Thermoelastic Stability of Aldo Model with Barber’s Condition

• Main Authors: Song-Ting Huang, 黃頌庭
• Other Authors: 盧中仁
• Format: Others
• Language: zh-TW
• Published: 2011
• Online Access: http://ndltd.ncl.edu.tw/handle/80152028081895481427

碩士 === 國立臺灣大學 === 機械工程學研究所 === 99 === Thermoelasticity has important applications in different fields. Traditionally, the thermal resistance is defined as infinite between non-contact surfaces and zero for contact surfaces. With this kind of thermal resistance, a static thermoelastic problem may not have solutions. To overcome this difficulty, Barber proposed a new thermal resistance concept: the thermal resistance depends continuously on the pressure or gap between two interacting surfaces. Using this new thermal resistance, Barber analyzed a simplified surface model, the Aldo model, and obtained some general properties regarding the thermoelastic interactions between two contact surfaces. The Aldo model is composed of two elastic rods. However, Barber did not consider the effects of important mechanical properties of the rods, e.g. damping and wave velocity. This thesis aims to study the effects of the mechanical properties of the rods on the stability of the Aldo model. To this end, we first investigated the bifurcation of the Aldo model on the basis of the load-deflection curve of a single rod. Then, we derived the nonlinear governing equations of the Aldo system. The stability of an equilibrium solution was determined by the eigenvalues of the assoicated linearized system. The results were verified using numerical integration. Finally, we studied the bifurcation behavior and stability of the Aldo model with the variation of parameters, and compared the results with those of Barber’s. Results of this study indicate that mechanical properties of the rods significantly influence the stability of the Aldo model. Barber’s results correspond to the cases with high damping values.