Dynamics of rotating thermoelastic disks with stationary heat source

Disk brakes or sawing processes represent complicated thermo-mechanical systems where the dynamic interaction of the different components involved including heat effects establish a physical problem very interesting for theory and practical applications. In both cases the main structural element is a rotating disk where heat and mechanical loads are induced via frictional or cutting force contact between stationary pads or work piece, respectively. The discussion of dynamic thermoelasticity in rotating disks with both stationary heat sources and mechanical excitation at localized areas is a preliminary problem of basic interest to understand the interaction of temperature and displacement fields in such structural elements The objective of the present contribution is to solve the governing boundary value problem for typical cases of configuration. To be relatively general, a 3-dimensional formulation will be the starting point before (due to computation time reasons) a thin annular disk within a planar stress theory will be considered without significant restrictions. Basically either body-fixed material coordinates or stationary Euler coordinates depending from the specific application may be applied deriving the governing boundary value problem For problems with a finite rigid body rotation of constant angular speed and an excitation by stationary source terms due to mechanical forces or heat production, a stationary reference frame seems to be adequate since then time-variant coefficients describing the boundary surface can be avoided. It is assumed that there is an angular speed of moderate rate so that centrifugal stiffening effects can be neglected and a linear deformation theory is sufficient. In general, there are localized stationary heat sources feeding within a bounded area heat into the passing disk together with simultaneously acting stationary mechanical loads. It is assumed that at the inner radius, the rotating disk is rigidly fixed and thermally insulated, while with the exception of those parts of the structure where the prescribed source terms are applied, all other disk volume or surface parts there is no mechanical traction and there is a heat exchange with the environment of reference temperature. Well-known is the mathematical model to describe thermoelastic vibrations of a circular disk at rest using a stationary cylindrical reference system. It is straightforward to translate the formulation for the disk performing a rigid-body rotation using body-fixed cylindrical coordinates. The field equations remain unchanged with one exception. The inertia terms now contain additional Coriolis and centrifugal components. The relevant mechanical and thermal volume sources or boundary actions for …