Experimental validation of theoretical methods to estimate the energy radiated by elastic waves during an impact

Abstract

Estimating the energy lost in elastic waves during an impact is an important problem in seismology and in industry. We propose three complementary methods to estimate the elastic energy radiated by bead impacts on thin plates and thick blocks from the generated vibration. The first two methods are based on the direct wave front and are shown to be equivalent. The third method makes use of the diffuse regime. These methods are tested for laboratory experiments of impacts and are shown to give the same results, with error bars of 40 percent and 300 percent for impacts on a smooth plate and on a rough block, respectively. We show that these methods are relevant to establish the energy budget of an impact. On plates of glass and PMMA, the radiated elastic energy increases from 2 percent to almost 100 percent of the total energy lost as the bead diameter approaches the plate thickness. The rest of the lost energy is dissipated by viscoelasticity. For beads larger than the plate thickness, plastic deformation occurs and reduces the amount of energy radiated in the form of elastic waves. On a concrete block, the energy dissipation during the impact is principally inelastic because only 0.2–2 percent of the energy lost by the bead is transported by elastic waves. The radiated elastic energy estimated with the presented methods is quantitatively validated by Hertz׳s model of elastic impact.