, Volume 48, Issue 4, pp 213–219 | Cite as

On the mean square stability of a class of nonstationary coupled partial differential equations

  • G. Ahmadi


The stability of the equilibrium solution of a class of coupled partial differential equations with nonstationary random coefficients is studied. Several theorems in regard to mean square stability of the equilibrium state of the system are established. Some examples of the applications of the results to engineering problems are presented and significant improvements on stability region are observed.


Differential Equation Neural Network Equilibrium State Complex System Partial Differential Equation 
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Für eine Klasse von gekoppelten partiellen Differentialgleichungen mit nichtstationären Zufallskoeffizienten wird die Stabilität der Gleichgewichtslage untersucht. Dabei werden mehrere Sätze über die Quadratmittel-Stabilität der Gleichgewichtslage aufgestellt. Die Ergebnisse werden auf Beispiele aus dem Ingenieurbereich angewandt und ergeben bedeutende Vergrößerungen der Stabilitätsgebiete.


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  1. 1.
    Samuels, J. S.; Eringen, A. C.: On Stochastic Linear Systems. Math. Phys. 38 (1959). 83–103Google Scholar
  2. 2.
    Bertram, J. E.; Sarachik, P. E.: Stability of Circuits with Randomly Time Varying Parameters. Trans. IRE, PGIT-5 (1959) Special Supplement, 260–270Google Scholar
  3. 3.
    Kozin, F.: On Almost Sure Stability of Linear Systems with Random Coefficients. J. Math. Phys. 42 (1963) 59–67Google Scholar
  4. 4.
    Caughey, T. K.; Gray, A. H., Jr.: On the Almost Sure Stability of Linear Dynamical Systems with Stochastic Coefficients. J. Appl. Mech. 32 (1965) 365–372Google Scholar
  5. 5.
    Infante, E. F.: On Stability of Some Linear Nonautonomous Random System. J. Appl. Mech. 35 (1968) 7–12Google Scholar
  6. 6.
    Kozin, F.: A Survey of Stability of Stochastic Systems. Automatica 5 (1969) 95–112Google Scholar
  7. 7.
    Ahmadi, G.; Sattaripour, A.: Dynamic Stability of a Column Subjected to an Axial Random Load. Industrial Mathematics 26 (1976) 67–77Google Scholar
  8. 8.
    Ahmadi, G.; Mostaghel, N.: On the Stability of Nonstationary Nonlinear Random Systems. Int. J. System Science 7 (1976) 685–689Google Scholar
  9. 9.
    Ahmadi, G.: On the Stability of Nonstationary Stochastic Differential Equations. Iranian J. Sci. Techn. 7, No. 2 (1977) 75–80Google Scholar
  10. 10.
    Ahmadi, G.: On the Stability of a Class of Continuous Systems with Nonstationary Random Coefficients. Int. J. System Science (1977) 1201–1207Google Scholar
  11. 11.
    Plant, R. H.; Infante, E. F.: On the Stability of Continuous Systems Subjected to Random Excitation. J. Appl. Mech. 37 (1970) 623–628Google Scholar
  12. 12.
    Wang, P. K. C.: On the Almost Sure Stability of Linear Stochastic Distributed-Parameter Dynamical Systems. J. Appl. Mech. (1966) 182–186Google Scholar
  13. 13.
    Lee, T. H.; Hsu, C. S.: Liapunov Stability Criteria for Continuous Systems Under Parametric Excitation. J. Appl. Mech. 39 (1972) 244–250Google Scholar
  14. 14.
    Yavin, Y.: On the Stochastic Stability of a Parabolic Type System. Int. J. System Science 5 (1974) 623–632Google Scholar
  15. 15.
    Yavin, Y.: On the Modelling and Stability of a Stochastic Distributed Parameter System. Int. J. System Science 6 (1975) 301–311Google Scholar
  16. 16.
    Hsu, C. S.; Lee, T. H.: A Stability Study of Continuous Systems under Parametric Excitation via Liapunov's Direct Method. In: Instability of Continuous Systems, Ed. H. Leipholz, Berlin-Heidelberg-New York 1971, 112–118Google Scholar
  17. 17.
    Ahmadi, G.: On the Stability of Systems of Coupled Partial Differential Equations with Random Excitation. J. Sound Vibr. 52 (1977) 27–35Google Scholar
  18. 18.
    Bisplanghoff, R. L.; Ashley, H.; Halfman, R. L.: Aeroelasticity. Reading Mass. 1955Google Scholar
  19. 19.
    Bolotin, V. V.: The Dynamic Stability of Elastic Systems. London 1964Google Scholar

Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • G. Ahmadi
    • 1
  1. 1.Department of Mechanical EngineeringShiraz UniversityShirazIran

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