Optimal configuration for vibration frequencies in a ring of harmonic oscillators： The nonidentical mass effect

• Published in: Frontiers of physics 2015-06, Vol.10 (3), p.89-100
• Main Authors: Liu, Shuai, Zhang, Guo-Yong, He, Zhiwei, Zhan, Meng
• Format: Article
• Language: English
• Subjects: Astronomy; Astrophysics and Cosmology; Atomic; complex systems; Condensed Matter Physics; Configurations; Dynamical systems; Extreme values; Harmonic oscillators; Mass-spring systems; Molecular; Nonlinear dynamics; normal modes; Optical and Plasma Physics; Parameters; Particle and Nuclear Physics; Physics; Physics and Astronomy; Research Article; synchronization; Vibration; vibration frequencies; 全相; 动态特性; 振动频率; 最优配置; 最佳配置; 谐振子; 质量效应; 非线性动力学
• ISSN: 2095-0462; 2095-0470
• DOI: 10.1007/s11467-015-0462-4

The parameter diversity effect in coupled nonidentical elements has attracted persistent interest in nonlinear dynamics. Of fundamental importance is the so-called optimal configuration problem for how the spatial position of elements with different parameters precisely determines the dynamics of the whole system. In this work, we study the optimal configuration problem for the vibration spectra in the classical mass-spring model with a ring configuration, paying particular attention to how the configuration of different masses affects the second smallest vibration frequency （ω2） and the largest one （ωN）. For the extreme values of ω2 and ωN, namely, （ω2）min, （ω2）max, （ωN）min, and （ωN）max, we find some explicit organization rules for the optimal configurations and some approximation rules when the explicit organization rules are not available. The different distributions of ω2 and ωN are compared. These findings are interesting and valuable for uncovering the underlying mechanism of the parameter diversity effect in more general cases.