有限元素法於樁型地震超材料之數值模擬

Numerical Simulations on Pile-type Seismic Metamaterials using Finite Element Method

李宇軒(Yu-Hsuan Lee)

指導教授 ： 張國鎮

國立臺灣大學/工學院/土木工程學研究所/碩士(2020年)

https://doi.org/10.6342/NTU202003254

摘要

近年來隔減震系統已為成熟之抗震技術，透過將隔減震裝置安裝於建築物內部以改變其耐震行為，並應用於許多建築結構中。地震超材料為一研發中之概念性材料，其由波傳角度出發，藉由超材料在帶隙範圍內發生局部共振產生濾波機制，將帶隙涵蓋地震主頻或結構物自然頻率，可避免地表與結構物間產生共振行為，進而降低結構物之反應。本文針對基樁形式之地震超材料進行分析，其透過單元結構以週期性排列構成地震超材料，將其設置於建築物外圍，可用於保護範圍內之結構體。
本文利用有限元素分析軟體ABAQUS進行數值模擬，在二維模型中假設為平面應變進行分析，由三種對應不同帶隙頻率所組成之多類型複合模型，透過地震歷時分析結果發現，其可有效降低加速度反應，對於近斷層之速度脈衝也具有折減效果，且因帶隙內之濾波機制使反應譜中對應頻率之譜加速度下降。在三維實尺模型分析發現，由於超材料發生局部共振而造成較大之反應，因此超材料前方會產生放大的結果，並從模擬結果圖看出濾波機制僅發生於包含超材料之深度範圍，因此在相同深度模型下，超材料長度較深者其折減效果較佳。接著進行土壤結構互制分析，發現地震主頻位於帶隙內時，在峰值範圍內結構物之絕對加速度顯著降低，此時對應之頂層相對位移與基底剪力、柱底軸力與彎矩皆呈下降趨勢，且結構體層間變位並無明顯上升，相比隔震系統藉由延長建築物的週期，使建築物因地震而產生的加速度反應下降而導致位移反應上升，地震超材料可在不增加位移反應情況下降低帶隙頻率範圍內之加速度反應。最後透過縮尺試驗模型之單元結構掃頻分析發現，當模型縮小十倍則帶隙頻率放大十倍，由整體模型通過超材料後之不同深度結果，與同尺寸土體模型相比發現於表面反應的衰減情形最為明顯。

關鍵字

地震超材料 ； 有限元素法 ； 數值模擬 ； 土壤結構互制 ； 縮尺試驗

並列摘要

Recently, the application of seismic isolation and energy dissipation systems had become more and more developed. The seismic behavior of structure could be modified through installing the passive control systems to the structure. Until now, seismic metamaterials were known as a conceptual material still in development. From the perspective of wave propagation. The resonance between the ground and the structure could be prevented, and also, reduce the structure response by blocking seismic waves with local resonance of metamaterials in the band gap that covers the frequency content of ground motions or the natural frequency of the structure. This study focused on the pile-type seismic metamaterials, which consists of periodic cell units. Buildings surrounded by the seismic metamaterials could be protected from seismic wave.
In this research, the finite element analysis software ABAQUS was used for numerical simulation, and the plane strain state was assumed in the two-dimensional model. The ABAQUS model consists of three types of cell units with broad band gap. Through the time history analysis, it was found that the metamaterials could not only effectively reduce the acceleration response, but also reduce the effects of near-fault pulse-like ground motions. The spectral acceleration of the corresponding frequency in the response spectrum is decreased due to the wave mitigation in the band gap. The analysis result of the three-dimensional full-scale model showed that a larger reaction will occur in front of the metamaterials caused by the local resonance. Furthermore, the degradation of wave only took place at the corresponding depth with metamaterials. Therefore, by observing the models with identical total depth, the deeper the length of metamaterials is, the better attenuation characteristics shows. Through the analysis of cell units, it was found that when the model was scaled down by ten times, the frequency would amplify by ten times. After the analysis of metamaterials models with different depth, most of the difference occur at the surface compared with the soil model. Last but not least, the analysis result of the soil-structure interaction indicated that when the frequency content of ground motions was within the attenuation zone, the peak of roof absolute acceleration would significantly be reduced. Likewise, the peak of roof relative displacements, base shears, column axial forces and bending moments of the structure all tended to decrease, besides, there was no conspicuous increase in the interlayer displacement of the structure. Though seismic isolation system could decrease the acceleration response through extending the natural period of the structure. It may increase the displacement response of structure at the same time. Based on these drawbacks of seismic isolation system, seismic metamaterials could decrease the acceleration response within the attenuation zone without increasing the displacement response.

並列關鍵字

Seismic Metamaterials ； Finite Element Method ； Numerical Simulation ； Soil-Structure Interaction ； Lab-Scale Experiment

參考文獻

[1] Oiles Corporation., FPS Sliding Pendulum Type Seismic Isolation Device Friction Pendulum System, http://www.oiles.co.jp/en/menshin/building/menshin/products/fps/

[2] Taiwan Pillar Industry Co. Ltd., Lead Rubber Bearing, http://www.taiwanpillar.com.tw/en/about12c4.html?mode=3 id=14

[3] Freyssinet Products Company Italia. High Damping Rubber Bearings Isosism HDRB, http://www.fpcitalia.it/freyssinet/fpc-italia_en.nsf/sb/products-and-solutions.seismic-protection..high-damping-rubber-bearings-isosism-hdrb

[4] K.C. Tsai, H.W. Chen, C.P. Hong, and Y.F. Su, “Design of Steel Triangular Plate Energy Absorbers for Seismic-Resistant Construction,” Earthquake Spectra, vol. 9,no. 3, pp. 505 - 528, 1993.

[5] K.C. Tsai, J.W. Lai, Y.C. Hwang, S.L. Lin, and C.H. Weng, “Research and Application of Double-Core Buckling Restrained Braces in Taiwan,” World Conference on Earthquake Engineering, no. 2179, 2004.