Mathematical analysis of the safety system, sensitive to impact loading using Laplace technique

The safety of the car is one of the high attentions of car customers. Then, automobile manufactures make a lot of effort to improve safety. Because of the high attention of buyers towards the safety of car, car manufacturers make a huge effort to improve this safety. Among them, we can refer to the airbag, which in turn is the most important safety component on a vehicle. In this paper, the mathematical analysis of a simple mechanical system is discussed which is lightweight, low cost, and can be reasonably accurate. The system consists of a cantilever beam in which a  Current-carrying wire is placed .when  occur accidents due to the high acceleration shock, the beam is broken and the current will be out of circuit. So, secondary factors such as cutting of the petrol circuit, unlocking the doors and deactivation of the alarm system may happen. The Analysis is performed using Laplace technique. . The results show that the accidents with speeds above 40 miles per hour, choosing   a beam with a height of 8 cm and a cross-section of 3* 0.3cm2, the system will work smoothly and efficiently.  Keywords: Mathematical modeling, safety, airbags, Laplace transformations, bending of beam