  1aPA3. A nonlinear analysis of a simple thermoacoustic system.
Ronald E. Kumon  Appl. Res. Labs., Univ. Texas at Austin, 10000
Burnet Rd., Austin, TX 78713  A simple thermoacoustic system was
studied to try to better understand the interaction between the
temperature, pressure, and velocity modes of the system. The
system considered was a one-dimensional ``tube,'' closed and
isothermal at both ends and filled with a helium gas. Initially,
the gas is static but with a sinusoidal temperature
distribution. To obtain a simplified model of the system, a
Galerkin-type method was applied to the full hydrodynamic
equations in one spatial dimension and the ideal gas law
equation of state. By substituting highly truncated sine and
cosine series in the spatial variable with time-dependent
amplitudes into the aforementioned PDEs, the model was reduced
to a set of coupled nonlinear ODEs. First, these equations were
linearized and examined for series expansions with different
number of terms. Next, the nonlinear ODEs we