Modeling and Simulation of Elastic Structures with Parameter Uncertainties and Relaxation of Joints

Joint preload uncertainties and associated geometrical nonlinearities have a direct impact on the design process and decision making of structural systems. Thus, it is important to develop analytical models of elastic structures with bolted joint stiffness uncertainties. The conventional boundary value problem of these systems usually involves time-dependent boundary conditions that will be converted into autonomous ones using a special coordinate transformation. The resulting boundary conditions will be combined with the governing nonhomogeneous, nonlinear partial differential equation that will include the influence of the boundary conditions uncertainty. Two models of the joint stiffness uncertainty are considered. The first represents the uncertainty by a random variable, while the second considers the relaxation process of the joint under dynamic loading. For a single mode random excitation the response statistics will be estimated using Monte Carlo simulation. The influence of joint uncertainty on the response center frequency, mean square, and power spectral density will be determined for the case of clamped-clamped beam. For the case of joints with time relaxation the response process is found to be nonstationary and its spectral density varies with time. Under random excitation, the response bandwidth is found to increase as the excitation level increases and becomes more stationary. Under sinusoidal excitation, it is shown that the relaxation process of the joints may result in bifurcation of the response amplitude, when even all excitation parameters are fixed.