Abstract
The dynamics of vibroimpact is posed in terms of an initial value problem for a vertical impact pair, which consists of a primary mass constrained to move vertically within a massive hollow shell. Harmonic excitation drives the shell, while gravity and shell contact govern the dynamic response of the primary mass. This non-linear dynamics problem is formulated as an initial-value problem, which is numerically solved on a personal computer. The equations of motion for the separate domains controlling the mass are expressed as functional relationships; therefore, no numerical time integration is necessary. A numerical time-stepping method determines which of three domains controls mass motion at a given time and applies the appropriate equations. Also, the exact time of transition from one domain to another is iteratively calculated to within a small tolerance. The physical response of the primary mass is presented for several excitation conditions, and the accuracy of these solutions is investigated through numerical tests. Experimental results for a specific vertical impact pair system testify to the accuracy of the solution technique.
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