A survey of the precise integration method

Gao, Qiang; Tan, Shujun; Zhong, Wanxie

doi:10.1360/n092016-00205

Cited by 6 publications

(3 citation statements)

References 9 publications

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“…The precise integration method's unique conception and intelligent algorithm make its calculation result very accurate. [30][31][32][33] The method has excellent characteristics such as compatibility, convergence, stability, zero amplitude attenuation rate, zero period extension rate, no transcendence, etc. The precise integration method can obtain numerical results approximating the machine when solving linear steady structural equations.…”

Section: Determination Of Control Parameters Of the 2-dof Vibration S...mentioning

confidence: 99%

Theoretical and Experimental Research on Active Suspension System with Time‐Delay Control

Wu,

Ren,

et al. 2023

Advcd Theory and Sims

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Time‐delay significantly impacts the control system's performance and even leads to the unexpected instability of the control system. This paper aims at the adverse effect of time‐delay on the control effect and stability of the active suspension system. This paper proposes to suppress vehicle body vibration by applying time‐delay displacement feedback. In this paper, the time‐delay control characteristics of the system are studied by combining theory with experiment. This paper first establishes the suspension system's dynamic Equation with time‐delay. Then, the frequency domain sweep method is used to analyze the stability of the control system. Finally, the time‐delay simulation model is established, and the single‐frequency excitation is used as the external excitation to compare with passive and backstepping control. The simulation results verify the superiority of the time‐delay control under external excitation. In this paper, through the 1/4 model bench test of the active suspension system, the simulation results and the test results under the same working conditions are compared, and it is found that the two have good consistency. The results show that the research is credible and can provide a reference for the actual design and application of active vehicle suspension controllers.

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Section: Determination Of Control Parameters Of the 2-dof Vibration S...mentioning

confidence: 99%

Theoretical and Experimental Research on Active Suspension System with Time‐Delay Control

Wu,

Ren,

et al. 2023

Advcd Theory and Sims

View full text Add to dashboard Cite

show abstract

“…Wang and Au [21] developed a Gaussian quadrature method and piece wise interpolation polynomial method [22]. In addition, Simpson, Romberg, Cots, and other direct integration methods were used to find the nonhomogeneous terms [23,24]. For order reduction in systems of secondorder dynamic differential equations, others [25] have combined the Newmark method therein for order reduction and adopted series solution methods to deal with nonhomogeneous terms.…”

Section: Introductionmentioning

confidence: 99%

Earthquake Response Spectra Analysis of Bridges considering Pounding at Bilateral Beam Ends Based on an Improved Precise Pounding Algorithm

Zhang

Yan

Yue

et al. 2021

Shock and Vibration

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Asynchronous vibration was generated between the main bridge and approach spans or abutments due to differences in stiffness and mass during an earthquake, thus further leading to pounding at the bilateral beam ends. By taking a T-shaped rigid frame bridge as an example, the bilateral pounding model was abstracted, and the earthquake response spectra considering pounding at the bilateral beam ends were studied, including the maximum displacement spectrum, the acceleration dynamic coefficient spectrum, the pounding force response spectrum, and the response spectrum for the number of pounding events. An improved precise pounding algorithm was proposed to solve the dynamic equation of the bilateral pounding model. This algorithm is based on the precise integration method for solving the second-order dynamic differential equation and reduces the order thereof by introducing a new velocity vector and uses the series method to find the nonhomogeneous term. The system matrix is simpler, and the inversion of the system matrix can be avoided. On this basis, a multipoint earthquake-induced pounding response spectrum program was developed. A total of 18 seismic waves from Class II sites were selected, and the response spectra of 18 waves were analyzed using this new program. Furthermore, the effects of structural stiffness, mass, stiffness of contact element, pounding recovery coefficient, and peak ground acceleration (PGA) on the earthquake response spectrum were studied. Through the analysis of earthquake response spectra and a parametric study, the phenomenon of earthquake-induced pounding of bridges was clarified to the benefit of the analysis and engineering control of earthquake-induced pounding of bridges.

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“…Nowadays, it has been applied to many fields, including optimal control, heat conduction, wave propagation, partial differential equation, etc. [5]. The concept of PIM is to convert the second-order ordinary differential equation (ODE) to a first-order ODE by introducing a vector, through which more accurate results can be obtained with high numerical stability.…”

Section: Introductionmentioning

confidence: 99%

An Improved Explicit-Implicit Precise Integration Method for Nonlinear Dynamic Analysis of Structures

2020

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In this paper, an improved explicit-implicit precise integration method (EIPIM) is proposed for nonlinear dynamic analysis of structures based on the refined precise integration method (RPIM). The RPIM may face a numerical instability problem when using large time steps while the proposed EIPIM uses an explicit predictor-implicit corrector scheme to provide more stable and accurate results and allow for large time steps. When using EIPIM, the unknown displacements at the sta rting point are predicted by an explicit function, and the trial displacements at the second step are corrected by the implicit Lagrange interpolation method. In terms of numerical stability and precision, eight explicit formulas have been evaluated to develop a better predictor for EIPIM, i.e., two third-order, four fourth-order and two fifth-order functions. Four examples involving both linear and nonlinear problems illustrate the high stability and numerical efficiency of the proposed method. It is found that the explicit predictors EIPIM_O31 and EIPIM_O41 show good performance and are recommended for nonlinear dynamic analysis.

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A survey of the precise integration method

Cited by 6 publications

References 9 publications

Theoretical and Experimental Research on Active Suspension System with Time‐Delay Control

Theoretical and Experimental Research on Active Suspension System with Time‐Delay Control

Earthquake Response Spectra Analysis of Bridges considering Pounding at Bilateral Beam Ends Based on an Improved Precise Pounding Algorithm

An Improved Explicit-Implicit Precise Integration Method for Nonlinear Dynamic Analysis of Structures

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