Numerical analysis of dynamic stability under random excitation

It is well known that an elastic column subjected to a harmonically-varying axial force exhibits parametric resonance over a range of applied frequencies and amplitudes. In this paper, the effect of white noise on the dynamic stability properties of a model system is investigated. Because of the complex nature of the applied loads and the nonlinearity of the governing equilibrium equation, three different numerical integration procedures are considered for determining the response of the model structure, and the accuracy of each scheme is studied. Results from the numerical investigation show that the method of Successive Symmetric Quadratures provides greater accuracy than the conventional Newmark Method or Harmonic Acceleration Method for nonlinear dynamic systems under random excitation. Computation of the model response shows that band-limited low frequency noise can limit the maximum deformation of the model system relative to the unperturbed case. Wide-band white noise, however, was observed only to enhance the destabilizing effect of the applied loads.