Elasto-plastic analysis of foundations during emergency shutdown due to blast loading

Behaviour of machine foundations is investigated in this study under harmonic loading with varying frequency and pulse loading. Owing to excessive vibrations from the pulse, the machine encounters an emergency shutdown where the machine’s exciting frequency reduces to zero exponentially. The analysis is performed considering an elastic plastic single degree of freedom system with hardening and softening behaviour. Two cases are analysed depending on the time of application of pulse loading to the foundation system. For both the cases, the governing equations of motion are acquired and solved numerically using the fourth order Runge-Kutta method. Using these solutions, displacement-time graphs are obtained for a variety of parameters such as time constant, hardening/softening index, mass of machine and the foundation block, stiffness, pulse load magnitude, damping ratio and decay coefficient to study their influence on the behaviour of the machine-foundation system. The study helps in predicting the dynamic response of foundations under the emergency shutdown conditions due to pulse loading. Further, these also help in taking the decision if there exists a need for vibration barriers to have the displacements well within the permissible limits.