Deformation and Stress Fields in Thin Metallic Partially Fixed Plate Induced by Electromagnet with Constant Flux Obtained by Analytical Method and FEM

Abstract

In the paper the behavior of thin elastic metallic partially fixed plate produced by electromagnet with constant flux is considered. Plate is simply supported along three edges and fixed along the fourth one. As nonstationary electromagnetic field in one part of the plate varies with time, conducting currents appear. Distribution of the power of eddy-current losses is obtained by using complex calculation. The power of the volume heat source (Joule’s heat) depends of permeability and conductivity of the plate and frequency of the alternative-current in electromagnet. Characteristics of the electromagnet are described by using Pulsation, Heaviside and similar functions. Differential equation governing temperature field is solved using by integral transform technique. The mathematical form of the transversal vibrations is obtained in analytical way using only simple finite Fourier transforms because the differential equation describing transverse vibrations is adapted to form which enabling very easy simulation of the bending moments along the fixed edges. Vibrations and stress in the middle surface of the plate are calculated by using program package KOMIPS, based on the finite element method.