A Foundational Study on Rational Optimization of Damping Ratio for Accurate Dynamic Simulation with Ultra Large Displacement

Abstract

The integration of dynamic simulation analysis has become widespread in general-purpose software, providing enhanced capabilities. However, accurately tracking deformations based on complete equilibrium solutions remains a significant challenge in problems characterized by strong geometric nonlinearity. This study examines the accuracy of the combined Newmark β method and Tangent stiffness method in dynamic analysis with ultra large displacements and evaluates the utility of Rayleigh proportional damping in numerical simulations compared to experimental models. An experimental model of a slender steel plate undergoing free vibrations after being released from a deformed state was created. Video footage capturing the deformation histories was compared to computational simulations to verify accuracy. The study also examines the appropriate values of the damping ratio (ζ) and the Newmark β value in the simulations. The results indicate that adjusting various damping ratio and a β value of 1/2 yield more realistic simulations with longer conservation of mechanical energy. The findings suggest that incorporating numerical damping into actual damping settings can achieve a more realistic simulation of dynamic behaviour with ultra-large displacements. Furthermore, experiments and analyses were performed to correct natural frequency by changing Young’s modulus, which is a key factor influencing natural frequencies, with observed correlations to plate thickness, setting the stage for further research under varied conditions to develop a more rational methodology for structural analysis.