Supercritical vibration of nonlinear coupled moving beams based on discrete Fourier transform

Ding, Hu; Zhang, Guoce; Chen, L.Q.

doi:10.1016/j.ijnonlinmec.2011.09.010

Cited by 19 publications

(9 citation statements)

References 29 publications

(53 reference statements)

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“…For a set of given parameters k f , k 1 , and c, the complex functions / n1 x ð Þ and / n2 x ð Þ can be determined from Eqs. (29) and (30). The following results can be deduced from Eqs.…”

Section: Governing Equationmentioning

confidence: 87%

“…Pellicano and Vestroni [11] performed a convergence test on the Galerkin method and proved that the difference becomes small when the term is bigger than four. Ding and Chen argued that the four-term Galerkin truncation yields rather accurate results for axially moving beams with the simply supported boundary conditions [13], and eight-term Galerkin truncation for the fixed boundary conditions [30]. In the present paper, the eight-term Galerkin method will be used to analyze the natural frequencies and modes for the linear standard form with space-dependent coefficients.…”

Section: Introductionmentioning

confidence: 96%

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Forced Vibrations of Supercritically Transporting Viscoelastic Beams

Ding

Zhang

Yang

2012

Journal of Vibration and Acoustics

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This study focuses on the steady-state periodic response of supercritically transporting viscoelastic beams. In the supercritical speed range, forced vibrations are investigated for traveling beams via the multiscale analysis with a numerical confirmation. The forced vibration is excited by the spatially uniform and temporally harmonic vibration of the supporting foundation. A nonlinear integro-partial-differential equation is used to determine steady responses. The straight equilibrium configuration bifurcates in multiple equilibrium positions at supercritical translating speeds. The equation is cast in the standard form of continuous gyroscopic systems via introducing a coordinate transform for nontrivial equilibrium configuration. The natural frequencies and modes of the supercritically traveling beams are analyzed via the Galerkin method for the linear standard form with space-dependent coefficients under the simply supported boundary conditions. Based on the natural frequencies and modes, the method of multiple scales is applied to the governing equation to determine steady-state responses. To confirm results via the method of multiple scales, a finite difference scheme is developed to calculate steady-state response numerically. Quantitative comparisons demonstrate that the approximate analytical results have rather high precision. Numerical results are also presented to show the contributions of foundation vibration amplitude, viscoelastic damping, and nonlinearity to the response amplitude for the first and the second mode.

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Section: Governing Equationmentioning

confidence: 87%

Section: Introductionmentioning

confidence: 96%

Forced Vibrations of Supercritically Transporting Viscoelastic Beams

Ding

Zhang

Yang

2012

Journal of Vibration and Acoustics

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“…The transient response of the B-ISG system is investigated during the restart procedure driven by the ISG. Compared with the traditional dynamic analysis of the belt drive system driven by the crankshaft pulley, 15 this section focuses on the engine-start process. The transient response in ISG driving mode is calculated to investigate the vibration and shock of the B-ISG system during the start process.…”

Section: Model Applicationsmentioning

confidence: 99%

“…14 The finite belt bending stiffness causes nontrivial transverse span equilibria, in contrast to string models with straight span equilibria. The natural frequencies of the accessory drive system are investigated by Ding et al 15 The belt is considered as moving beams in the supercritical transport speed ranges.…”

Section: Introductionmentioning

confidence: 99%

Modeling and dynamic analysis of accessory drive systems with integrated starter generator for micro-hybrid vehicles

Xiao

Shangguan

Deng

et al. 2018

Proceedings of the Institution of Mechanical Engineers, Part D:

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Belt-driven integrated starter generator system is a hybrid transmission that resembles the conventional serpentine belt-driven system. The system contains an integrated starter generator that performs a “start-stop” function on the engine. A two-pulley tensioner mechanism is attached to the integrated starter generator to maintain belt tension. The objectives of this paper are to develop modeling and calculation methods for estimating the performances of the belt-driven integrated starter generator system and to investigate the influence of damping of the two-pulley tensioner on vibration and shock. A systematic modeling and analysis method is proposed. The modeling method for the two-pulley tensioner is distinguished from any existing studies, which are generic for modeling the tensioner in belt-driven integrated starter generator systems with different layouts. A typical belt-driven integrated starter generator system is presented and a model is established to predict the dynamic response of rotational vibrations of pulleys, tensioner motions, and tension fluctuations. A parametric analysis is conducted to evaluate the two-pulley tensioner parameters with respect to their impact on the performances of the belt-driven integrated starter generator system.

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“…Since accounts for the belt bending stiffness, Figures 4(d) and 4(e) illustrate that the nontrivial equilibrium solutions are very sensitive to the belt bending stiffness. Mathematical Problems in Engineering = 1, 2, yields the governing equation of motion measured from the nontrivial equilibrium [32,33] ,…”

Section: The Iterative Solutionmentioning

confidence: 99%

Equilibria and Free Vibration of a Two-Pulley Belt-Driven System with Belt Bending Stiffness

Ding

2014

Mathematical Problems in Engineering

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Nonlinear equilibrium curvatures and free vibration characteristics of a two-pulley belt-driven system with belt bending stiffness and a one-way clutch are investigated. With nonlinear dynamical tension, the transverse vibrations of the translating belt spans and the rotation motions of the pulleys and the accessory shaft are coupled. Therefore, nonlinear piecewise discrete-continuous governing equations are established. Considering the bending stiffness of the translating belt spans, the belt spans are modeled as axially moving beams. The pattern of equilibria is a nontrivial solution. Furthermore, the nontrivial equilibriums of the dynamical system are numerically determined by using two different approaches. The governing equations of the vibration near the equilibrium solutions are derived by introducing a coordinate transform. The natural frequencies of the dynamical systems are studied by using the Galerkin method with various truncations and the differential and integral quadrature methods. Moreover, the convergence of the Galerkin truncation is investigated. Numerical results reveal that the study needs 16 terms after truncation in order to determine the free vibration characteristics of the pulley-belt system with the belt bending stiffness. Furthermore, the first five natural frequencies are very sensitive to the bending stiffness of the translating belt.

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Supercritical vibration of nonlinear coupled moving beams based on discrete Fourier transform

Cited by 19 publications

References 29 publications

Forced Vibrations of Supercritically Transporting Viscoelastic Beams

Forced Vibrations of Supercritically Transporting Viscoelastic Beams

Modeling and dynamic analysis of accessory drive systems with integrated starter generator for micro-hybrid vehicles

Equilibria and Free Vibration of a Two-Pulley Belt-Driven System with Belt Bending Stiffness

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