Coupling homogeneous chains of damped harmonic oscillators

• Autor(a) principal: Bandeira, Luís
• Data de Publicação: 2024
• Outros Autores: Correia Ramos, Carlos
• Tipo de documento: Artigo
• Idioma: por
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10174/36114; https://doi.org/Bandeira, L., Correia Ramos, C. Coupling homogeneous chains of damped harmonic oscillators. Meccanica 59, 19–32 (2024). https://doi.org/10.1007/s11012-023-01721-x; https://doi.org/10.1007/s11012-023-01721-x
• topic: Dynamical system; Harmonic oscillators; Non-homogeneous chains; Recursion

We study vibrational properties of nonhomogeneous materials. We consider idealized materials composed of one dimensional chains of damped harmonic oscillators represented by a sequence of particles, springs and dampers. The system is linear, thus possesses exact explicit solutions, nevertheless the formulas can be very complicated. Homogeneous chains are used as basic building blocks for characterizing global dynamics of the system. In particular, we determine the solutions for a system composed of two distinct homogeneous chains in terms of the original solutions for these two homogeneous chains, and the original parameters, when uncoupled. Two types of coupling are considered, one with a gluing particle, the other with a gluing spring and damper.