Nonlinear Friction-Induced Vibration of a Slider-Belt System

A mass–spring–damper slider excited into vibration in a plane by a moving rigid belt through friction is a major paradigm of friction-induced vibration. This paradigm has two aspects that can be improved: (1) the contact stiffness at the slider–belt interface is often assumed to be linear and (2) this contact is usually assumed to be maintained during vibration (even when the vibration becomes unbounded at certain conditions). In this paper, a cubic contact spring is included; loss of contact (separation) at the slider–belt interface is allowed and importantly reattachment of the slider to the belt after separation is also considered. These two features make a more realistic model of friction-induced vibration and are shown to lead to very rich dynamic behavior even though a simple Coulomb friction law is used. Both complex eigenvalue analyses of the linearized system and transient analysis of the full nonlinear system are conducted. Eigenvalue analysis indicates that the nonlinear system can become unstable at increasing levels of the preload and the nonlinear stiffness, even if the corresponding linear part of the system is stable. However, they at a high enough level become stabilizing factors. Transient analysis shows that separation and reattachment could happen. Vibration can grow with the preload and vertical nonlinear stiffness when separation is considered, while this trend is different when separation is ignored. Finally, it is found that the vibration magnitudes of the model with separation are greater than the corresponding model without considering separation in certain conditions. Thus, ignoring the separation is unsafe.</jats:p

Simultaneous identification of structural parameters and dynamic loads in time-domain using partial measurements and state-space approach

Structural identification is an essential process in structural health monitoring, condition assessment and structural safety evaluation. This inverse problem becomes more challenging when information on the dynamic loads is missing or not fully known. Hence, it is important to establish methods to identify structural parameters and dynamic loads simultaneously from the measured structural responses which are easy to obtain compared to dynamic loads. This paper proposes a novel method to identify simultaneously structural parameters and dynamic loads from structural responses measured on a limited set of degrees-of-freedom. Firstly, an objective function is defined as the difference between the measured structural responses and the theoretically computed responses, and then the derivative of the residual function with respect to structural parameters is calculated numerically using the forward-difference method. The derivative of the residual function with respect to the external dynamic loads is computed using the state-space formulation and the system matrix composed of Markov parameters to facilitate the derivative-based identification. Secondly, the nonlinear optimization problem is solved using the Levenberg–Marquardt algorithm. Several numerical examples are analysed to demonstrate the effectiveness and robustness of the method. Finally, the effect of initial estimates of the parameters and dynamic loads and the effect of measurement noise, as well as the effects of number of measurements are investigated. The proposed method is also shown to achieve a satisfactory solution even when the initial estimates of parameters and dynamic loads are far from their true values