MODELING A ROCKET ELASTIC STRUCTURE AS A BECK’S COLUMN UNDER FOLLOWER FORCE

Authors

  • Leandro Forne Brejão UFABC
  • Reyolando M. L. R. F. Brasil UFABC

DOI:

https://doi.org/10.26512/ripe.v2i19.15019

Abstract

It is intended, in this paper, to develop a mathematical model of an elastic space rocket structure as a Beck’s column excited by a follower (or circulatory) force. This force represents the rocket motor thrust that should be always in the direction of the tangent to the structure deformed axis at the base of the vehicle. We present a simplified two degree of freedom rigid bars discrete model. Its system of two second order nonlinear ordinary differential equations of motion are derived via Lagrange’s energy method, allowing for a general understanding of the main characteristics of the problem. The proposed equations consider up to third order (cubic) inertia, stiffness and
forcing terms. Among other rich nonlinear dynamic behavior of this model, depending on parameters and initial conditions choices, either stable or unstable limit cycle solutions are possible. The unstable solution is, of course, an interesting simple example of flutter instability.
Keywords: Beck’s column, follower force, nonlinear dynamics, flutter.

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References

Brasil, R. M. L. R. F., 1995. O Fenômeno de Localização de Modos em Dinâmica e Estabilidade de Estruturas Modulares de Comportamento Linear ou Não-Linear, Tese de Livre Docência, Escola Politécnica da USP, São Paulo, 1996.

Mazzilli, C.E.N., Dinâmica não linear e estabilidade: uma formulação para sistemas submetidos a excitação de suporte ou carregamentos não conservativos. Tese de Livre Docência, Escola Politécnica da USP, São Paulo, 1988.

Timoshenko, S.P., Theory of elastic Stability 2nd Ed., Dover, Mineola, 2009.

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Published

2017-02-08

How to Cite

Brejão, L. F., & Brasil, R. M. L. R. F. (2017). MODELING A ROCKET ELASTIC STRUCTURE AS A BECK’S COLUMN UNDER FOLLOWER FORCE. Revista Interdisciplinar De Pesquisa Em Engenharia, 2(19), 42–52. https://doi.org/10.26512/ripe.v2i19.15019

Issue

Vol. 2 No. 19 (2016): MODELING SIMULATION AND CONTROL OF AEROSPACE AND NAVAL STRUCTURES DYNAMICS (I)

Section

Artigos

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