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It is well known that, under broad conditions, the local statistics of the eigenvalues of a random matrix tend towards a universal distribution if the matrix is sufficiently random, regardless of the statistics of the matrix entries. This distribution is the same as that associated with a class of random matrix known as the Gaussian Orthogonal Ensemble (GOE). The underlying reason for this behaviour is explored here, and it is concluded that the source of the universal statistics lies in the Vandermonde determinant, which appears in the Jacobian of the transformation between the entries of a matrix and its eigenvalues and eigenvectors. Attention is then turned to the application of this result to natural frequency statistics, and to the prediction of the response statistics of a random built-up system. Recent work is reviewed in which it is shown that, away from low frequencies, the mean and variance of the system response can be predicted in an efficient way without knowledge of the statistics of the underlying system uncertainties. [ABSTRACT FROM AUTHOR]

A key ingredient in the Hybrid deterministic-statistical approach to the vibroacoustic analysis of complex uncertain structures (Shorter and Langley 2005) is the power absorbing dynamic stiffness matrix. The derivation of such a matrix associated with the flexural motion of a thin, flat, homogeneous plate, based on the cylindrical wave representation of the displacement field over a single convex domain (Lande 2005), is presented here. Key theoretical concepts are discussed, and the numerical results from a simple application are compared against Monte Carlo simulation results. [ABSTRACT FROM AUTHOR]

High amplitude vibration of drill-strings can lead to damage or loss of down-hole equipment costing the industry hundreds of millions of dollars per year. Theoretical models of drill-string dynamics are often limited to lumped parameter models of subsections of the drilling assembly that are difficult to correlate with real systems, or high resolution finite elements models that are more realistic but computationally demanding and do not provide clear insight into the fundamental mechanisms at play. In addition, drill-strings are subject to many uncertainties: to model these using Monte-Carlo simulations can be prohibitively slow. This paper presents a digital filter implementation of the transfer matrix method that allows time-domain coupling of the full length of a periodic drill-string to other systems or arbitrary, localised non-linearities. In this way the dynamics of the complete drill-string are included and the computational effort is focussed on those parts of the system that are harder to model while retaining the efficiency of the linear model where it applies. The efficiency makes the use of Monte-Carlo simulations to explore uncertainties a feasible approach. [ABSTRACT FROM AUTHOR]