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Article

Effect of Thrust on the Structural Vibrations of a Nonuniform Slender Rocket

by
Desmond Adair
1,*,
Aigul Nagimova
1 and
Martin Jaeger
2
1
Department of Mechanical & Aerospace Engineering, Nazarbayev University, Nur-Sultan 010000, Kazakhstan
2
College of Sciences & Engineering, University of Tasmania, Hobart TAS7001, Australia
*
Author to whom correspondence should be addressed.
Math. Comput. Appl. 2020, 25(2), 29; https://doi.org/10.3390/mca25020029
Submission received: 17 February 2020 / Revised: 28 April 2020 / Accepted: 28 April 2020 / Published: 15 May 2020
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Abstract

The 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.
Keywords: vibrations; slender rocket; Adomian modified decomposition method; natural frequency vibrations; slender rocket; Adomian modified decomposition method; natural frequency

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MDPI and ACS Style

Adair, D.; Nagimova, A.; Jaeger, M. Effect of Thrust on the Structural Vibrations of a Nonuniform Slender Rocket. Math. Comput. Appl. 2020, 25, 29. https://doi.org/10.3390/mca25020029

AMA Style

Adair D, Nagimova A, Jaeger M. Effect of Thrust on the Structural Vibrations of a Nonuniform Slender Rocket. Mathematical and Computational Applications. 2020; 25(2):29. https://doi.org/10.3390/mca25020029

Chicago/Turabian Style

Adair, Desmond, Aigul Nagimova, and Martin Jaeger. 2020. "Effect of Thrust on the Structural Vibrations of a Nonuniform Slender Rocket" Mathematical and Computational Applications 25, no. 2: 29. https://doi.org/10.3390/mca25020029

APA Style

Adair, 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/mca25020029

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