Modeling and Analysis of Dynamic Loads on a (2D) Frame Using an MDOF System

Abstract

Dynamic safety assessment of engineering structures under loads is an topic in structural engineering due to the complexity of energy transfer in multi degree of freedom (MDOF) systems. The main limitation of conventional analytical methods lies in their inability to accurately predict dynamic behavior, in addition to their computational cost, especially when analyzing transient responses. The equation of motion was used and solved numerically in MATLAB using the fourth-order Runge–Kutta (RK4) method. Different loading cases were applied by varying the load matrix while keeping the mass, stiffness, and damping matrices constant. The results showed that the proposed model is capable of accurately representing the dynamic response, as the time histories exhibited stable behavior during transient and steady state phases. Furthermore, the results indicated that variations in load magnitude and location influence displacement behavior, with an effect of dynamic coupling in energy transfer between nodes. The proposed model enhances prediction accuracy while maintaining computational efficiency, reduces the need for complex simulations, and provides a reliable tool for structural design.