Phi-bits, the classical mechanical counterparts to qubits, are vital for the development of quantum-inspired computing. They exist as acoustic waves in nonlinearly coupled arrays of waveguides, capable of maintaining coherent superpositions of states under external driving forces. In our system, three aluminum rods coupled with epoxy generate nonlinearities that result in various frequency components beyond the driving frequencies. Understanding these nonlinear interactions is crucial for controlling phi-bit states, which can be manipulated through adjustments in external drivers' frequency, amplitude, and phase. We developed a discrete element model to simulate the system, treating the rods as mass-spring systems with epoxy acting as a spring-like coupling between them. This model captures key nonlinearities—such as side and end spring effects—arising from both intrinsic medium coupling and external elements like signal generators and transducers. By incorporating different strengths and orders of nonlinearities, along with damping effects, we explore the impact of these factors on the modulus and phases of phi-bit states. Our findings show that high relative damping between rod masses, coupled with end spring nonlinearity, enhances phase predictability and stability. This research provides crucial insights for optimizing phi-bit control and mitigating unwanted nonlinearities, paving the way for advancements in phi-bit-based quantum-analogue computing. Through continued interdisciplinary collaboration, we aim to harness phi-bits for enhanced algorithmic performance and novel computational paradigms.