Abstract
This paper describes the influence of intensity of external additive white noise on the nonlinear dynamics of rectangular plates as mechanical systems with an infinite number of degrees of freedom. A new scenario is discovered, which is a combination of the classic Feigenbaum and Pomeau–Manneville scenarios. The classical methods of nonlinear dynamics and wavelet transforms were used to reveal the peculiarities of a modified scenario. The noise-induced transitions are investigated, and it is shown that the noise exposure is accompanied with the transition to chaotic fluctuations with a lower amplitude of the driving load. It is determined that the presence of external fluctuations does not affect the scenario of transition from harmonic to chaotic fluctuations.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
J. Awrejcewicz, V. A. Krysko, and A. Vakakis, Nonlinear Dynamics of Continuous Elastic Systems (Springer, Berlin, 2004).
V. A. Krys’ko, M. I. Koch, M. V. Zhigalov, and A. V. Krys’ko, “Chaotic Phase Synchronization of Vibrations of Multilayer Beam Structures,” Prikl. Mekh. Tekh. Fiz. 53 (3), 166–175 (2012) [J. Appl. Mech. Tech. Phys. 53 (3), 451–459 (2012)].
V. A. Krysko, M. V. Zhigalov, O. A. Saltykova, and A. V. Krysko, “Effect of Transverse Shears on Complex Nonlinear Vibrations of Elastic Beams,” Prikl. Mekh. Tekh. Fiz. 52 (5), 186–193 (2011) [J. Appl. Mech. Tech. Phys. 52 (5), 834–840 (2011)].
E. Yu. Krylova, T. V. Yakovleva, I. V. Papkova, and V. A. Krys’ko, “Chaotic Dynamics of Flexible Plates Rectangular in Plan under Longitudinal Loads,” Probl. Prochn. Plast. 77 (3), 235–243 (2015).
W. Horsthemke and R. Lefever, Noise-Induced Transitions: Theory and Applications in Physics, Chemistry, and Biology (Springer-Verlag, Berlin–Heidelberg, 1987).
Jinqing Feng, Wei Xu, and Rui Wang, “Stochastic Responses of Vibro-Impact Duffing Oscillator Excited by Additive Gaussian Noise,” J. Sound Vibrat. 309 (3), 730–738 (2008).
Jinqing Feng, Wei Xu, and Rui Wang, “Stochastic Responses of Duffing–Van der Pol Vibro-Impact System under Additive and Multiplicative Random Excitations,” Int. J. Non-Linear Mech. 44 (1), 51–57 (2009).
Y. J. Wu and R. H. Huan, “First-Passage Failure Minimization of Stochastic Duffing–Rayleigh–Mathieu System,” Mech. Res. Comm. 35 (7), 447–453 (2008).
V. D. Potapov, “On the Stability of Stochastic Systems Viscoelastic,” Probl. Mashinostr. Nadezh. Mash., No. 6, 85–90 (2009).
N. van de Wouw, A. de Kraker, D. H. van Campen, and H. Nijmeijer, “Non-Linear Dynamics of a Stochastically Excited Beam System with Impact,” Int. J. Non-Linear Mech. 38 (5), 767–779 (2003).
J. Awrejcewicz, E. Yu. Krylova, I. V. Papkova, and V. A. Krysko, “Regular and Chaotic Dynamics of Flexible Plates,” Shock Vibrat. (2014); http://dx.doi.org/10.1155/2014/937967.
H. G. Schuster, Deterministic Chaos: An Introduction (VCH Publ., 1984).
A. S. Volmir, Nonlinear Dynamics of Plates and Shells (Moscow, Nauka, 1972) [in Russian].
J. Awrejcewicz, V. A. Krysko, I. V. Papkova, and A. V. Krysko, “Routes to Chaos in Continuous Mechanical Systems. 1. Mathematical Models and Solution Methods,” Chaos, Solitons Fractals 45 (6), 687–708 (2012).
J. Awrejcewicz, E. Y. Krylova, I. V. Papkova, and V. A. Krysko, “Wavelet-Based Analysis of the Regular and Chaotic Dynamics of Rectangular Flexible Plates Subjected to Shear-Harmonic Loading,” Shock Vibrat. 19 (5), 979–994 (2012).
M. C. Kornishin, Nonlinear Problems of the Theory of Plates and Shallow Shells and the Methods for Their Solution (Nauka, Moscow, 1964) [in Russian].
J. Awrejcewicz, V. A. Krysko, E. Yu. Krylova, and I. V. Papkova, “Analysis of Nonlinear Dynamics of Plates and Shells Using the Lyapunov Exponents and Wavelets,” in Dynamical Systems: Theory (Tech. Univ. of Lodz Press, Lodz, 2013).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 57, No. 4, pp. 163–169, July–August, 2016.
Rights and permissions
About this article
Cite this article
Krylova, E.Y., Papkova, I.V., Erofeev, N.P. et al. Complex fluctuations of flexible plates under longitudinal loads with account for white noise. J Appl Mech Tech Phy 57, 714–719 (2016). https://doi.org/10.1134/S0021894416040167
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0021894416040167