Modelling of Contact Interfaces using Non-homogeneous Discrete Elementsto predict dynamical behaviour of Assembled Structures

In this dissertation a new approach of modelling contact interfaces with equivalent discrete elements is presented. Various fastening techniques used for assembling structures not only account for transfer of loads but also adds damping to the structure. With vast usages of the jointed structures, the effect of contacts on the global dynamical behaviour of an assembled structure is of prime interest. Assembled structures with contact interfaces show a non-linear behaviour, with a predominance of the local energy dissipation at interfaces in comparison to the inherent material damping losses. With increasing complexity of structures used in the industrial applications, a continuous demand of robust and efficient numerical modelling exists for a better prediction of the system behaviour. Hence, numerical models capable of predicting the dynamic behaviour to good accuracy can be used as a replacement for expensive experimental investigations. Various theoretical and empirical models have been successful in capturing the influence of the non-linearity induced through the contact interfaces, but their implementation for complex and large structures experience convergence difficulties with high computational time. To improve the computational cost, frequency domain description based on family of Harmonic Balance Methods provide a good alternative, but they have been restricted to cases involving periodic excitations. This thesis describes an equivalent localized discrete contact model, which can predict the effects of contact non-linearity on the dynamical behaviour of structure with considerable enhancements on the computational time efficiency. The proposed notion is to use an explicit non-homogeneous description to en-capture the global non-linear behaviour and a local linearized definition to retain the advantages of a linear system. The new approach used in modelling of contacts is based on the characterization of discrete spring-damper system at the contact interface. A Damped-Pressure Dependent Joint (D-PDJ) model is developed to obtain the required local contribution of the contact stiffnesses and damping. The normal and tangential contact stiffnesses are calculated from the resulting contact pressure, based on a modified exponential pressure-penetration law and Mindlin law respectively. The contact damping is defined through the use of the discrete hysteretetic-structural damper elements at the contact interface. Based on numerical investigation for a beam fastened with a bolted joint, regions of stick, micro-slip and slide are defined. The numerical investigations show that the maximum dissipation is obtained in the micro-slip region. A Rayleigh probability distribution function based on the contact pressure is chosen for describing the contact damping distribution over the interface, with parameters governing the position of the maximum damping and magnitude of damping. Quantitative experimental validations of the proposed D-PDJ model are done for a set of test structures. The first test structure is a double layered beam (made of stainless steel) fastened with four M6 bolted joints. The double layered beam structure is used to study the influence of operational factors such as bolting torque and excitation amplitude. Later, a copper-prepreg-copper plate is fastened between the beams to study the influence of contact pair of different materials. All investigations have shown good correlation between the experiment and simulation results for test structure experiencing moderate non-linearity (bolting torque 3 Nm and 5 Nm) in comparison to strong nonlinearity (bolting torque 1 Nm). The second test structure is a set of prototype structures to resemble a large and complex structure like Electronic Control Unit (ECU). The first prototype structure is a system resembling an Engine ECU, having large contact area with localized pressure distribution near the bolt region. The Experimental Modal Analysis(EMA) results when compared to D-PDJ model showed good correlation till 2 kHz, with the results of the modal damping highly appreciable. Also, the result’s accuracy and computational time efficiency have proved to be significantly better than the conventional methods. The second prototype structure is a system resembling an Airbag ECU. The second prototype structure verifies the use of model having combination of material and contact non-linearities. The comparison for the transmissibility results showed good match between the experiment and D-PDJ simulation, for base excitation setup of the prototype structure. The proposed D-PDJ model has shown good match with various sets of experimental results and is concluded to have the capability of describing the dynamical behaviour of the assembled structures with moderate non-linearity. Also, the significant reduction in computational time motivates its usage for the complex and large structures used in industrial application.