Jerk hypothesis in seismic loading of structures with the development of Duhamel's integral: part II

This research examined the hypothesis of the existence of a force due to acceleration changes in structures. The existence of a jerk force was first mathematically proven in the presence of initial acceleration conditions. By defining a third-order equation that has the capability to consider the jerk force, its solution was derived. The solution of this differential equation was performed both directly with initial conditions and through generalisation of Duhamel's integral. Comparison of the solutions of second- and third-order equations with experimental results using the proportional jerk coefficient showed good agreement. The greatest differences were when the ratio of loading frequency to the natural frequency of the structure, considering the damping ratio, was greater than 6.75. The effect of earthquakes as loads on structures, considering the ground jerk effect, showed that, in the third-order equation, the acceleration of tall or damaged structures with a small natural frequency and high damping was greater than in the second-order equation. Due to the out-of-phase nature of acceleration and jerk, the maximum values of these two do not occur together. The ratio of maximum jerk to maximum acceleration is an important variable in calculating the jerk effect.