Analytical approximations for elastic limit angular velocities of rotating annular disks with hyperbolic thickness

Kutsal, Servet Mert; Coşkun, Safa Bozkurt

doi:10.1007/s40430-023-04132-x

Cited by 3 publications

(3 citation statements)

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“…The results of analytical studies on disks of variable thickness under the mode of radial vibrations are limited because of known difficulties of a mathematical nature that arise when trying to solve the differential equation of the problem. Our review of current literature [2][3][4][5][6][7][8][9][10][11][12][13] revealed that the solutions to the problems of oscillations of disks of variable thickness are extremely necessary for specialists in the field of mechanics and applied acoustics. This is confirmed by the presence of a significant number of various practical applications of disks as structural elements of machines.…”

Section: Literature Review and Problem Statementmentioning

confidence: 99%

“…In theoretical paper [10], a disk with a hyperbolic profile was considered and the maximum rotational speeds were calculated. Two methods of analytical approximation were used for calculations.…”

Section: Literature Review and Problem Statementmentioning

confidence: 99%

“…Disks of variable thickness are one of the most important structural elements of turbines for various purposes, engines, and other high-speed machines and mechanisms, in particular in aircraft and rocket engineering [1][2][3][4][5][6][7][8][9][10][11][12][13]. Of practical importance are special-purpose disks in which radial vibrations are deliberately excited for technological purposes.…”

Section: Introductionmentioning

confidence: 99%

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Results of the analytical solution of the problem of radial vibrations of disks of variable thickness

Trapezon,

Kalinichenko

et al. 2024

EEJET

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An analytical solution is obtained for the problem of radial vibrations of disks of variable thickness. A disk is considered that is rigidly fixed along the inner circular contour (ρ=0.2) and free on the outer contour (ρ=1). The thickness of the disk varies according to the law H=H0(ρν+μ+Cρν-μ)2, where H0,C,μ are arbitrary constants; ν is the Poisson's ratio. The exact solution of the problem is known only for H=const and H=1/ρ3. However, these solutions are not sufficient to study the vibrations of disks of other configurations. The proposed law of thickness variation H(ρ) allows us to obtain exact solutions to the problem at any value of the constant coefficients H0, C, μ, ν. By varying the values of these coefficients within a single given function, it is possible to set the disk profile of the desired appearance. The methods used to obtain these solutions are based on appropriate mathematical transformations of the original equation. The problem of disk oscillations is solved for four variants of thickness change. The natural frequencies for the first three forms of vibration are calculated. Comparison of the natural frequencies found for the three cases of the disk profile gently sloping indicates an increase in their values with an increase in the bending of the disk thickness. Based on the obtained eigenfunctions, the stresses were calculated and the nature of their distribution along the radial coordinate of the disk was determined. The strength of the disks under resonant radial vibrations was evaluated using a special criterion. It is found that the most limiting, i.e., destructive principal stress σ1=σr at the first (main) form of vibration should be chosen from the ratio σr≈0.79 [σ-1], where [σ-1] is the endurance limit of the disk material under uniform loading. The results obtained can be used to predict the stress-strain state of disks of variable profile under their radial vibrations

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