Group-Theoretical Analysis of the Clustered Launch Vehicle Dynamics

Авторы: Pavlov A.M. Опубликовано: 03.09.2019
Опубликовано в выпуске: #4(127)/2019  

DOI: 10.18698/0236-3941-2019-4-20-30

Раздел: Авиационная и ракетно-космическая техника | Рубрика: Динамика, баллистика, управление движением летательных аппаратов  
Ключевые слова: launch vehicle, beam system, symmetry group, vibration frequency, irreducible representation, orthoprojector

In this paper we considered representation-theory-based eigenfunction classification of clustered launch vehicles vibration problems. Classification of vibrations modes was obtained by using projection operators, related with corresponding subspaces of irreducible representations of considered mechanical system symmetry group. For multiple frequencies we proposed the approach which allows to reduce corresponding vibrations modes to launch vehicle stabilization planes. In addition, for the launch vehicle with four boosters, the projections onto irreducible representations subspaces of right-hand side of the motion equations were found


[1] Karmishin A.V., Likhoded A.I., Panichkin N.G., et al. Osnovy otrabotki prochnosti raketno-kosmicheskikh konstruktsiy [Fundamentals of spacecraft construction strength optimization]. Moscow, Mashinostroenie Publ., 2007.

[2] Pavlov A.M., Temnov A.N. Symmetry exploitation in the natural vibrations of rod systems. Vestn. Mosk. Gos. Tekh. Univ. im. N.E. Baumana, Mashinostr. [Herald of the Bauman Moscow State Tech. Univ., Mechan. Eng.], 2017, no. 4, pp. 28--41 (in Russ.). DOI: 10.18698/0236-3941-2017-4-28-41

[3] D’yachenko M.I., Pavlov A.M., Temnov A.N. Longitudinal elastic vibrations of multistage liquid-propellant launch vehicle body. Vestn. Mosk. Gos. Tekh. Univ. im. N.E. Baumana, Mashinostr. [Herald of the Bauman Moscow State Tech. Univ., Mechan. Eng.], 2015, no. 5, pp. 14--24 (in Russ.). DOI: 10.18698/0236-3941-2015-5-14-24

[4] Pavlov A.M., Temnov A.N. System of rods longitudinal vibrations. Vestn. Mosk. Gos. Tekh. Univ. im. N.E. Baumana, Estestv. Nauki [Herald of the Bauman Moscow State Tech. Univ., Nat. Sci.], 2014, no. 6, pp. 53--66 (in Russ.).

[5] Balakirev Yu.G. Study on flexible body-fuel pipelines-engines system sustainability for the liquid propellant clustered launch vehicle. Izv. AN. MTT, 1994, no. 2, pp. 129--137 (in Russ.).

[6] Dokuchaev L.V., Sobolev O.V. Improvements in methods of research in dynamics of a clustered launch vehicle considering its symmetry. Kosmonavtika i raketostroenie [Cosmonautics and Rocket Engineering], 2005, no. 2, pp. 112--121 (in Russ.).

[7] Balakirev Yu.G. Osobennosti matematicheskoy modeli zhidkostnoy rakety paketnoy komponovki kak ob’’ekta upravleniya. Izbrannye problemy prochnosti sovremennogo mashinostroeniya [Features of the mathematical model of the liquid propellant lateral-staging rocket as a controlled object. In: Selected strength problems of modern engineering]. Moscow, Fizmatlit Publ., 2008.

[8] Balakirev Yu.G., Borisov M.A. Features of frequency spectrum of elastic oscillations of bodies of multi-block launch vehicles with symmetric structure. Kosmonavtika i raketostroenie [Cosmonautics and Rocket Engineering], 2016, no. 3, pp. 54--59 (in Russ.).

[9] Yang T.L. Symmetry properties and normal mode vibrations. J. Nonlinear Mech., 1968, vol. 3, no. 3, pp. 367--381. DOI: 10.1016/0020-7462(68)90008-5

[10] Zingoni A. Symmetry recognition in group-theoretic computational schemes for complex structural systems. Comput. Struct., 2012, vol. 94--95, pp. 34--44. DOI: 10.1016/j.compstruc.2011.12.004

[11] Kaveh A., Nikbakht M. Improved group-theoretical method for eigenvalue problems of special symmetric structures, using graph theory. Adv. Eng. Softw., 2010, vol. 41, no. 1, pp. 22--31. DOI: 10.1016/j.advengsoft.2008.12.003

[12] Mohan S., Pratap R. A natural classification of vibration modes of polygonal ducts based on group theoretic analysis. J. Sound Vib., 2004, vol. 269, no. 3--5, pp. 745--764. DOI: 10.1016/S0022-460X(03)00129-9

[13] Zingoni A. On the symmetries and vibration modes of layered space grids. Eng. Struct., 2005, vol. 27, no. 4, pp. 629--638. DOI: 10.1016/j.engstruct.2004.12.004

[14] Zingoni A. Group-theoretic insights on the vibration of symmetric structures in engineering. Philos. Trans. A. Math. Phys. Eng. Sci., 2014, vol. 372, no. 2008. DOI: 10.1098/rsta.2012.0037

[15] Hamermesh M. Group theory and its application to physical problems. Dover Publications, 1962.

[16] Dunford N., Schwartz J.T. Linear operators. Part II. Spectral theory. Wiley, 1958.