I am pleased to submit my original research manuscript titled "Environment-Frequency Coupling Law (EFCL): Core Derived Model and Theoretical Framework" for consideration as a research article in your esteemed journal. This study introduces a novel physical framework (EFCL) that mathematically couples internal energy, external frequency variations, and environmental parameters to predict force responses in particle systems. Our findings demonstrate a quadratic dependency between frequency and effective force (\Delta F \propto \nu^2), providing a robust tool for precision control in vibration-sensitive environments. I believe this work aligns perfectly with the scope of the Journal of Vibration Engineering & Technologies, particularly in the fields of theoretical vibration and dynamic system modeling. This manuscript is original, has not been published elsewhere, and is not under consideration by any other journal. Thank you for your time and consideration. I look forward to hearing from you. Sincerely, Ibrahim Ramadan Al-Shtiwie Independent Researcher & Inventor Tripoli, Libya