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Stress analysis in an isotropic hyperbolic rotating disk fitted with rigid shaft

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Abstract

The purpose of this paper is to present study of stresses distribution and displacement in an isotropic hyperbolic rotating disk fitted with rigid shaft and having variable density parameter by using transition theory. It has been seen that the convergent disk made of rubber material requires a higher angular speed at the inner surface as compared to aluminum alloy material on the initial yielding stage, but for the fully plastic stage divergent disk requires higher angular speed at the inner surface as compared to a uniform/convergent disk. With the introduction of density parameter, the values of angular speed increase in the inner surface the initial/fully plastic stage. The convergent disk made of rubber material requires maximum radial stress at the inner surface as compared to aluminum alloy material. With the increasing value of density parameter, the radial stress increases in the intermediate surface of the hyperbolic rotating disk. Results have been discussed numerical and depicted graphically.

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Abbreviations

\(e_{kk} \) :

First strain invariant

\(T_{ij} ,e_{ij} \) :

Stress and strain tensors

u, v, w :

Displacement components

E :

Young’s modulus

\(\nu \) :

Poisson’s ratio

c :

Compressibility factor

\(\lambda ,\mu \) :

Lame’s constants

\(\Omega ^{2}\) :

Angular speed

\(\omega \) :

Speed factor

Y:

Yielding stress

k, m :

Thickness and density parameters

\(\delta _{ij} \) :

Kronecker’s delta

\(h_{i} ,\rho _{0} \) :

Thickness at inner and density at outer surface

r :

Function of x and y

\(\beta \) :

Function of r only

\(\Psi \) :

Transition function

\(\rho \) :

Density

d :

Constant

\(A_{1} ,A_{2} \) :

Constants of integration

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Authors and Affiliations

  1. Department of Mathematics, ICFAI University, Baddi, Himachal Pradesh, India

    Pankaj Thakur, Monika Sethi, Naresh Kumar & Neeru Gupta

  2. Department of Physics, ICFAI University, Baddi, Himachal Pradesh, India

    Kanav Gupta & R. K. Bhardwaj

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  1. Pankaj Thakur
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  2. Monika Sethi
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Thakur, P., Sethi, M., Kumar, N. et al. Stress analysis in an isotropic hyperbolic rotating disk fitted with rigid shaft. Z. Angew. Math. Phys. 73, 23 (2022). https://doi.org/10.1007/s00033-021-01663-y

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