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In this paper, a bolted joint of two prismatic parts subjected to a shear impact force applied in the structure’s longitudinal direction is studied. The base part is made from steel and the connected one is from aluminum alloy. An elastomeric layer is inserted between the assembled parts in order to reduce vibration resulting from external excitation. An equivalent dynamic model is developed to analyze the behavior of bolted structure. The formulation of the problem gives a system of nonlinear equations. Solving differential equations is based on Euler’s method. Dynamic responses which correspond to the two degrees of freedom of the model are shown. The joint nonlinear behavior strongly depends on the interface properties. A cubic stiffness and damping factor are considered for the layer in the model, which gives it more realistic responses. Experimental tests are done for a case study of bolted joint under transient hummer impact. Model results are agreed with those issued from experiments. The damping layer (DL) effect is experimentally observed as well as in the model results.

This paper presents a simultaneous state-input-stiffness estimation framework for nonlinear systems. The technique combines an unbiased minimum variance estimator (MVE) from the data assimilation context with the Moore–Penrose pseudo-inverse. The investigation employs synthetically generated measurement data with additive Gaussian noise to replicate the field measurements. In the first stage of the algorithm, the MVE estimates a total force component, a function of the unknown system parameters and unknown input excitation. In the second stage, a system of over-determined equations is established by representing the input excitation with a Fourier series (with N coefficients) expansion. A least-squares solution for the unknown stiffness parameters and the Fourier coefficients is then achieved using the Moore–Penrose inverse. A dimensionless transformation handles the scale difference between the Fourier coefficients and unknown parameters. The novelty of the work is that the inputs and the parameters of the nonlinear systems are estimated simultaneously, circumventing any linearization of the system, and the associated computational hassles. The method by construction has a unique solution and an upper bound for stiffness estimation error is derived. The method is demonstrated numerically for Duffing oscillator systems excited by random inputs. The robustness of the technique is assessed by conducting various parametric studies. Numerical results reveal that the developed method accurately estimates the nonlinear cubic stiffness parameter, input force, and state responses.

This paper establishes a simplified model of a flexible beam with multiple nonlinear supports that present cubic stiffness to study the potential application of cubic nonlinearities in the vibration control of beams. The Lagrangian method (LM) is used to predict transverse dynamic responses of the flexible beam with multiple nonlinear supports that present cubic stiffness, whereas the harmonic balance method (HBM) and Galerkin truncation method (GTM) are utilized to study the accuracy of the LM. Against the background, the effect of nonlinear supports that present cubic stiffness on the nonlinear transverse dynamic responses of the beam is studied. For this study, the accuracy of the LM is guaranteed under the 4-term truncation number. Nonlinear transverse dynamic responses of the flexibly constrained beam with multiple nonlinear supports that present cubic stiffness are sensitively influenced by their initial calculation values. For different boundary conditions or working statuses, the maximum restoring forces at both ends of the flexible beam can be suppressed effectively by optimizing the parameters of nonlinear supports that present cubic stiffness. Appropriate parameters of nonlinear supports that present cubic stiffness are good at vibration control of the flexibly constrained beam. In addition, complicated dynamic responses of the flexible beam with multiple nonlinear supports that present cubic stiffness are motivated under some inappropriate parameters of nonlinear supports.