Simon, N.R., 1971: Second-order pulsations in polytropes. Astrophys. J., 164, 331-340, doi:10.1086/150842.
A theory due to Eddington is employed to calculate second-order corrections to the usual linear, quasi-adiabatic pulsational amplitudes. Such corrections are necessary in order to evaluate the pulsational stability of stars in thermal imbalance (dS0/d& <> 0). The second-order quantities are calculated, and their properties discussed, for a wide variety of polytropic models. Subsequently, a number of these models are tested for pulsational stability, and the conclusions drawn in an earlier, more preliminary work are re-evaluated on the basis of the results. In particular, it is found that stars in pre-main-sequence contraction are probably stable against pulsations energized via thermal imbalance.