An Optimization Method for Vibration Suppression and Energy Dissipation of an Axially Moving String with Hybrid Nonclassical Boundaries

The axially moving string model is widely used in engineering applications and is of great significance in research. To suppress transverse vibration and facilitate energy dissipation of the axially moving string with nonclassical boundaries, a bi-objective optimization model and methodology are proposed for its boundary parameters’ design. First, an approximate numerical model for an axially moving string with a nonclassical boundary is established, which is based on the finite element method (FEM) and Newmark-beta method. Then, a bi-objective model is proposed, including the average transverse vibration and the average system energy in a single traveling wave period, and a particle swarm optimization (BOPSO) algorithm is established for optimization. Finally, the proposed optimization model is applied in a numerical example, and the results are compared with NSGA-II, a multi-objective cuckoo search algorithm (MOCSA), and multi-objective flower pollination algorithm (MOFPA) to verify the feasibility of the proposed methodology.