This paper presents the results of a probabilistic flutter study of a mistuned bladed disk using a high fidelity model including both structural and aerodynamic coupling. The approach used in this paper is relatively fast because it does not require any additional information than that required of a tuned flutter analysis, with the exception of the mistuned blade frequencies. The case study shows that the stability of the fleet can be significantly affected by the standard deviation of blade frequencies and the pattern in which they are arranged in the wheel. A method for understanding and identifying the beneficial patterns is presented.

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Chaotic mixing is generated in a lid driven cavity through a temporal forcing of the lid, which exploits repeated stretching and folding. The fluid flow features are simulated by solving mass and momentum conservation equations along with particle tracking, over a range of frequencies and amplitudes. By locating a passive circular plug inside the cavity, chaotic mixing is found to be dramatically altered. The mixing efficiency is assessed for the Reynolds number range of 50 to 5000. A new measure for the quantification of mixing efficiency called σ measure is introduced. Numerical particle tracking is performed by placing passive massless and inertialess particles along the vertical centerline of the cavity. The two parameters which influence mixing efficiency, viz. frequency and amplitude of the lid are varied. The advantage of the proposed σ measure is brought out vis-á-vis the existing techniques, such as stretching rate (SR) and mixing in weak sense ( ws  ).

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A wavelet-based model for stochastic analysis of beam structures is presented. In this model, the random processes representing the stochastic material and geometric properties are treated as stationary Gaussian processes with specified mean and correlation functions. Using the Karhunen-Loeve expansion, the process is represented as a linear sum of orthonormal eigenfunctions with uncorrelated random coefficients. The correlation and the eigenfunctions are approximated as truncated linear sums of compactly supported orthogonal wavelets, and the integral eigenvalue problem is converted to a finite dimensional eigenvalue problem. The energy-principle-based finite element approach is used to obtain the equilibrium and boundary conditions. Neumann expansion of the stiffness matrix is used to write the nodal displacement vector in terms of random coefficients. The expectation operator is applied to the nodal displacements and their squares to obtain the mean and standard deviation of the displacements. Studies show that the results obtained using this method compare well with Monte Carlo and semianalytical techniques.