Retracted Article: Application of correction factors in Rayleigh method in calculation of the fundamental frequency of vibration Cylindrical shell with rectangular cross section

Abstract

A number of gas turbine engine components, in particular, combustion chamber flame tube hoods, jet nozzles, afterburner chambers and some elements of the power body can be considered as thin-walled shells. Loads which excite vibrations of these assemblies are gas-dynamic forces of gas flow pulsation, loads transferred from supports from rotation of the unbalanced rotor, non-stationary flowing by an incoming air stream, dynamic loads, transferred to the engine through its attachment units to the aeroplane at landing and run, etc. The magnitude and nature of variation of these loads in time are not always describable, but their spectral composition is well studied. In this connection it is advisable to set and solve the problem of dynamic calculation of such assemblies as a problem of calculation of frequencies of their own vibrations in order to tune out dangerous resonance modes. Most of the GTE structures of thin-walled nodes are carried out as cylindrical shells. Therefore, below the shells of this configuration will be considered. In addition, it should be noted that the basic properties of the frequency spectrum of shells of rotation with curvilinear formations have a great qualitative similarity with the features of the frequency spectrum of cylindrical shells. We consider using correction factors in the Rayleigh method for calculating the fundamental frequency of cylindrical shell vibrations with rectangular cross section. The regularities of the behaviour of the correction coefficients are systematised. The relation between the type of correction coefficients and properties of the obtained approximated formula has been analyzed.