受人為引致振動下體育場館樓板之調諧質量阻尼器最佳化設計

Abstract

隨著人們對建築外觀的美感要求越來越高，使得桿件趨於細長且跨距較大，例如人行橋、大跨度樓板等。對於跨度較大的樓板結構，其主頻率較低，使得結構對於人為引致的外力更加敏感，易產生共振現象。因此，在設計大跨度、低頻率的樓板時，除了滿足強度和最大位移要求外，仍須充分考慮振動舒適度的問題。目前建築中已廣泛使用各種類型的阻尼器來控制振動以及消能，調諧質量阻尼器即為常見之減震裝置，多用於橋梁、高層建築、大跨度樓板中，以減振並提高舒適性。

本研究以體育場館作為主要研究之結構，首先利用建模軟體SAP2000建立兩個頻率不同之體育館模型，並加載人為外力，觀察大跨度樓板的垂直向振動，以及探討加裝TMD後振動加速度的折減效果。利用National Building Code (NBC1990)規範中定義的人為活動來分析不同活動下樓板振動的情形，比較不同目標函數對TMD設計參數之影響效果。此外，也利用NBC1990規範中定義的舒適性限制標準作為最佳化之束制條件，以控制TMD的設計參數，決定最小之TMD總質量比。當結構物與外力產生共振之頻率不只一個時，需同時考慮會產生共振的多個模態，決定TMD擺放之位置，使樓板在不同活動、外力頻率、外力分布位置的情況下，其振動加速度在加裝TMD後都能得到良好的折減效果，確保振動的控制及提高人為使用上之舒適性。

With the increasing demand for aesthetic appeal in architectural design, structural elements are becoming slender and spanning larger distances, such as pedestrian bridges and large-span floor structures. For large-span floor structures with lower natural frequencies, they are more sensitive to externally induced forces and prone to resonance phenomena. Therefore, in the design of large-span, low-frequency floor structures, in addition to meeting strength and maximum displacement requirements, careful consideration must be given to vibration comfort. Various types of dampers have been widely used in buildings to control vibration and dissipate energy, and Tuned Mass Dampers (TMD) are commonly employed as vibration control devices in bridges, high-rise buildings, and large-span floor structures to reduce vibration and improve comfort.

This study focuses on sports stadiums as the main structural subject. Firstly, two stadium models with different frequencies are established using the SAP2000 modeling software. Artificial external forces are applied to observe the vertical vibrations of large-span floor structures and investigate the reduction effect of vibration acceleration after installing Tuned Mass Dampers (TMD). The analysis is conducted based on the human activities defined in the National Building Code (NBC1990) to examine the floor vibrations under different activities. The impact of different objective functions on the design parameters of TMD is compared. Additionally, the comfort limit criteria defined in the NBC1990 code are utilized as constraint conditions for optimization to control the design parameters of TMD and determine the minimum total mass ratio of TMD. When the structure resonates with multiple frequencies, the placement of TMD needs to consider multiple modes of resonance, ensuring that the floor achieves a good reduction effect in vibration acceleration after installing TMD under various activities, external force frequencies, and distribution positions. This ensures effective vibration control and improves the comfort of human use.