The Dynamic Similitude Design Method of Thin Walled Structures and Experimental Validation

Abstract

For the applicability of dynamic similitude models of thin walled structures, such as engine blades, turbine discs, and cylindrical shells, the dynamic similitude design of typical thin walled structures is investigated. The governing equation of typical thin walled structures is firstly unified, which guides to establishing dynamic scaling laws of typical thin walled structures. Based on the governing equation, geometrically complete scaling law of the typical thin walled structure is derived. In order to determine accurate distorted scaling laws of typical thin walled structures, three principles are proposed and theoretically proved by combining the sensitivity analysis and governing equation. Taking the thin walled annular plate as an example, geometrically complete and distorted scaling laws can be obtained based on the principles of determining dynamic scaling laws. Furthermore, the previous five orders’ accurate distorted scaling laws of thin walled annular plates are presented and numerically validated. Finally, the effectiveness of the similitude design method is validated by experimental annular plates.

A Review of Similitude Methods for Structural Engineering

“…The method is applied to simply supported plates numerically [131] and experimentally [132], and to coated thin plates in Ref. [133]. Sensitivity analysis is then introduced to support STAGE in Ref.…”

Accurate prediction approach of dynamic characteristics for a rotating thin walled annular plate considering the centrifugal stress requirement

“…A principle [23] is employed to determine the accurate distorted scaling law by combining governing equation and sensitivity analysis. Sensitivity of the structural vibration behavior is defined by the changing rate of vibration characteristic parameters with respect to structural parameters (mass, stiffness and geometrical parameters) [25,26].…”

“…Similitude theory is usually employed to derive the scaling laws based on the governing equation. A different method is developed to obtain approximate scaling laws of thin walled plates and shells by Luo [21][22][23], where the determination principle and structural size intervals are proposed to predict the natural characteristics and dynamic response. The distorted models of coating thin plates are investigated for predicting the responses, and the effects of different coating thickness and coating forms are discussed by Luo et al [21].…”

“…The distorted models of coating thin plates are investigated for predicting the responses, and the effects of different coating thickness and coating forms are discussed by Luo et al [21]. Particularly in Luo [22,23], the applicability of determination method of the structural size intervals and the design principles of accurate scaling laws are presented.…”

Dynamic Similitude Design Method of the Distorted Model on Variable Thickness Cantilever Plates

“…Most recently, Luo and Zhu et al [23][24][25] presented a series of methods in the design of geometrically distorted models of plates and shells. In their work, the sensitivity analysis was employed in deriving accurate distorted scaling laws to predict the dynamic characteristics of the prototype [26,27]. In this study, in order to address the problem in designing a scaled model for a VT plate, a simplified ST plate, which has the same dynamic properties of the VT plate, is introduced.…”