Conservative Numerical Methods for Nonlinear String Dynamics: Non-planar Vibration
For researchers studying nonlinear string dynamics, this work provides stable numerical schemes with conservation properties, though it is an incremental contribution to existing numerical methods.
The paper presents numerical methods for simulating nonlinear nonplanar string vibrations, focusing on discrete conservation of energy and angular momentum to achieve stability under strongly nonlinear conditions.
Nonlinear string vibration, in particular the case of nonplanar motion, has been an area of intense study for many years. Numerical simulation methods, essential for the comparison between measured data and theory, have received somewhat less attention. In this article, various numerical schemes for nonlinear nonplanar string dynamics are presented, with an emphasis on discrete conservation of energy and angular momentum. Simple numerical stability conditions may be arrived at, even under strongly nonlinear conditions, by employing these conservation properties. Full implementation details and various numerical examples are presented, and several topics, including a discussion of numerical loss models and spectral methods, are dealt with in the Appendix.