Modified Central Difference Method for Negative Stiffness SDoF System Under Ground Seismic Excitation

The present paper deals with the analytical and numerical solution of the motion equation of a single degree of freedom (SDoF) oscillator with damping and negative stiffness (NS) due to seismic excitation at its base. The resulting solution shows that the structure's response displacement increases exponentially; thus, practically, there is no vibration. Moreover, a well‐known numerical procedure is selected to be modified in order to be suitable for the calculation of the response of the abovementioned NS‐SDoF oscillator. Specifically, an appropriate modification of the central difference method is presented, taking into account the damping and NS of the oscillator. The effectiveness of this proposed procedure is examined by comparing the extracted results to those obtained through the exact mathematical solution. The accuracy and precision of the proposed modified numerical method are investigated through numerical examples by comparing the results obtained with the analytical process. The results show that the new modified numerical method, as well as the analytical one, led to similar results; thus, the modified central difference method can be efficiently and safely used for the calculation of the response of NS‐SDoF systems.