Wave blade finite element with six node degrees of freedom

Аuthors

Shchemelev V. I.^*, Ermakov A. I.

Samara National Research University named after Academician S.P. Korolev, 34, Moskovskoye shosse, Samara, 443086, Russia

*e-mail: shchemelev.vi@ssau.ru

Abstract

As of today, the problems of dynamic strength of the impellers of any gas turbine engine are solved mainly by the frequency detuning from resonances located near its main operating modes. Frequency detuning can often only be achieved successfully by optimal design. The task of performing frequency detuning becomes significantly more complicated if the rotor impellers significantly affect each other oscillations. In this case, the time required to perform the adjustment, even when employing powerful computers, becomes unacceptably large. One of the options for solving this problem is to application of methods for computing vibrations of impellers that are more efficient in terms of computational performance. These include the wave finite element method. A wave blade finite element with six degrees of freedom in each node has been developed. It represents a discrete annular set of identical sections of impeller blades. For its developing a defining system of equations, which was obtained by transforming differential equations describing the torsional-flexural oscillations of the blades was employed. The transformation is performed based on the use of the properties of the proper motions spectra of structures with rotational symmetry. The stiffness and mass matrices of the wave blade element were obtained by the Galerkin method wth the defining system of equations and linear shape functions. These matrices are Hermitian and establish a linear relationship between the amplitudes of traveling waves of displacements and forces on the inner and outer boundaries of the blade element. The developed finite element allows determining dynamic characteristics of the GTE blade rings.

Keywords:

finite element method, wave blade finite element, modal analysis

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