Vibration suppression for strings with distributed loading using spatial cross-section modulation

For analyzing the problem considered a novel approach named the method of varying amplitudes is employed. This approach is applicable for solving differential equations without a small parameter, and may be considered as a natural continuation of the classical methods of harmonic balance and averaging. As a result, optimal parameters for the string cross-sectional area modulation are determined for the cases of harmonically, uniformly and arbitrarily distributed load, which allows for completely suppressing or considerably reducing vibration in the prescribed part of the string (compared to the case without modulation).