4H-6 Guided Elastodynamic Waves in Radially Graded Cylindrical Structures

The three-dimensional time boundary value problem for axisymmetric elastic waves in radially graded full cylinders is solved numerically. Elastic waves are initiated with a linear-sweep-displacement signal multiplied by a Hanning window in the time domain. The displacement excitation is applied to the cross section at the end of the cylinder. Time shots of the displacement fields for various structural configurations and material gradients are presented and discussed. Due to axisymmetry the displacement field remains two-dimensional, consisting of a radial- and a longitudinal component. Material properties of aluminum and gold are chosen for the numerical simulations. The multimode nature of the guided waves propagating along the axis is analyzed with a two dimensional spectrum analysis method. The spectrum analysis in the space domain i.e. the longitudinal axis, and in the time domain leads to the projections of the dispersion curves into a plane formed by the real part of the wave number of the guided waves and the frequency. Influences of the radial material gradient on the shapes of the dispersion diagrams are presented