Time integration scheme for nonlinear structural dynamics, FAM, including structural vibration control

In this study, a method for the integration of the equation of motion for the inelastic analysis of structures utilizing the Force Analogy Method (FAM) and nonlinear control systems is proposed. The method is implicit, unconditionally stable, one-step scheme, multi-stage, with second-order precision, self-start capability, and high-frequency response filtering, exhibiting low overshooting. It enables consideration of sources of nonlinearity from the inelastic behavior of materials and the incorporation of control systems in structures. Four numerical examples are used to validate the proposed method, encompassing a diverse range of application scenarios, including varying numerical stiffness, dynamic load sources, and nonlinearity sources. The obtained results demonstrate excellent agreement with expected solutions, highlighting the method capacity to suppress high-frequency responses while maintaining solution accuracy. Our study suggests that the proposed method holds significant potential as a dynamic integration tool in analyzing complex systems. Its application in structures with nonlinear control systems and material nonlinearity represents a substantial contribution to the field, providing a robust and efficient solution for understanding structural response to dynamic actions.