Symplectic Method-Based Analysis of Axisymmetric Dynamic Thermal Buckling of Functionally Graded Circular Plates

Zhang, J. H.; Liu, X.; Zhao, Xin

doi:10.1007/s11029-019-09825-w

Cited by 6 publications

(7 citation statements)

References 22 publications

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“…Our analysis of current publications [1,2,[9][10][11][12][13][14][15] leads to the conclusion that solving the problem about bending oscillations of circular plates is in high demand for research-ers and specialists in applied acoustics and mechanics. This judgment is supported by the presence of a huge number of technical applications of circular plates and various ways to solve the relevant eigenvalue problem.…”

Section: Literature Review and Problem Statementmentioning

confidence: 95%

“…This judgment is supported by the presence of a huge number of technical applications of circular plates and various ways to solve the relevant eigenvalue problem. However, most of the methods and algorithms considered in [1,2,[9][10][11][12][13][14][15] are specific and focus on iterative numerical approaches. In addition, the results reported in the cited papers typically refer to plates of constant thickness.…”

Section: Literature Review and Problem Statementmentioning

confidence: 99%

“…Work [12] considers a ceramic circular plate of the constant thickness (h=1 cm), exposed to thermal loads at the surface. A simplex method is recommended to analyze the dynamic thermal bend of the plate.…”

Section: Literature Review and Problem Statementmentioning

confidence: 99%

Section: Literature Review and Problem Statementmentioning

confidence: 99%

“…In articles [12,13], the object of the study is a circular metallic-ceramic plate of constant thickness, which is subject to increased temperature loads. However, in contrast to work [12], it is suggested to use a free grid method of interpolation for a bend analysis. Under conditions of considering the surface temperature of the plate (from 20 °C to 200 °C) and the associated change in the thickness of the plate, the reported theory and results are not possible to use for the analysis of free axisymmetric oscillations of a continuous circular plate of parabolic profile.…”

Section: Literature Review and Problem Statementmentioning

confidence: 99%

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Analytical solution to the problem about free oscillations of a rigidly clamped circular plate of variable thickness

Trapezon¹,

Trapezon²

2020

EEJET

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This paper reports an analytical solution to one of the problems related to applied mechanics and acoustics, which tackles the analysis of free axisymmetric bending oscillations of a circular plate of variable thickness. A plate rigidly-fixed along the contour has been considered, whose thickness changes by parabola h(ρ)=H0(1+µρ) 2. For the initial assessment of the effect exerted by coefficient µ on the results, the solutions at µ=0 and some µ≠0 have been investigated. The differential equation of the shapes of a variable-thickness plate's natural oscillations, set by the h(ρ) function, has been solved by a combination of factorization and symmetry methods. First, a problem on the oscillations of a rigidly-fixed plate of the constant thickness (µ=0), in which h(1)/h(0)=η=1, was solved. The result was the computed natural frequencies (numbers λ i at i=1...6), the constructed oscillation shapes, as well as the determined coordinates of the nodes and antinodes of oscillations. Next, a problem was considered about the oscillations of a variable-thickness plate at η=2, which corresponds to µ=0.4142. Owing to the symmetry method, an analytical solution and a frequency equation for η=2 were obtained when the contour is rigidly clamped. Similarly to η=1, the natural frequencies were calculated, the oscillation shapes were constructed, and the coordinates of nodes and antinodes of oscillations were determined. Mutual comparison of frequencies (numbers λ i) shows that the natural frequencies at η=2 for i=1...6 increase significantly by (28...19.9) % compared to the case when η=1. The increase in frequencies is a consequence of the increase in the bending rigidity of the plate at η=2 because, in this case, the thickness in the center of both plates remains unchanged, and is equal to h=H 0. The reported graphic dependences of oscillation shapes make it possible to compare visually patterns in the distribution of nodes and antinodes for cases when η=1 and η=2. Using the estimation formulae derived from known ratios enabled the construction of the normalized diagrams of the radial σ r and tangential σ θ normal stresses at η=1 and η=2. Mutual comparison of stresses based on the magnitude and distribution character has been performed. Specifically, there was noted a more favorable distribution of radial stresses at η=2 in terms of strength and an increase in technical resource

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Section: Literature Review and Problem Statementmentioning

confidence: 95%

Section: Literature Review and Problem Statementmentioning

confidence: 99%

Section: Literature Review and Problem Statementmentioning

confidence: 99%

Section: Literature Review and Problem Statementmentioning

confidence: 99%

Section: Literature Review and Problem Statementmentioning

confidence: 99%

See 3 more Smart Citations

Analytical solution to the problem about free oscillations of a rigidly clamped circular plate of variable thickness

Trapezon¹,

Trapezon²

2020

EEJET

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Effect of Material Properties in the Direct and Inverse Thermomechanical Analyses of Multilayer Functionally Graded Solids

2021

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Herein, the effect of material inhomogeneity on the temperature and stress distributions in functionally graded solids is analyzed. Assuming the inaccessibility of the inner surface of a multilayer functionally graded hollow sphere for the direct monitoring of the temperature in real time, the problem on identifying the temperature on this surface is formulated by implementing the temperature and circumferential strain given on the outer surface. The material properties within each sphere layer are assumed to be arbitrary functions of the radial coordinate. By representing the material properties of the sphere in the form of stepwise‐variable functions and implementing the generalized derivative technique, a method for the reduction of the formulated problem to an inverse thermoelasticity problem is developed. Using the finite difference method, a numerical algorithm for solving the inverse problem is suggested. The stability of the proposed numerical algorithm concerning the input perturbation is verified.

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Elastoplastic buckling of FGM beams in thermal environment

Zhang

Zheng

2020

Continuum Mech. Thermodyn.

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Symplectic Method-Based Analysis of Axisymmetric Dynamic Thermal Buckling of Functionally Graded Circular Plates

Cited by 6 publications

References 22 publications

Analytical solution to the problem about free oscillations of a rigidly clamped circular plate of variable thickness

Analytical solution to the problem about free oscillations of a rigidly clamped circular plate of variable thickness

Effect of Material Properties in the Direct and Inverse Thermomechanical Analyses of Multilayer Functionally Graded Solids

Elastoplastic buckling of FGM beams in thermal environment

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