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There is an increasing reliance in the engineering community on the use of mathematical models to characterize physical system behavior. This is happening even though mathematical models rarely simulate real system behavior perfectly. Due to this reliance, we require objective, well-founded mathematical techniques for model validation. This paper develops a formal approach to the validation of mathematical models of structural dynamics systems. It uses a probabilistic/statistical approach to the characterization of an important measure of behavior of dynamic systems subjected to random excitations, and seeks to validate a mathematical model in a statistical sense. An example is presented.

In recent years, great progress has been made in the construction and solution of large finite element models of complex structural dynamic systems. For example, structural models with millions of degrees of freedom are being built and used to approximate responses of structural systems. Further, great progress is being made in stochastic system analysis. Techniques for the construction of stochastic system models have been developed and solution techniques proposed. However, the two areas have not been combined, on a large scale, because stochastic finite element approaches appear very intrusive in their pure form. That is, substantial modifications of deterministic finite element codes are required to accommodate stochastic analysis. In view of this, a technique that uses the techniques of stochastic finite elements in a non-intrusive manner is required. This research provides one such approach. Specifically, the problem is divided into three parts: (1) model structural dynamic excitations using traditional approaches, and model physical system randomness using techniques of stochastic finite elements, namely, the Karhunen-Loeve expansion and polynomial chaos; (2) generate stochastic structural realizations and realizations of the random excitation using a Monte Carlo approach, and analyze structural responses with parallel computation in a suitable, large-scale finite element code; and (3) analyze structural dynamic responses using the techniques of stochastic finite elements, namely, the Karhunen-Loeve expansion and polynomial chaos. This paper supplies the details of the analytical approach. A numerical example is presented.

Numerous investigations have studied the potential for chaotic vibrations of nonlinear systems. It has been shown for many simple nonlinear systems, that when they are excited severely enough, or with the appropriate parametric combinations, that they will execute chaotic vibrations. The present investigation considers the potential for the occurrence of chaos in a practical nonlinear system -- the isolated accelerometer. A simple, first order model is proposed for the isolated accelerometer, and it is shown that chaos can occur in the isolated accelerometer. A preliminary investigation into the bearing that this chaos potential has on the measurement of shock response is summarized. 7 refs.