Editorial Board

JMI2013A-4 Vibration-fracture model for one dimensional spring-mass system (pp.25-32)

Author(s): Kazunobu Abe and Masato Kimura

J. Math-for-Ind. 5A (2013) 25-32.

We propose a fracture model of a vibrating wire modeled as a one dimensional spring-mass system. We introduce a phase field variable for damage of the springs and represent a fracture of the wire by a cutting of the spring. The model we propose consists of a system of ordinary differential equations and admits rigorous mathematical analysis, such as global existence of a unique solution and an energy decay estimate. The validity of our fracture model and its estimate is confirmed using numerical simulations.

Keyword(s).  fracture model, vibration analysis, spring-mass system, phase filed model