Finite Element Analysis of Thermoelastodynamic Instability Involving Frictional Heating

A finite element method is used to solve the problem involving thermoelastodynamic instability (TEDI) in frictional sliding systems. The resulting matrix equation contains a complex eigenvalue that represents the exponential growth rate of temperature, displacement, and velocity fields. Compared to the thermoelastic instability (TEI) in which eigenmodes always decay with time when the sliding speed is below a critical value, numerical results from TEDI have shown that some of the modes always grow in the time domain at any sliding speed. As a result, when the inertial effect is considered, the phenomenon of hot spotting can actually occur at a sliding speed below the critical TEI threshold. The finite element method presented here has obvious advantages over analytical approaches and transient simulations of the problem in that the stabilities of the system can be determined for an arbitrary geometry without extensive computations associated with analytical expressions of the contact condition or numerical iterations in the time domain.