On the longitudinal harmonic motion of an elastic bar embedded in an elastic half-space

Abstract

The present study is concerned with the motion of a long cylindrical elastic bar which is partially embedded in a homogeneous elastic half-space and subjected to a harmonic axial load. Initially Green's functions corresponding to axisymmetric harmonic ring loads are derived and presented explicitly. It is found that the direct extension of elastostatic solution schemes to solve elastodynamic problems may lead to erroneous solutions due to the inability of these algorithms to properly account for inertia effects. Some discrepancies in existing solutions with respect to the inertia component of the bar are shown. An efficient solution scheme, based on Lagrange's equation of motion and a discretization technique, is presented to solve the title problem. Numerical results are presented to illustrate the influence of bar flexibility, mass density, geometry, and frequency of excitation on the axial impedance of the system.