Branching and Stability of Elasic Rod Equilibrium Forms

In our article from the positions of branching theory the classical Euler task about stability of thin elastic rod under action of vertical compressive load is considered. With using of turn-tensor and accompanying vector the deformation of rod is described. In result the conditions of equilibrium in a case of linear determining equation are reduced to boundary problem relatively turn angle of cross section, described by the differential equation of pendulum. With help elliptic functions the diagrams of branching are constructed and are received the exact formulas of rod deformation at the loss of stability of vertical position. Analogy the task of stability of rod at turned force on end of rod is considered. Also, the oscillating loss of rod stability at tracking load is studied.

A Model of the Contact Thermal Resistance of Vertical Carbon Nanotube Arrays

This paper developes a model to predict the thermal contact resistance of the vertically aligned carbon nanotubes (VACNTs). The model includes the effects of CNT array properties and surface roughness, with the aim of providing useful information for optimizing CNT array thermal contact resistance. The contact resistance is consisted of two parts: interfacial thermal resistance and constriction thermal resistance. The carbon nanotube (CNT) is treated as a thin elastic rod and macroscopic mechanical is used to calculate the mechanical properties of CNT. Greenwood-Williamson (GW) model is used to describe the roughness. The interfacial thermal resistance is calculated by molecular dynamics. The calculated values are in good agreement with experimental data. The interfacial thermal resistance is the domain major factor.