Forced asymmetric vibrations of an axisymmetric body in contact with an elastic half-space—A Global-Local Finite Element Approach

Abstract

Forced asymmetric vibrations of an axisymmetric structure in contact with an elastic half-space are investigated by means of an extended version of the Global-Local Finite Element Method (GLFEM). In GLFEM, the structure and part of the surrounding medium are modeled by conventional finite elements. The behavior beyond this finite element model, i.e., in the remainder of the half-space region, is represented by analytical functions (called global functions) in the form of spherical harmonics. The solution process requires that both displacement and traction continuity at the finite element interface with the outer field be satisfield. Also, to satisfy traction-free surface conditions, the non-vanishing spherical harmonic tractions on the free surface beyond the finite element mesh are constrained in the form of weighted-average integrals that express zero net work due to these stress components. The results for rocking vibration of a rigid circular plate in frictionless contact with the half-space compare well with existing analytical data. Response results that illustrate the effects of various embedment conditions of a rigid circular plate completely bonded to the half-space are presented. Lastly, an example on flexible transducers fully bonded to a half-space is considered. Data describing the transducers' contact displacement distribution near resonance are given.