معرفی و تحلیل عددی میراگر میله‌ای تحت خمش چهار نقطه‌ای

Tapered steel bar dampers are recognized as efficient passive energy dissipation devices due to their simple geometry, stable hysteretic response, and high ductility. Previous studies have investigated their behavior under three-point bending. To enhance the energy dissipation capacity, this study extends the loading configuration to four-point bending, thereby enlarging the constant moment region and involving a greater volume of material in plastic deformation. Nonlinear finite element analyses were performed using ABAQUS to evaluate the cyclic response and energy efficiency of the proposed configuration. The modeling incorporated an isotropic–kinematic hardening law calibrated from experimental steel stress–strain curves. Boundary conditions were defined by hinged ends and intermediate supports. A mesh sensitivity analysis was conducted to check the stability of results, confirming that variations in dissipated energy and forces remained below 3% for further mesh refinement. The analysis included parametric variations in bar diameter (4–8 cm), bar length (100–200 cm), yield stress (245–322 MPa), number of bars, and spacing between intermediate supports (15–30 cm). Results demonstrated that among all parameters, the bar diameter had the most pronounced effect. Increasing the diameter from 4 cm to 8 cm enhanced the dissipated energy by approximately 850%, while the total weight increased by only 180%, indicating improved material utilization efficiency. Conversely, increasing the bar length drastically reduced stiffness and energy absorption (by up to 82%) due to reduced bending moment magnitude. Raising the yield strength increased energy dissipation by 20–25%, although excessive strength may reduce ductility. Doubling the number of bars nearly doubled total energy dissipation while maintaining a constant efficiency ratio, confirming linear scalability. For the four-point bending configuration, increasing the intermediate support distance from 15 cm to 30 cm produced a 28% rise in energy dissipation and a 30% increase in effective stiffness, mainly because the constant-moment region becomes significantly wider. The equivalent plastic strain (PEEQ) exhibited only a slight increase (0.73 to 0.79), indicating that additional plastic deformation occurred without concentrated damage. A comparative analysis between three- and four-point bending showed that, at the base configuration (H = 15 cm), the four-point system dissipated 20–22% more energy and achieved 10–15% higher E/Wbar with only 5–8% weight increase. When H = 30 cm, the total energy dissipation rose by approximately 56% relative to the three-point model. The efficiency ratio (ΔE/ΔW) ranged between 2.5 and 4, meaning that energy dissipation increased nearly twice as fast as mass. The von Mises stress and PEEQ contours confirmed a relatively uniform stress distribution along the tapered geometry, with larger yielding volume in the four-point bending model. The PEEQ values were interpreted as a relative damage index and used qualitatively to assess plastic strain concentration. In summary, transitioning from three-point to four-point bending significantly improves the energy dissipation efficiency of tapered steel bar dampers while maintaining a moderate weight increase. Overall, the results suggest that the four-point bending mechanism can be considered a practical and material-efficient option for seismic applications, although further experimental work is still needed. Future studies are recommended to include cyclic fatigue testing and optimization of intermediate support spacing to achieve enhanced durability and performance consistency.