General analytical solution for vibrations of pipes with arbitrary discontinuities and generalized boundary condition on Pasternak foundation

Li, M.; Chen, Xiaochao; Chang, Xueping; Qin, Yin; Li, Y.H.

doi:10.1016/j.ymssp.2021.107910

Cited by 19 publications

(1 citation statement)

References 53 publications

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“…Hence, nonlinear oscillators have attracted numerous attention due to their significant applications [15][16][17]. The governing differential equation of a nonlinear system can be investigated numerically [18][19][20][21][22][23][24][25] or analytically [26][27][28][29][30]. However, analytical methods are of great interest because they provide closed-form solutions, making it easier to investigate the impact of various parameters on nonlinear frequency.…”

Section: Introductionmentioning

confidence: 99%

Improved harmonic balance method for analyzing asymmetric restoring force functions in nonlinear vibration of mechanical systems

Mohammadian,

Ismail

2024

Phys. Scr.

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The non-linear differential equation governing some mechanical systems, such as the non-linear vibrations of FG beams resting on a nonlinear foundation, behaves similarly to the oscillations of a non-linear oscillator with an asymmetric restoring force function that includes both odd and non-odd non-linear terms. The objective of this research is to obtain higher-order approximate analytical solutions for such problems by introducing an enhanced harmonic balance method. By building upon the original problem, two new symmetric systems with odd non-linear terms are introduced, and their higher-order approximate analytical solutions are derived using a novel approach. In proposed method, the restoring force function is represented by its Fourier series expansion. Unlike previous papers, linearizing the equation or taking the first derivative of the Fourier series in the subsequent iteration is unnecessary. However, to enhance the solution’s accuracy, the remaining error from each iteration is utilized in the next one. Finally, by combining the results from the two introduced systems, the analytical period and corresponding periodic solution of the original problem can be obtained. This method is applied to the governing differential equation of FG beams resting on non-linear foundations, a physical non-natural oscillator, and conservative Toda oscillator. The key advantages of this approach are its simplicity and its ability to provide highly precise solutions for both small and large amplitudes in a single iteration.

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Section: Introductionmentioning

confidence: 99%

Improved harmonic balance method for analyzing asymmetric restoring force functions in nonlinear vibration of mechanical systems

Mohammadian,

Ismail

2024

Phys. Scr.

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Analytical solutions for free and forced vibrations of elastically supported pipes conveying super-critical fluids

et al. 2022

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Dynamic modeling of fluid-conveying pipes restrained by a retaining clip

Dou¹,

Ding²,

Mao³

et al. 2023

Appl. Math. Mech.-Engl. Ed.

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Although most pipes are restrained by retaining clips in aircrafts, the influence of the clip parameters on the vibration of the fluid-conveying pipe has not been revealed. By considering the clip width, a new dynamic model of a fluid-conveying pipe restrained by an intermediate clip is established in this paper. To demonstrate the necessity of the proposed model, a half pipe model is established by modeling the clip as one end. By comparing the two models, it is found that the half pipe model overestimates the critical velocity and may estimate the dynamical behavior of the pipe incorrectly. In addition, with the increase in the clip stiffness, the conversion processes of the first two modes of the pipe are shown. Furthermore, by ignoring the width of the clip, the effect of the flow velocity on the accuracy of a concentrated restraint clip model is presented. When the flow velocity is close to the critical velocity, the accuracy of the concentrated restraint clip model significantly reduces, especially when the width of the clip is large. In general, the contribution of this paper is to establish a dynamic model of the fluid-conveying pipe which can describe the influence of the clip parameters, and to demonstrate the necessity of this model.

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General analytical solution for vibrations of pipes with arbitrary discontinuities and generalized boundary condition on Pasternak foundation

Cited by 19 publications

References 53 publications

Improved harmonic balance method for analyzing asymmetric restoring force functions in nonlinear vibration of mechanical systems

Improved harmonic balance method for analyzing asymmetric restoring force functions in nonlinear vibration of mechanical systems

Analytical solutions for free and forced vibrations of elastically supported pipes conveying super-critical fluids

Dynamic modeling of fluid-conveying pipes restrained by a retaining clip

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