Continuum modeling for lithium storage inside nanotubes

Alsaud, Huda; Alshehri, Mansoor H.

doi:10.3389/fphy.2023.1221720

Cited by 1 publication

(1 citation statement)

References 29 publications

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“…Due to the recent technological development in engineering practice, the characteristic size of structures become smaller and smaller [33][34][35][36], including the micro beam [37][38][39] with Winkler elastic foundation [40], micro torus plate [41], micro cylindrical shell [42,43], micro-structure on elastic foundation [44], and fluidconveying micro pipe [45]. The study of micro-scale pipes is an important research direction of the dynamics of fluid-conveying pipes.…”

Section: Introductionmentioning

confidence: 99%

Periodic motion of macro- and/or micro-scale cantilevered fluid-conveying pipes with O(2) symmetry: a finite dimensional analysis

Guo

2024

Front. Phys.

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Introduction: In this study, the spatial bending vibration of macro- and/or micro-scale cantilevered fluid-conveying pipes is investigated through finite dimensional analysis.Methods: Firstly, the Galerkin method is employed to discretize the partial differential equations of motion of the system into a system of ordinary differential equations. Then, the projection method based on center manifold-normal form theory is adopted to derive the coefficient formula that determines the pipe’s nonlinear dynamic behaviors, i.e., the change rate of the real part of the critical eigenvalue with respect to the flow velocity and the nonlinear resonance term, thereby obtaining reduced-order equations. Compared to previous studies that relied on the numerical solution of ordinary differential equations to determine the existence and stability of periodic motion, this paper concludes the existence and stability of periodic motion by utilizing the coefficients of the Galerkin discretized equations and the reduced-order equations, significantly saving time in determining the dynamic properties of pipes.Results and discussion: Subsequently, by investigating the reduced-order equations under specific parameters, the existence and stability of the two types of periodic motion of the pipe are studied. For macro pipes, the truncated mode numbers are set incrementally to calculate the coefficients of the reduced-order equations, investigate the distribution of the stability of the two types of periodic motions with the mass ratio, and carry out a longitudinal comparison (i.e., the comparison between the results obtained under different truncated mode numbers) as well as a horizontal comparison (i.e., the comparison of results between the finite dimensional analysis and the infinite dimensional analysis). It is found that the reasonable truncated mode number required to study this type of system is 15. Previous studies primarily focused on the convergence of frequency and amplitude when determining the truncated mode numbers. On this basis, our study further examines the convergence of motion forms with respect to the truncated mode numbers. Finally, based on the Galerkin discretization equations of 15 modes, the distribution of the stability of two types of the periodic motion of micro pipes with the mass ratio is analyzed. For macro- and micro-scale pipes, when the truncated mode number is 15, the error between the finite dimensional analysis results and the infinite dimensional analysis results is calculated to be about 7%. The above results are verified by obtaining the numerical solution to Galerkin discretization equations.

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Section: Introductionmentioning

confidence: 99%

Periodic motion of macro- and/or micro-scale cantilevered fluid-conveying pipes with O(2) symmetry: a finite dimensional analysis

Guo

2024

Front. Phys.

View full text Add to dashboard Cite

show abstract

Continuum modeling for lithium storage inside nanotubes

Cited by 1 publication

References 29 publications

Periodic motion of macro- and/or micro-scale cantilevered fluid-conveying pipes with O(2) symmetry: a finite dimensional analysis

Periodic motion of macro- and/or micro-scale cantilevered fluid-conveying pipes with O(2) symmetry: a finite dimensional analysis

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