Longitudinal elastic stress impulse induced by impact through a spring-dashpot system: Optimization and inverse problems for the spring stiffness

In the present paper, an exact analytical solution is obtained for the problem of a semi-infinite elastic rod struck by a rigid mass through a linear Kelvin–Voigt element. The optimization problem resulting in generating compressed pulses of minimum duration is addressed. The case of undamped impact has been studied in detail, and the optimal value for the spring stiffness is presented in a closed form. Inverse problems of recovery of the impact system parameters from the parameters of the strain wave impulse are also considered.