Elastic impact of sphere on large plate

Different from the Hertz impact, a sphere impacting on plate has an extra dissipation by flexural wave propagating plate. This been noticed Zener (1941), who introduced this term into governing equation. Because of wave, equation cannot be treated as same way in impact problem. As result, past 80 years, except few numerical tries for equation, no analytical solution provided evolution compressive displacement or contact force during impact. In paper, using homotopy analysis method, we analytically solved After constructing auxiliary linear operator, derived up to first order embedding parameter. Present model can take full account elongation time compliance, which is impossible model. Comparisons with finite element simulation show that prediction history high accuracy. With history, explicit expression energy loss type, different dependence velocity Hunter does. Also, both motions and are able predicted addition, zeroth-order solution, expressions coefficient restitution duration.