Analysis and Simulations of a Contact Problem for a Nonlinear Dynamic Beam with a Crack

作者：Kuttler K L^*; Purcell J; Shillor M

来源：Quarterly Journal of Mechanics and Applied Mathematics, 2012, 65(1): 1-25.

DOI：10.1093/qjmam/hbr018

This work studies and simulates the dynamics of a Gao beam that may come in contact with a reactive foundation and which has an evolving symmetric edge crack. The problem is set as a variational inequality coupled with a differential equation for the evolution of the damage variable, which measures the severity of the crack. The existence of a local weak solution for the model is proved using approximations, result for abstract problems in Hilbert spaces, and a priori estimates. A finite-element scheme for the problem is proposed, and representative simulations presented. In particular, the dependence of the beam%26apos;s vibration frequency on the crack%26apos;s position and size is depicted.

• 出版日期2012-2