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Your search keyword '"Zhou, Taoran"' showing total 6 results
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6 results on '"Zhou, Taoran"'

1. A refined uniqueness result of Leray's problem in an infinite-long pipe with the Navier-slip boundary

Author

Li, Zijin, Liu, Ning, and Zhou, Taoran

Subjects
Mathematics - Analysis of PDEs, 35Q35, 76D05
Abstract

We consider the generalized Leray's problem with the Navier-slip boundary condition in an infinite pipe $\mathcal{D}=\Sigma\times\mathbb{R}$. We show that if the flux $\Phi$ of the solution is no larger than a critical value that is \emph{independent with the friction ratio} of the Navier-slip boundary condition, the solution to the problem must be the parallel Poiseuille flow with the given flux. Compared with known related 3D results, this seems to be the first conclusion with the size of critical flux being uniform with the friction ratio $\alpha\in]0,\infty]$, and it is surprising since the prescribed uniqueness breaks down immediately when $\alpha=0$, even if $\Phi=0$. Our proof relies primarily on a refined gradient estimate of the Poiseuille flow with the Navier-slip boundary condition. Additionally, we prove the critical flux $\Phi_0\geq\frac{\pi}{16}$ provided that $\Sigma$ is a unit disk., Comment: 20 pages. All comments are welcome!

Published
2024

5. Three-Dimensional Vibration Analysis of a Functionally Graded Sandwich Rectangular Plate Resting on an Elastic Foundation Using a Semi-Analytical Method

Author

Jie Cui, Oleg Gaidai, Li Zichao, Shenghui Tao, Zhou Taoran, and Renchuan Ye

Subjects
Materials science, Physics::Instrumentation and Detectors, 02 engineering and technology, lcsh:Technology, Functionally graded material, Article, Ritz method, 0203 mechanical engineering, Normal mode, functionally graded sandwich plate, General Materials Science, three-dimensional plate vibration, Boundary value problem, lcsh:Microscopy, Fourier series, lcsh:QC120-168.85, Sine and cosine transforms, general boundary conditions, elastic foundation, lcsh:QH201-278.5, lcsh:T, business.industry, Structural engineering, 021001 nanoscience & nanotechnology, Vibration, 020303 mechanical engineering & transports, lcsh:TA1-2040, lcsh:Descriptive and experimental mechanics, lcsh:Electrical engineering. Electronics. Nuclear engineering, lcsh:Engineering (General). Civil engineering (General), 0210 nano-technology, Material properties, business, lcsh:TK1-9971
Abstract

The three-dimensional vibration of a functionally graded sandwich rectangular plate on an elastic foundation with normal boundary conditions was analyzed using a semi-analytical method based on three-dimensional elasticity theory. The material properties of the sandwich plate varied with thickness according to the power law distribution. Two types of functionally graded material (FGM) sandwich plates were investigated in this paper: one with a homogeneous core and FGM facesheets, and another with homogeneous panels and an FGM core. Various displacements of the plates were created using an improved Fourier series consisting of a standard Fourier cosine series along with a certain number of closed-form auxiliary functions satisfying the essential boundary conditions. The vibration behavior of the FGM sandwich plate, including the natural frequencies and mode shapes, was obtained using the Ritz method. The effectiveness and accuracy of the suggested technique were fully verified by comparing the natural frequencies of sandwich plates with results from investigations of other functionally graded sandwich rectangular plates in the literature. A parametric study, including elastic parameters, foundation parameters, power law exponents, and layer thickness ratios, was performed, and some new results are presented.

Published
2019
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6. Three-Dimensional Vibration Analysis of a Functionally Graded Sandwich Rectangular Plate Resting on an Elastic Foundation Using a Semi-Analytical Method.

Author

Cui, Jie, Zhou, Taoran, Ye, Renchuan, Gaidai, Oleg, Li, Zichao, and Tao, Shenghui

Subjects
*ELASTIC foundations, *FUNCTIONALLY gradient materials, *ELASTIC plates & shells, *RITZ method, *MODE shapes, *FOURIER series, *SANDWICH construction (Materials)
Abstract

The three-dimensional vibration of a functionally graded sandwich rectangular plate on an elastic foundation with normal boundary conditions was analyzed using a semi-analytical method based on three-dimensional elasticity theory. The material properties of the sandwich plate varied with thickness according to the power law distribution. Two types of functionally graded material (FGM) sandwich plates were investigated in this paper: one with a homogeneous core and FGM facesheets, and another with homogeneous panels and an FGM core. Various displacements of the plates were created using an improved Fourier series consisting of a standard Fourier cosine series along with a certain number of closed-form auxiliary functions satisfying the essential boundary conditions. The vibration behavior of the FGM sandwich plate, including the natural frequencies and mode shapes, was obtained using the Ritz method. The effectiveness and accuracy of the suggested technique were fully verified by comparing the natural frequencies of sandwich plates with results from investigations of other functionally graded sandwich rectangular plates in the literature. A parametric study, including elastic parameters, foundation parameters, power law exponents, and layer thickness ratios, was performed, and some new results are presented. [ABSTRACT FROM AUTHOR]

Published
2019
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