The similitude design method of thin-walled annular plates and determination of structural size intervals

Abstract

For the design problem of dynamic similitude models of an aero engine's turbine discs, distorted scaling laws and structural size intervals of thin walled annular plates are established in the research. According to the governing equation, the geometrically complete scaling law of thin walled annular plates is firstly established. In order to determine accurate distorted scaling laws of thin walled annular plates, three significant principles are proposed and theoretically proved combining the governing equation and the sensitivity analysis. According to results of the sensitivity analysis, accurate distorted scaling laws of thin walled annular plates are obtained based on significant principles. In addition, structural size intervals of distorted scaling laws of thin walled annular plates are calculated by the numerical method. Finally, the previous six orders' natural frequencies of thin walled annular plates are discussed as examples to verify the theory presented in this research, and distorted scaling laws of each order's natural frequency are obtained and the corresponding structural size intervals are analyzed.

A Review of Similitude Methods for Structural Engineering

“…Luo et al [62] employ sensitivity analysis to derive the similitude conditions for distorted models. The authors enunciate four principles to get distorted laws.…”

“…3.6) relating the design scale factors to the sensitivities of the system. The method is used to investigate thin walled plates [133] and annular thin plates [62].…”

“…Sensitivity analysis does not just support already existing similitude methods [62,133], but can also be used to find scaling laws independently. This is the approach used by Adams et al [63], who use GSA to derive sensitivity-based scaling laws.…”

“…Whereas DA has proven to be versatile, STAGE has been shown to support some interesting variations, such as the modular approach [48], the determination of size applicable intervals [131][132][133], and the support of sensitivity analysis [62,133].…”

“…Sensitivity analysis has shown to be an approach that can support already existing methods like STAGE [62,133] or derive sensitivity-based scaling laws [63,64] independently from the classical similitude procedures. The global approach is useful to obtain the effects of the parameters and their combinations on the structural response, even for complex systems.…”