The ubiquitous nature of radio frequency waves in modern technology creates a niche for research and drives innovation. While the ability to transmit and receive radio frequency signals has been possible for nearly a century, the ability to recover weak signals is still a challenge that plagues several areas of research, including radio astronomy, medical imaging, navigation, and classical and quantum communication. The optoelectromechanical transducer analyzed in this thesis utilizes nanomembrane technology to recover radio frequency signals as weak as -180 dBm, and then converts the signal into an optical carrier. This transducer operates at room temperature, making it far more efficient, and dramatically more sensitive than current devices such as SQUID, which has the potential to recover signals around -100 dBm, but requires cryogenic cooling. In this thesis, we present analysis of the optoelectromechanical transducer by utilizing the nonlinear dynamical systems approach. A special zero equilibrium case of the model equations is studied first, and an attempt to put the equations in their normal form is made. Unfortunately, this exposes a degeneracy that is inherent to the physics and engineering governing the device. In an attempt to gain insight, perturbation analysis for three cases is performed, and their approximate solutions are analyzed. Finally, bifurcation diagram are created for three unique cases.
