An Assessment of the Influence of Random Deviation of Parameters on the Dynamic Characteristics Using the Interpolation Method

The development of methods for stochastic analysis of the dynamic characteristics of rocket and space systems and their response to external random forces is an important engineering task. Vibrations of the elastic structure are described by a vector nonlinear equation in the normal Cauchy form. The differentiability of nonlinear dependencies is not required. Limitations on the magnitude of the displacements, velocities, and accelerations of individual elements formalize the conditions for the functioning of the system. The interpolation method is used to solve the multiparametric problem. The roots of orthogonal Lagrangian polynomials serve as interpolation nodes. Under this condition, the mean quadruple approximation error of probabilistic characteristics assumes a minimum value. The functionality of the system is associated with the probability estimates of the random vector elements distribution in the corresponding one-dimensional domain. The method is designed for the probabilistic analysis of nonlinear systems with a large number of random parameters. The results are illustrated by an example.

References

[1] Bezmozgii I.M., Bobylev S.S., Sofinskii A.N., Cherniagin A.G. Nagruzhenie i prochnost’ konstruktsii transportnogo kosmicheskogo korablia pri vozdeistvii otsechki tiagi dvigatelia tret’ei stupeni rakety-nositelia [The effect of thrust cut-off of the third stage of the launch vehicle on the loading and strength of the transport cargo vehicle structure]. Kosmicheskaia tekhnika i tekhnologii [Space technique and technologies]. 2017, no. 2(17), pp. 63–79.

[2] Barmin I.V., Zverev V.A., Ukrainskii A.Iu., Iazykov A.V. Raschetnyi analiz protsessov otvoda konstruktsii startovoi sistemy, nakhodiashchikhsia pod vozdeistviem strui dvigatelei rakety-nositelia «Soiuz» [Design Analysis of Processes of Withdrawal of Launch System Structures Subjected to Action of Rocket Exhaust Jets of Soyuz Launch Vehicle]. Vestnik MGTU im. N.E. Baumana. Ser. Mashinostroenie [Herald of the Bauman Moscow State Technical University. Ser. Mechanical Engineering]. 2011, no. 1, pp. 31–39.

[3] Venttsel’ E.S., Ovcharov L.A. Teoriia veroiatnostei i ee inzhenernye prilozheniia [Probability theory and its engineering applications]. Moscow, Akademiia publ., 2003. 464 p.

[4] Mikhailov G.A., Voitishek A.V. Chislennoe stokhasticheskoe modelirovanie. Metod Monte-Karlo [Numerical stochastic simulation. Monte Carlo method]. Moscow, Akademiia publ., 2006. 368 p.

[5] Rozenvascer E.N., Iusupov R.M. Chuvstvitel’nost’ sistem upravleniia [Sensitivity of control systems]. Moscow, Nauka publ., 1981. 456 p.

[6] Arinchev S.V., Fediushkin A.S. Chuvstvitel’nost’ vynuzhdennykh kolebanii ramy s nesbalansirovannym rotorom k variatsiiam zhestkostei raskrepleniia [Sensitivity of Forced Vibrations of the Frame with an Unbalanced Rotor to the Variations of Bracing Stiffness]. Izvestiia vysshikh uchebnykh zavedenii. Mashinostroenie [Proceedings of Higher Educational Institutions. Маchine Building]. 2016, no. 4 (673), pp. 92–104.

[7] Khog E., Choi K., Komkov V. Analiz chuvstvitel’nosti pri proektirovanii konstruktsii [The sensitivity analysis for the design of structures]. Moscow, Mir publ., 1988. 428 p.

[8] Tushev O.N., Berezovskii A.V. Chuvstvitel’nost’ spektral’nykh kharakteristik konechnoelementnykh modelei konstruktsii raketno-kosmicheskoi tekhniki [Sensitivity of spectral characteristics of finite-element models of rocket and space technology constructions]. Oboronnaia tekhnika [Defence equipment]. 2007, no. 3–4, pp. 87–93.

[9] Tushev O.N., Korostylev A.V. K zadache opredeleniia parametricheskoi chuvstvitel’nosti dinamicheskikh system [Determination of parametric sensitivity of dynamical systems]. Izvestiia RAN. Mekhanika tverdogo tela [Mechanics of Solids]. 2005, no. 3, pp. 34–41.

[10] Chernetskii V.I. Analiz tochnosti nelineinykh sistem upravleniia [Accuracy analysis of nonlinear control systems]. Moscow, Mashinostroenie publ., 1968. 247 p.

[11] Perov S.N., Skvortsov Iu.V. Predstavlenie sluchainykh protsessov s pomoshch’iu nekanonicheskogo razlozheniia [Random process presentation by non-canonical decomposition]. Vestnik Samarskogo universiteta. Aerokosmicheskaia tekhnika, tekhnologii i mashinostroenie [Vestnik of Samara University. Aerospace and Mechanical Engineering]. 2008, no. 1(14), pp. 226–235.

[12] Statisticheskie metody v proektirovanii nelineinykh sistem avtomaticheskogo upravleniia [Statistical methods in the design of nonlinear automatic control systems]. Ed. Dostupov B.G. Moscow, Mashinostroenie publ., 1970. 405 p.

[13] Vibratsii v tekhnike. Spravochnik. vol. 1. Kolebaniia lineinykh system [Vibrations in technology. Handbook. Vol. 1. Oscillations of linear systems]. Ed. Bolotin V.V. Moscow, Mashinostroenie publ., 1999. 504 p.

[14] Tushev O.N., Beliaev A.V. Optimizatsiia tekhnicheskikh kharakteristik pnevmogidravlicheskikh amortizatorov iz usloviia maksimuma nadezhnosti mekhanicheskoi sistemy. Inzhenernyi vestnik. MGTU im. N.E. Baumana [Engineering bulletin. BMSTU]. 2013, no. 6. Available at: http://engsi.ru/doc/597480.html (accessed 10 January 2018).

[15] Tushev O.N., Sychev M.P. Approximate target functionals in problems of parametric optimization of damping systems with presence random factor. Dynamic Strength and Wear-Resistance of Machines, 2001, vol. 8, pp. 8–16.