Proper orthogonal decomposition of the dynamics in bolted joints

Joints play an important role in the dissipation of vibration energy in built-up structures. The highly nonlinear nature of joints with micro-slip is the main hurdle in developing a reduced-order model which can simulate the dynamic behaviour of a joint for a wide range of excitation conditions and geometries. In this paper, the proper orthogonal decomposition is applied to joint dynamics in an attempt to arrive at a generic reduced-order model without a compromise on the physics of the system. Only the linear part of the system of equations is reduced. The nonlinear part is determined in the full space and then reduced before the numerical integration phase. The major reduction in computational time is achieved by the increase in the size of the stable time step and the reduced number of coordinates in the integration phase. The reduced-order model, which is derived for an isolated and harmonically excited joint, is successfully applied to separate joints with different geometries and excitation conditions, e.g. harmonic and impulsive. The model is also capable of simulating the dynamics of structures with joints. The results of the reduced-order model show good agreement with a full model both in terms of the state of the system and its hysteretic behaviour.