Abstract
A method of calculating a possible stability loss by a rotating circular annular disc of variable thickness is suggested within the theory of perfect plasticity with the help of small parameter method. A characteristic equation for a critical radius of a plastic zone is obtained as a first approximation. The formula for the critical angular velocity, determining the stability loss of the disc according to the self-balanced form, is derived. The method using which we can take into account the disc’s geometry and loading parameters is also specified. The efficiency of the proposed method is shown in Section 5 while considering an illustrative example. The values of critical angular velocity of rotating are found numerically for different parameters of the disc.
Highlights
The analytical methods of studying the stability loss [1,2,3,4,5,6] at radial tension are known to be applied to plane discs in elastoplastic state
A method of calculating a possible stability loss by a rotating circular annular disc of variable thickness is suggested within the theory of perfect plasticity with the help of small parameter method
This method underlies the present approach to approximate calculation of critical radius of the plastic zone and critical angular velocity of the rotating annular disc of variable thickness
Summary
The analytical methods of studying the stability loss [1,2,3,4,5,6] at radial tension are known to be applied to plane discs (with constant thickness) in elastoplastic state. In [7] a method of calculation of possible stability loss was proposed for the case of the simplest non-planar rotating circular disc, namely, the stepped disc, loaded by radial stress on the boundary. This method underlies the present approach to approximate calculation of critical radius of the plastic zone and critical angular velocity of the rotating annular disc of variable thickness. The applicability of the algorithm to the analysis of the small perturbations dynamics in case of the discs with arbitrary profiles is discussed
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