This paper introduces a damage detection scheme based on changes in the period of limit cycles (LCs) realized by nonlinear output feedback. The parameterized feedback law is selected to make the dynamic equilibrium of the actuated coordinate approximate that of a generalized van der Pol oscillator and potential model-related difficulties are avoided by fixing the parameters from experimental results. It is found that not all sensor/actuator arrangements are suitable for generating a LC in closed loop, so a methodology to determine which arrangements are viable is presented. Numerical results show that LC periods are adequately stable with respect to noise and system changes from environmental effects and have sensitivity to localized damage that is often orders of magnitude larger than those of the modal frequencies.