We present a theoretical model on the effects of mechanical perturbations on the output power instability of singly-resonant optical parametric oscillators (SR-OPOs). Numerical simulations are performed based on real experimental parameters associated with a SR-OPO designed in our laboratory, which uses periodically-poled LiNbO3 (PPLN) as the nonlinear crystal, where the results of the theoretical model are compared with the measurements. The out-coupled power instability is simulated for a wide range of input pump powers the SR-OPO oscillation threshold. From the results, maximum instability is found to occur at an input pump power of ~1.5 times above the OPO threshold. It is also shown theoretically that the idler instability is susceptible to variations in the cavity length caused by vibrations, with longer cavities capable of generating more stable output power. The validity of the theoretical model is verified experimentally by using a mechanical vibrator in order to vary the SR-OPO resonator length over one cavity mode spacing. It is found that at 1.62 times threshold, the out-coupled idler suffers maximum instability. The results of experimental measurements confirm good agreement with the theoretical model. An intracavity etalon is finally used to improve the idler output power by a factor of ~2.2 at an input pump power of 1.79 times oscillation threshold.