Advertisement

Approximate Analysis of Nonlinear Systems under Narrow Band Random Inputs

  • R. N. Iyengar
Part of the IUTAM Symposia book series (IUTAM)

Abstract

Dynamic analysis of systems with nonlinear stiffness characteristics is important in many earthquake engineering problems. Eventhough the base seismic excitation could be modelled as a wideband random process, due to the filtering action of the primary structure, the excitation to the equipments at higher floor levels are narrowbanded. This problem has received considerable attention in recent years [1, 2, 3]. While, under a broadband excitation, atleast simple nonlinear oscillators can be solved, the corresponding solutions under a narrowband input are not available. Since a gaussian narrowband process is essentially a filtered whitenoise, the dimensionality of the system response vector would be atleast four. The Fokker-Planck (FP) equation for the transitional probability density can be easily written down, but obtaining a solution to this equation is a formidable task. The stochastic averaging technique reduces the number of variables to three [4], but the resulting FP equation is still difficult to handle. Thus equivalent linearization or closure methods have to be used to get approximate solutions. However, in the absence of solution error estimates these methods can only be evaluated with reference to extensive numerical simulations.

Keywords

Random Excitation Duffing Oscillator White Noise Excitation Broadband Excitation Steady State Variance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    W.C. Lennox and Y.C. Kuak (1976), “Narrow-band excitation of a nonlinear oscillator”, J. of App. Mech., 43, 340–344.CrossRefMATHADSGoogle Scholar
  2. 2.
    H.G. Davies and D. Nand Lall (1981), “Phase plane for narrowband random excitation of a Duffing oscillator”, J. of Sound and Vib., 104, 277–283.CrossRefMathSciNetGoogle Scholar
  3. 3.
    R.N. Iyengar (1988), “Stochastic response and stability of the Duffing oscillator under narrowband excitation”, J. of Sound and Vib., 126, 255–263.CrossRefADSMathSciNetGoogle Scholar
  4. 4.
    R.N. Iyengar (1989), “Response of nonlinear systems to narrowband excitation”, Structural Safety, 6, 177–185.CrossRefGoogle Scholar
  5. 5.
    C.S. Manohar and R.N. Iyengar (1991), “Narrowband random excitation of a limit cycle system”, Arch. of App. Mech., 61, 133–141.MATHGoogle Scholar
  6. 6.
    G.V. Rao and R.N. Iyengar (1990), “Nonlinear planar response of a cable under random excitation”, Prob. Engg. Mech., 5, 182–191.CrossRefGoogle Scholar
  7. 7.
    P.T.D. Spanos and W.D. Iwan (1979), “Harmonic analysis of dynamic systems with nonsymmetric nonlinearities”, J. Dyn. Syst., 101, 31–36.MATHGoogle Scholar
  8. 8.
    R.L. Stratonovich (1963), Topics in the Theory of Random Noise, Vol. I. Gordon and Breach, New York.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • R. N. Iyengar
    • 1
  1. 1.Department of Civil EngineeringIndian Institute of ScienceBangaloreIndia

Personalised recommendations