Abstract
As was indicated above, the general equation (1.28) can be integrated in closed form even if the disk features a hyperbolic profile, i.e., one defined by an equation of the following type (Stodola [70]):
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Notes
- 1.
Historically, Stodola’s hyperbolic profile (1924) analyzed here was the second variable thickness profile introduced in rotating disk theory.
- 2.
A variant of Stodola’s hyperbolic function was also introduced, in which thickness is defined by the relation \( h = {{h}_0} \cdot {{\left( {1 + \rho } \right)}^a} \), where h 0 is thickness on the axis and a is a negative exponent. This does not give rise to a singularity for ρ = 0, and can thus be used to describe the hyperbolic profile of a solid disk. With this relation, differential equation (1.28) can be integrated by means of the linear combination of two mutually independent hypergeometric functions (see Chap. 7).
Reference
Stodola, A.: Dampf und Gas-Turbinen, 6th edn. Julius Springer, Berlin (1924)
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© 2013 Springer-Verlag Italia
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Vullo, V., Vivio, F. (2013). Hyperbolic Disks. In: Rotors: Stress Analysis and Design. Mechanical Engineering Series. Springer, Milano. https://doi.org/10.1007/978-88-470-2562-2_4
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DOI: https://doi.org/10.1007/978-88-470-2562-2_4
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