On Stability of Pin-Jointed Beam Affected by Random Pulsating Load

Jevgeòijs Carkovs; Andrejs Matvejevs

doi:10.1515/prolas-2017-0011

.blurhash-client-img { display: none !important; }

On Stability of Pin-Jointed Beam Affected by Random Pulsating Load

Proceedings of the Latvian Academy of Sciences. Section B. Natural, Exact, and Applied Sciences.

Volume 71 (2017): Issue 1-2 (April 2017)

By: Jevgeòijs Carkovs and Andrejs Matvejevs

Open Access

|Jun 2017

Abstract

This paper deals with stability analysis of pin-jointed beams that are affected to random pulsating load. The stability conditions of a pin-jointed beam are analysed using a mathematical model of the beam characterised by longitudinal force with Poisson characteristics and applying the stochastic modification of the second Lyapunov method.

References

Ariaratnam, S. T. (1972). Stability of mechanical systems under stochastic parametric excitation. Lecture Notes Math., 294, 291-302.10.1007/BFb0064949
Search in Google Scholar Back to article
Bogoljubov, N. N., Mitropoliskii, Ju. A., and Samojlenko, A. M. (1976). Methods of Accelerated Convergence in Nonlinear Mechanics. Springer-Verlag, New York. 291 pp.10.1007/978-3-642-61900-7
Search in Google Scholar Back to article
Bolotin, V. V. (1964). Dynamic Stability of Elastic Systems. Holden Day, San Francisco. 451 pp.
Search in Google Scholar Back to article
Carkovs, J. Matvejevs, A. (2015). On stochastic resonance in pipeline, induced by pulsed fluid flow. In: Proceedings of the 14th Conference on Applied Mathematics APLIMAT 2015. Slovak University of Technology in Bratislava, Publishing House of STU, pp. 167-174.
Search in Google Scholar Back to article
Carkovs, J., Stoyanov,J. (2005). Asymptotic methods for stability analysis of Markov dynamical systems with fast variables. In: Kabanov, Yu., Liptser, R. (eds.). From Stochastic Analysis to Mathematical Finance. Festschrift for Professor Albert Shiryaev. Springer-Verlag, Berlin, pp. 93-110.
Search in Google Scholar Back to article
Dynkin, E. B. (1965). Markov Processes. Berlin, New Jersey. 366 pp.
Search in Google Scholar Back to article
Katafygiotis, L., Tsarkov, Ye. (1996). Mean square stability of linear dynamical systems with small Markov perturbation. I. Bounded coefficients. Random Operators and Stochastic Equations, 4 (2), 133-154.
Search in Google Scholar Back to article
Kato, T. (1980) Perturbations Theory for Linear Operators. Springer-Verlag, Berlin. 619 pp.
Search in Google Scholar Back to article
Leipholz, H. H. E. (1978). Stability of Elastic Structures. Springer Verlag, Wien. 299 pp.10.1007/978-3-7091-2975-3
Search in Google Scholar Back to article
Li, J., Hua H., Shen, R., Jin, X. (2004). Stochastic vibration of axially loaded monosymmetric Timoshenko thin-walled beam. J. Sound Vibration. 274, 915-938.10.1016/S0022-460X(03)00654-0
Search in Google Scholar Back to article
Pavlovic , R. Kozic, P. (2003). Almost sure stability of the thin-walled beam subjected to end moments. Theor. Appl. Mech.. 30 (3), 193-207.10.2298/TAM0303193P
Search in Google Scholar Back to article
Rao, S. S. (2007). Vibraton of Continuous Systems. John Wiley & Sons, Inc., Hoboken, New Jersey. 737 pp.
Search in Google Scholar Back to article
Skorokhod, A. V. (1989). Asymptotic Methods of Theory of Stochastic Differential Equations. American Mathematical Society, Providence. 339 pp.
Search in Google Scholar Back to article
Timoshenko, S. P., Gere, J. M. (1961). Theory of Elastic Stability. McGraw-Hill, New York. 539 pp.
Search in Google Scholar Back to article
Tsarkov, Ye (J. Carkovs). (1993). Averaging in Dynamical Systems with Markov Impulse Perturbations. Bremen University, FRG. 9 Rep. Nr. 282. 41 pp.
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.1515/prolas-2017-0011 | Journal eISSN: 2255-890X | Journal ISSN: 1407-009X

Journal RSS Feed

Language: English

Page range: 63 - 68

Submitted on: Dec 13, 2016

Accepted on: Jan 5, 2017

Published on: Jun 1, 2017

Published by: Latvian Academy of Sciences

In partnership with: Paradigm Publishing Services

Publication frequency: 6 issues per year

Keywords:

beam dynamics,

perturbation theory,

second Lyapunov method,

random harmonic oscillator

Related subjects:

General interest,

Mathematics,

General mathematics

© 2017 Jevgeòijs Carkovs, Andrejs Matvejevs, published by Latvian Academy of Sciences
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 71 (2017): Issue 1-2 (April 2017)