Browsing by Author "Rao, Vallabhajosyula Ravi Shankar"
Now showing 1 - 2 of 2
Results Per Page
Sort Options
Item A wavelet-based numerical scheme for stochastic mechanics(2000) Rao, Vallabhajosyula Ravi Shankar; Spanos, Pol D.Uncertainty is an inherent part of many physical systems. This is often ignored to simplify mathematical models thereby leading to a deterministic treatment of the system. Incorporation of the uncertainty into the model, particularly in the presence of strong correlation across scales is a difficult task for the conventional modeling techniques. This work studies a biorthogonal wavelet framework for the representation of random fields. It is shown that such a representation scheme leads to significantly decorrelated wavelet coefficients. The amount of decorrelation obtained is an improvement over that achieved with orthonormal wavelet basis functions. It is shown that a biorthogonal dual wavelets with sufficient number of vanishing moments and corresponding to a low primal order perform better than Daubechies wavelets at this task. These observations are used in pursuing the development of Wavelet based Galerkin and Petrov-Galerkin schemes for one-dimensional and two-dimensional stochastic mechanics problems.Item Dynamics of flexible mechanical systems with parameter stochasticity(1994) Rao, Vallabhajosyula Ravi Shankar; Spanos, Pol D.Equations of motion for flexible multibody systems with model uncertainty are developed using the Lagrangian formulation. The dynamic model developed serves to exemplify systems which possess undesirable flexibility by representing it as a stochastic process. Further, a novel methodology for treating uncertainties in flexible systems is proposed. The method uses concepts from stochastic finite elements to address the problem of uncertain parameters in flexible mechanical systems. In particular, the problem of random bending rigidity of a flexible beam is studied. The spatial random process is represented using the Karhunen-Loeve expansion. The response process of the beam, comprising of large rotation and elastic vibration is expressed as a projection on the Homogeneous Chaos. Expressions for the response statistics, including the coupling between the elastic vibration and the large displacements are derived. Comparison of the results obtained with those from Monte-Carlo simulation shows a fair amount of agreement.