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Thermoelastic Instability Analysis

Hi, I am new to iMechanica. I am also not sure whether this post is appropriate here or not.

I was doing some instability analysis of heat transfer between two rods
having a narrow gap in between them (they might have contacts and
separation with time, the gap is a function of temperature T, and
T=T(x,t)). I know about the matrix analysis used for stability of a
system of ODEs. I am not able to frame my problem (a 1-D transient heat
equation with non-linear boundary conditions) properly so that it
becomes amenable to the standard matrix method of stability analysis.
Does anyone have some references/examples where I can get some help
about this (like existence of limit cycles, under which conditions a
critical point becomes unstable, etc)? I have complete numerical
solution of the problem and I have seen that for certain input/initial
conditions (and parameter values) the solution becomes oscillatory or a
steady state solution cannot be obtained.

 Also, any comments on whether this kind of analysis can be done in Ansys (using gap elements, the gap contact conductance is a function of gap or the contact pressure in case of contact) will be highly apreciated.

 Thanks.

I guess you already know about this paper "J.R.Barber and Ronggang Zhang, Transient behaviour and stability for the thermoelastic contact of two rods of dissimilar
materials,
International Journal of Mechanical Sciences, Vol. 30 (1988), pp. 691-704"? If not, you can download it at http://www-personal.umich.edu/~jbarber/IJMS1988.pdf.

 

More generally, in order to analyze the stability of this class of problems, you would first need to linearize the boundary conditions about an appropriate condition (usually a steady state).

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