A procedure for generating vectors of time domain signals that are partially coherent in a prescribed manner is described. The procedure starts with the spectral density matrix,[Gxx(f)], that relates pairs of elements of the vector random process{X(t)},−∞<t<∞. The spectral density matrix is decomposed into the form[Gxx(f)]=[U(f)][S(f)][U(f)]'where[U(f)]is a matrix of complex frequency response functions, and[S(f)]is a diagonal matrix of real functions that can vary with frequency. The factors of the spectral density matrix,[U(f)]and[S(f)], are then used to generate a frame of random data in the frequency domain. The data is transformed into the time domain using an inverse FFT to generate a frame of data in the time domain. Successive frames of data are then windowed, overlapped, and added to form a vector of normal stationary sampled time histories,{X(t)}, of arbitrary length.

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The paper reviews several methods for the generation of stationary realizations of sampled time histories with non-Gaussian distributions and introduces a new method which can be used to control the cross-spectral density matrix and the probability density functions (pdfs) of the multiple input problem. Discussed first are two methods for the specialized case of matching the auto (power) spectrum, the skewness, and kurtosis using generalized shot noise and using polynomial functions. It is then shown that the skewness and kurtosis can also be controlled by the phase of a complex frequency domain description of the random process. The general case of matching a target probability density function using a zero memory nonlinear (ZMNL) function is then covered. Next methods for generating vectors of random variables with a specified covariance matrix for a class of spherically invariant random vectors (SIRV) are discussed. Finally the general case of matching the cross-spectral density matrix of a vector of inputs with non-Gaussian marginal distributions is presented.

The dynamic response of critical aerospace components is often strongly dependent upon the dynamic behavior of bolted connections that attach the component to the surrounding structure. These bolted connections often provide the only structural load paths to the component. The bolted joint investigated in this report is an inclined lap-type joint with the interface inclined with respect to the line of action of the force acting on the joint. The accurate analytical modeling of these bolted connections is critical to the prediction of the response of the component to normal and high-level shock environmental loadings. In particular, it is necessary to understand and correctly model the energy dissipation (damping) of the bolted joint that is a nonlinear function of the forces acting on the joint. Experiments were designed and performed to isolate the dynamics of a single bolted connection of the component. Steady state sinusoidal and transient experiments were used to derive energy dissipation curves as a function of input force. Multiple assemblies of the bolted connection were also observed to evaluate the variability of the energy dissipation of the connection. These experiments provide insight into the complex behavior of this bolted joint to assist in the postulation and development of reduced order joint models to capture the important physics of the joint including stiffness and damping. The experiments are described and results presented that provide a basis for candidate joint model calibration and comparison.4