Jacob Nagler



Notes on Mathematical Techniques in Rotational and Non-rotational Cylindrical Disks

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This paper presents new fresh theoretical expressions development for four special cases. The first case concerns steady-state rotating disk made of functionally graded material (FGM) whilst its material properties and geometry are both varying exponentially. In addition, the disk is subjected to thermal loadings, which have also been considered during calculation. Fully generalized analytical expressions for the displacement and the stress-strain relationships dependent on the material and geometrical parameters as well as on the rotational/spinning velocity and temperature conditions (thermal stresses) subjected to mechanical loadings, have been developed analytically using MAPLE program for special case – extending the analytic study performed by Wen-feng Lin. The second case concern three solid bodies' cylinders that are rotating in triangle partially contact configuration, such as there motion is dependent on each other. The main rationalism is to derive analytic expressions for their stability estimation using simple kinematic relations and body-force diagram as dependent on their geometry and the angular velocity. Finally, the third case concern asymmetrical beam/shaft section analysis in the context of moment instability involved with broad connection to increase the stability interval in relative to the center of mass location.


Disk; Cylinder; FGM; Angular velocity; Exponential variable properties; Thermal stress; Stability; Friction; Contact; Asymmetric beam; Connection joint width; Center of mass.


Cite this paper

Jacob Nagler. (2022) Notes on Mathematical Techniques in Rotational and Non-rotational Cylindrical Disks. International Journal of Theoretical and Applied Mechanics, 7, 1-11


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