Collisions are a vital part of the function of musical instruments. They occur in various forms and during different phases of oscillation, including transient and steady-state regimes. The non-smooth nature of the nonlinearity inherent to objects coming into contact and decoupling again poses several difficulties when it comes to formulating numerical models. Besides issues regarding numerical stability – that have recently been handled using energy methods – questions arise about how accurately different numerical schemes can approximate the trajectories of colliding objects. This paper presents a comparative analysis of two particular types of time-stepping algorithms (namely a two-point, two variable and a three-point, one-variable scheme) employed to simulate contact between a mass and a barrier. Focusing largely on cases for which the exact solution is known, the schemes are evaluated in terms of their ability to simulate the correct duration of contact.
|Title of host publication||The 2017 International Symposium on Musical Acoustics (ISMA), Montreal: Proceedings|
|Number of pages||4|
|Publication status||Published - 18 Jun 2017|