WIAS Preprint No. 100, (1994)

Effects of distributed delays on the stability of structures under seismic excitation and multiplicative noise


  • Karmeshu, Prof.
  • Schurz, Henri

2010 Mathematics Subject Classification

  • 74H55 74H50 26A15


  • Stochastic stability, weak and strong time delay, random oscillations, seismic excitation, stochastic differential equations, numerical methods, implicit Euler, Mil'shtein and Balanced methods




The effects of seismic excitation and multiplicative noise (arising from environmental fluctuations) on the stability of a single degree of freedom system with distributed delays are investigated. The system is modelled in the form of a stochastic integro-differential equation interpreted in Stratonovich sense. Both deterministic stability and stochastic moment stability are examined for the system in the absence of seismic excitation. The model is also extended to incorporate effects of symmetric nonlinearity. The simulation of stochastic linear and nonlinear systems are carried out by resorting to numerical techniques for the solution of stochastic differential equations.

Appeared in

  • SADHANA, 20 (1995), pp. 451--474

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