Probability Density Functions of Acoustically Induced Strains in Experiments with Composite Plates

Abstract

Composite structures, which are widely used in the design of flight vehicles, exhibit nonlinear behavior under in-service acoustic excitations typical of jet engine effluxes. Therefore, the responses of such structures can be non-Gaussian random processes. The dynamic strains in carbon fiber-reinforced plastic plates with clamped boundaries have been investigated experimentally in a progressive wave tube. Computer analysis concentrated on evaluation of the probability density function and its skewness and kurtosis parameters, which describe deviations from the Gaussian (normal) law model. The results show that a great lack of symmetry exists in the distribution plots of strain instantaneous values, and this influences peak probability density functions. The latter characteristic is the focus of attention for flight vehicles because it is associated directly with fatigue damage accumulation, which may be the cause of failure. The analytical description of these phenomena is also discussed. Approximation of instantaneous value distributions is made in the piecewise-Gaussain form and yields peak distribution formulas that are similarly constructed from Rayleigh law sections. The main advantage of both these solutions for experimental data fitting is that the probability density expressions obtained are convenient for use in subsequent theoretical modeling. Accuracy of the proposed method is demonstrated via a number of examples.