Abstract The shock response spectrum is a widely used design tool that engineers use when assessing the severity of transient excitation on a structure. The shock response spectrum is typically defined as the peak response of a series of single degree-of-freedom (DOF) oscillators each with a different natural frequency. For structures representable by a single DOF system, such is the case when only a single mode dominates the response, the shock response spectrum can be used to evaluate this response directly and a brief review of the existing accepted metrics is presented. In general, the response of many structures may comprise contributions from higher order modes leading to inadequate predictions from the shock response spectrum, especially for acceleration responses. In such cases a form of shock response spectrum can be obtained that accounts for all modes of vibration but as a function of shock duration. However, a multi-modal model of the structure is then required and its shock response obtained numerically over a range of shock durations which can be computationally expensive and less amenable to physical interpretation. This paper adopts a previously proposed modal approach to obtaining the shock response of systems with contributions from higher order modes, in which the transient response is calculated for each mode in turn which are then superposed. A key question that arises is the number of modes that need to be retained in the summation. Two numerical case studies are presented which explore modal convergence for displacement, velocity and acceleration shock response spectra. Results suggest that a priori mode selection is not generally possible although inspection of the mode shapes can offer guidance. However, the benefit of the modal approach to interpretability of the results is illustrated.
Read full abstract