Mathematical modelling of a vehicle crash with emphasis on the dynamic response analysis of extendable cubic nonlinear dampers using the incremental harmonic balance method

A new direction of crashworthiness improvement using a smart extendable front-end structure is introduced in this paper to support the function of the existing vehicle structure. The smart front-end structure consists of two extendable, independently controlled hydraulic cylinders (dampers) integrated with the front-end longitudinal members. The main objectives of the smart front-end structure are to find solutions of the trade-off problem faced by the designer for offset collision events and to mitigate full frontal collisions. The work carried out in this paper includes developing and analysing mathematical models of different vehicle crash scenarios, including vehicle-to-vehicle frontal collision in both full and offset events. In these models, vehicle components are modelled by lumped masses and cubic non-linear springs. The hydraulic cylinders are represented by cubic non-linear damper elements. In this paper, the dynamic responses of the crash events are obtained with the aid of an analytical approach using the incremental harmonic balance method. The intrusion injury as the maximum deformation of the front-end structure and the occupant deceleration injury are used for interpreting the results. It is demonstrated from simulation results that significant improvements to both intrusion and deceleration injuries are obtained using the smart front-end structures.