed to consider the randomness of passenger vibration, the difference of the psychosensory vibration, and the fuzziness of evaluation indicators. Compared to the fuzzy evaluation based on the ISO 2631 standard, the proposed annoyance rate based method gives a quantitative evaluation of human comfort. Not only the degree of comfort can be evaluated, but the percentage of people feeling uncomfortable can also be obtained. Finally, parametric studies were conducted to investigate the effects of road surface roughness, interlayer bonding condition, bus weight, bus speed, and sitting position. It is found that the road surface roughness has the most significant effect on human comfort.

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“…In order to make white noise smooth and have similar characteristics as seismic load or wind load, Butterworth filter is utilized to deal with the white noise. This filtered white noise is used as excitation signal, and Newmark- β method 24 is adopted to calculate the structural response. In addition, the disturbance of measurement noise should be also considered in this study.…”

Section: Numerical Examplementioning

confidence: 99%

Structural nonlinear damage identification using penalty conversion index of GARCH model

Guo

Heng

2014

Advances in Mechanical Engineering

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In the service period, some engineering structures may have cracks or other nonlinear damages. The nonlinear damages are the major influence to the safety of engineering structures, which should be detected as early as possible. Currently, the effective nonlinear damage detection method is still lacking. Therefore, a penalty conversion index based on generalized autoregressive conditional heteroskedasticity (GARCH) model is presented to identify the nonlinear damage. First, an exact expression of GARCH model is described, the bilinear stiffness characteristic of nonlinear damage is given, and acceleration responses are used to establish the GARCH model. Then, through the GARCH model analysis of nonlinear damages responses, it can be found that the variance of conditional variance are sensitive to the nonlinear damage information of acceleration responses, so a basic conversion index based on the variance of conditional variance is proposed. Finally, a penalty conversion index based on GARCH model is presented, which can reduce the interference induced by the adjacent unrelated factors. Numerical and experimental examples show that the identification results of the proposed penalty conversion index based on GARCH model are superior to those of the basic conversion index and the cepstral metric (CM) index.

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Improving Wilson-θ and Newmark-β Methods for Quasi-Periodic Solutions of Nonlinear Dynamical Systems

Cited by 9 publications

References 14 publications

Numerical methods and their application in dynamics of structures

Numerical methods and their application in dynamics of structures

Study on Passenger Comfort Based on Human–Bus–Road Coupled Vibration

Structural nonlinear damage identification using penalty conversion index of GARCH model

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