Dynamic Response of SDoF System with Negative Stiffness—A Relevant Key-Point for Machine Learning

The present article deals with the role of the negative stiffness of structures and the identification of negative stiffness by Artificial Intelligence and Machine Learning (ML). Generally, structures have positive stiffness combined with damping during earthquake-induced oscillations, which leads to energy loss and causes a reduction in the amplitude of the vibration. However, when a structure falls into the nonlinear region of a structure, the appearance of negative stiffness is possible. If this occurs, then the mathematical solution of equation of motion is changed drastically. This is the exact point covered by the present article and a suitable procedure (namely the key-point) for ML is given. This paper aims to define and solve the mathematical equation of motion for a Single Degree of Freedom (SDoF) oscillator with damping and negative stiffness due to various dynamic loading conditions. The derived solutions indicate that, for every case of dynamic loading, oscillation with negative stiffness is absent, and the structure’s response increases exponentially. The abovementioned facts are verified by the presentation of a benchmark example that gives the exact values of response of a SDoF system with negative stiffness.