Nonlinear Vibrations of Axially Moving Beams

Chen, Liqun

doi:10.5772/6948

Cited by 6 publications

(4 citation statements)

References 84 publications

(90 reference statements)

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“…Similarly, substituting equation (37) into equations ( 33), (35) and (36), the nonlinear ordinary differential governing equations for coupling of the d 31 and d 33 modes and the circuit equation can be expressed as:…”

Section: The Galerkin Methodsmentioning

confidence: 99%

“…Similarly, by substituting the derivative-difference schemes equations (55)-(63) into equations ( 26), (31), (33), (35) and (36), a group of algebraic equations for w i j and v i j can be obtained.…”

Section: Validation By the Finite Difference Methodsmentioning

confidence: 99%

“…Jing and Vakakis [32] studied energy harvesting from secondary resonances of a nonlinear piezoelectric beam. Jing et al [33][34][35] summarized nonlinear benefits for energy harvesting and proposed a system that consists of an adjustable inertia system and X-shaped support structures to enhance the operation range at low frequencies. The coupling of an X-shaped support structure with piezoelectric patches of certain arrangements has also been investigated.…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear energy harvesting via an axially moving piezoelectric beam with both d ₃₁ and d ₃₃ modes

Lu¹,

Chen²,

Fu³

et al. 2023

J. Phys. D: Appl. Phys.

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Piezoelectric energy harvesters (PEH) in the literature typically operate with a single conversion mechanism (either d31 or d33); the output power, therefore, is limited, and not sufficient to sustainably energize low-power electronics. In this study, a nonlinear PEH with couped d31 and d33 modes is designed and evaluated. An axially moving piezoelectric beam (AMPB) was applied to investigate the contribution of d31 and d33 to the output, and the critical parameters of the configuration were determined. A distributed parametric electromechanical model was established to characterize the non-linear dynamics of AMPB with d31 and d33 modes. The Galerkin approach and the harmonic-balance approach were employed conjointly to investigate the forced response of the energy harvesting system. The axial velocity’s effects upon energy harvesting were as well discussed. Comparison of the frequency response functions (FRFs) for voltage and power output between energy structures of d31 and d33 modes revealed several discrepancies. For instance, the voltage and power output of the d33 mode were greater than those of d31 mode for low frequencies, and the difference between the two modes decreased as the frequency increased. For the composite mode d31 and d33, under the same parameter conditions, the voltage and power output were greater than the output of any single mode. The analytical results were supported by a numerical method through the finite difference method. Both analytical and numerical results indicated the FRF could be increased by increasing the excitation amplitude, reducing the damping coefficient, or increasing the electrode spacing.The present study showed the efficiency of the use of the FRF using nonlinear transverse vibration of AMPB for d31 and d33 modes.

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Section: The Galerkin Methodsmentioning

confidence: 99%

Section: Validation By the Finite Difference Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Nonlinear energy harvesting via an axially moving piezoelectric beam with both d ₃₁ and d ₃₃ modes

Lu¹,

Chen²,

Fu³

et al. 2023

J. Phys. D: Appl. Phys.

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“…Many engineering system components in real-life, such as power transmission belts, paper, aerial cable cars, elevators in high-rise buildings, cables, and yarns used in car drives, can be modeled as axially moving continua. 1,2 Neglecting bending stiffness, the axially moving continuum can be modeled as an axially moving string, which has a straight static equilibrium position and can only bear axial tension. 3,4 However, yarn systems have low bending stiffness and exhibit flexible structural characteristics.…”

mentioning

confidence: 99%

Simulation and experimental study on transverse nonlinear vibration of axially moving yarn

Li,

Hu,

Peng

et al. 2024

Textile Research Journal

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This article focuses on the nonlinear dynamics of transverse vibration of the axially moving yarn system. In this article, the motion of yarn in actual production is analyzed, and the transverse nonlinear vibration equation of the viscoelastic axially moving yarn system with Kelvin model is established by using Newton’s second law. In the modeling process, the viscoelasticity of yarn material and the periodic fluctuation of tension in the process of movement are considered. The partial differential control equations of the system are transformed into ordinary differential equations by the Galerkin method. In the first three modes, when the speed is low, the related trial functions occupy the main part, and with the increase of speed, the trial functions of other orders occupy more proportion in the modal functions. Through numerical analysis, it is found that when the moving yarn is subjected to external excitation, the lateral vibration displacement has an increasing trend, and it is found that the nonlinear dynamic phenomenon alternates with the change of system parameters, such as single periodic motion, double periodic motion, and multiple periodic motion. Finally, an experimental platform for lateral vibration of yarn transmission was built and its working principle introduced. The lateral vibration of axially moving yarn was studied from the experimental point of view. It was proved that there are abundant phenomena of periodic motion, period doubling motion, and chaotic motion in the axially moving yarn system, which provides an experimental reference for theoretical research of lateral nonlinear vibration of axially moving yarn.

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Parametric and internal resonances of in-plane accelerating viscoelastic plates

Tang¹,

Chen

2011

Acta Mech

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Nonlinear Vibrations of Axially Moving Beams

Cited by 6 publications

References 84 publications

Nonlinear energy harvesting via an axially moving piezoelectric beam with both d ₃₁ and d ₃₃ modes

Nonlinear energy harvesting via an axially moving piezoelectric beam with both d ₃₁ and d ₃₃ modes

Simulation and experimental study on transverse nonlinear vibration of axially moving yarn

Parametric and internal resonances of in-plane accelerating viscoelastic plates

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Nonlinear Vibrations of Axially Moving Beams

Cited by 6 publications

References 84 publications

Nonlinear energy harvesting via an axially moving piezoelectric beam with both d 31 and d 33 modes

Nonlinear energy harvesting via an axially moving piezoelectric beam with both d 31 and d 33 modes

Simulation and experimental study on transverse nonlinear vibration of axially moving yarn

Parametric and internal resonances of in-plane accelerating viscoelastic plates

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Product

Resources

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Nonlinear energy harvesting via an axially moving piezoelectric beam with both d ₃₁ and d ₃₃ modes

Nonlinear energy harvesting via an axially moving piezoelectric beam with both d ₃₁ and d ₃₃ modes