Analysis of structural vibrations by taking the change of thickness into account

Abstract

The problem of longitudinal eigen-vibrations of a bar with circular cross section by taking into account the change of its radius is analyzed. The finite element is developed. The two nodal variables of the one-dimensional finite element are the displacement of the surface of the circular cross section of the bar in the radial direction and the displacement of the cross section in the axial direction. The problem of eigen-vibrations of a structure in the state of plane stress by taking into account the change of its thickness is analyzed. The finite element model is developed. The three nodal variables of the two-dimensional finite element are the plane displacements and the displacement of the upper surface. The obtained results are used in hybrid experimental-numerical procedures for the interpretation of the field of isopachics.