In the field of acoustics, the relationship between liquid height and the resonant frequencies of containers has been comprehensively explained within the framework of modern acoustic theory. However, once the container is set in motion, its acoustic behavior becomes significantly more complex and can no longer be described solely by existing static models. A complete understanding of such mechanisms holds promise for diverse applications, ranging from the design of novel musical instruments to advances in fluid monitoring and industrial diagnostics. This study focuses on the change in vibrational frequency of a fluid-contained cylinder under accelerated motion. Our theory extends the former research in AP French’s theory [1] to consider arbitrary modal shapes and liquid motion. And derived a series of coupled equations of motion for the interaction between the container and the fluid inside by first principle. The derived equations matched the form of the EOMs for coupled damped harmonic oscillators. Therefore, it allows us to better visualize and interpret the complex fluid-contained cylinder vibrational frequency by a well established coupled damped harmonic oscillators system. Moreover, by applying the new theory, we can use a semi-analytic procedure to calculate the vibration frequency, instead of computationally expensive simulations. The experimental results match the predicted trends from our derived theory. This study extends the understanding of container-fluid coupled interactions and shows the viability of analytical approaches in complex FSI systems.