Effect of Parameter Configuration on Free Vibration of Networked Harmonic Oscillators with Viscous Damping

Heterogeneous oscillator networks consist of a dynamical function that describes the state (containing several parameters) and topology reflects connections between oscillators. Revealing macroscopic dynamics systems under different configurations parameters is topic worthy discussion comes with great challenges. In this study, we discuss effect parameter on damped free vibration classical spring network. On regular network, give analytical expression satisfied by system over-damping critical damping. Furthermore, fastest slowest exponential rates decay for conditions. conjunction quadratic eigenvalue theory, extend above analysis from to complex networks. We general method calculating spectrum arbitrary configurations. stability rate rate, also numerical simulation results second largest smallest real parts eigenvalues system. Finally, through comparative results, relax matching relationship three (mass, damping, degree) two (mass damping).