Modeling and simulation of elastic structures with parameter uncertaintiesand relaxation of joints

Joint preload uncertainties and associated geometrical nonlinearities have a direct impact on the design process and decision making of structural sys tems. Thus, it is important to develop analytical models of elastic structu res with bolted joint stiffness uncertainties. The conventional boundary va lue problem of these systems usually involves time-dependent boundary condi tions that will be concerned into autonomous ones using a special coordinat e transformation, The resulting boundary conditions will be combined with t he governing nonhomogeneous, nonlinear partial differential equation that w ill include the influence of the boundary conditions uncertainty. Two model s of the joint stiffness uncertainty are considered. The first represents t he uncertainty by a random variable, while the second considers the relaxat ion process of the joint under dynamic loading. For a single mode random ex citation the response statistics will be estimated using Monte Carlo simula tion. The influence of joint uncertainty on the response center frequency, mean square, and power spectral density will he determined for the case of clamped-clamped beam. For the case of joints with time relaxation the respo nse process is found to be nonstationary and its spectral density varies wi th time. Under random excitation, the response bandwidth is found to increa se as the excitation level increases and becomes more stationary. Under sin usoidal excitation, it is shown that the relaxation process of the joints m ay result in bifurcation of the response amplitude, when even all excitatio n parameters are fixed.