Adair, DesmondNagimova, AigulJaeger, Martin2021-07-032021-07-032020-05Adair, D., Nagimova, A., & Jaeger, M. (2020). Effect of Thrust on the Structural Vibrations of a Nonuniform Slender Rocket. Mathematical and Computational Applications, 25(2), 29. https://doi.org/10.3390/mca250200291300-686Xhttp://nur.nu.edu.kz/handle/123456789/5527The vibration characteristics of a nonuniform, flexible and free-flying slender rocket experiencing constant thrust is investigated. The rocket is idealized as a classic nonuniform beam with a constant one-dimensional follower force and with free-free boundary conditions. The equations of motion are derived by applying the extended Hamilton’s principle for non-conservative systems. Natural frequencies and associated mode shapes of the rocket are determined using the relatively efficient and accurate Adomian modified decomposition method (AMDM) with the solutions obtained by solving a set of algebraic equations with only three unknown parameters. The method can easily be extended to obtain approximate solutions to vibration problems for any type of nonuniform beam.enAttribution-NonCommercial-ShareAlike 3.0 United StatesType of access: Open Accessvibrationsslender rocketAdomian modified decomposition methodnatural frequencyArticle