Harmonic analysis on a Lévy plate and its application to fatigue analysis

Abstract

This paper discusses a harmonic response estimation method on the Lévy plate with two opposite edges simply supported and the other two edges having free boundary conditions. Then, the harmonic response is processed to evaluate fatigue damage. Since the equation of motion of the plate is not self-adjoint, the modes are not orthogonal to each other on the structure domain. Noting that the Lévy plate can be expressed using one term sinusoidal function that is orthogonal to other sinusoidal functions, this paper suggested the calculation method that is equivalent to finding a least square error minimization solution of the finite number of algebraic equations. Example problems subjected to a distributed area loading and a distributed line loading are defined and their solutions are provided. The solutions are compared to those of the commercial code, ANSYS. The plate motion due to high frequency vibration can be seen in the nuclear fuels subjected to highly turbulent coolant flow. The dominant exciting frequency is dependent on the coolant velocity and Strouhal number, a dimensionless number describing oscillating flow mechanism. This paper also discusses fatigue damage considering the high frequency vibration using the Dirlik equation. © The Society for Experimental Mechanics, Inc. 2013.