A Simple Frequency Formulation for the Tangent Oscillator

In the process of guide roller transmission, the geometric nonlinearity caused by the lateral vibration of the flexible electronic membrane will result in the divergence and instability of the membrane velocity, thus affecting the printing accuracy. In this paper, in order to engineer the exact condition that affecting the printing accurancy, the Elliptic integral method, whose effectiveness has been verified for its soluted result, is consistent with the one concluded from L-P method and He's Frequency formula while soluting the nonlinear vibration equation, respectively, on basis of Von Karman’s large deflection theory and Hamilton’s principle, is mainly applied, and thus provide a theoretical support for the design and manufacture of high-precision flexible electronic printing press.

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“…Here, L-P perturbation method is compared with He's frequency formula. 21 The square of its frequency can be obtained, which is…”

Section: He's Frequency Formulamentioning

confidence: 99%

“…Here, L-P perturbation method is compared with He’s frequency formula 21. The square of its frequency can be obtained, which iswhere A is the amplitude,when f(T(t))=ω02T(t)+ω02εα1T3(t), the frequency of equation (19) is easily obtained as follows…”

Section: Introductionmentioning

confidence: 99%

Study on nonlinear vibration of flexible electronic membrane engendered by high-precision imprinting system

Feng

Wang

et al. 2022

Journal of Low Frequency Noise, Vibration and Active Control

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“…He [20][21][22] represents a genius idea in converting a nonlinear equation into an approximately linear equation. The frequency of a nonlinear vibration system is nonlinearly related to its amplitude, and this relationship is critical in the design of a packaging system and a microelectromechanical system (MEMS) [23]. The application of He's frequency leads to discuss the periodic property and the instability properties of a rotating pendulum system [24].…”

Section: Introductionmentioning

confidence: 99%

The periodic property of Gaylord’s oscillator with a non-perturbative method

El‐Dib

2022

Arch Appl Mech

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The Gaylord's oscillator is a vibrating of a uniform rigid rod without slipping on a rigid circular surface with a definite radius. The dominant equation of motion was the outcome of a strongly nonlinear pendulum equation of the second order. The run article is interested in obtaining the frequency–amplitude equation and the approximate solution of Gaylord's oscillator by a simpler approach. The frequency–amplitude relationship is derived in terms of the Bessel function. Quasi-exact periodic solution derived depends on a non-perturbative approach. The validation of the analytical solution is made through the comparison with the numerical solution which shows excellent approval. Finally, the non-perturbative method is of high accuracy besides simplicity if it is compared with the other perturbative techniques in analyzing the behavior of oscillators with strong nonlinearities.

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“…In recent years, structural vibration control has received extensive attentions, especially the vibration control of stay cables in cable-stayed bridges. [1][2][3] Stay cables, as the critical load-bearing component of cable-stayed bridges, are highly vulnerable to environmental excitations such as wind, wind-rain, and parametric excitations. [4][5][6] Frequent vibrations may shorten the cable life and impair public confidence in the safety of cable-stayed bridges.…”

Section: Introductionmentioning

confidence: 99%

Free vibration of a taut cable with a parallel-connected viscous mass damper and a grounded cross-tie

Cheng

Fan

2022

Journal of Low Frequency Noise, Vibration and Active Control

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Recent studies have shown that the combination of external dampers and cross-ties can overcome their respective deficiencies while retaining their respective merits. Inspired by the advantages of a viscous damper (VD) and a cross-tie on a single stay cable, the coupled damping effect of a parallel-connected viscous mass damper (PVMD) and a grounded cross-tie on a single stay cable is investigated in this paper. The complex wave number equations of the cable–PVMD–cross-tie system are first formulated through the complex modal analysis. Subsequently, the asymptotic and iterative complex wave numbers are compared to evaluate the applicability of the asymptotic and iterative solutions. Furthermore, parametric studies are carried out to investigate the effects of the stiffness coefficients and the installation positions of the cross-tie on the first supplemental modal damping ratio and frequency of the cable. Finally, the installation positions of the cross-tie are optimized to achieve the optimal vibration control of the cable with the PVMD and the cross-tie.

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A Simple Frequency Formulation for the Tangent Oscillator

Cited by 78 publications

References 34 publications

Study on nonlinear vibration of flexible electronic membrane engendered by high-precision imprinting system

Study on nonlinear vibration of flexible electronic membrane engendered by high-precision imprinting system

The periodic property of Gaylord’s oscillator with a non-perturbative method

Free vibration of a taut cable with a parallel-connected viscous mass damper and a grounded cross-tie

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