基於多孔介質之調諧液體阻尼器參數最佳化設計及振動控制

Abstract

本研究以數學解析方法系統性地探討了附加多孔介質之調諧液體阻尼器（Porous Media Tuned Liquid Dampers, PMTLD）中多孔介質的布置方式對液體動力特性的影響，並分析了 PMTLD 在控制結構振動行為上的效果。 基於流場滿足淺水波方程(Shallow Water Equations, SWE)的假設，在無黏性、非旋性、不可壓縮的條件下，以勢流理論 (Potential Flow Theory)對矩形儲水容器中的兩種不同多孔介質安裝方式，建立了對應的數學模型。第一種 (type1) 將多孔介質安裝在自由液面附近，第二種 (type2) 則安裝在容器底部。透過將流場分解為簡單流體子域，利用分離變數法求解各子域速度勢分量，並根據各子域交界面的速度及壓力連續條件和自由液面運動方程處理流場耦合，進一步推導求解待定係數，研究多孔介質參數對晃動模態頻率、自由液面樣態及基底剪力的影響。 根據所得流場動力特性建立 PMTLD 系統之等效機械模型，並依 J. P. Den Hartog 提出的最佳化設計概念，針對模態頻率、模態質量及模態阻尼比等參數進行設計，以提升 PMTLD 系統的強健性 (robustness)。本文研究在其他參數固定下，type1 模型所提供的模態阻尼比相較於 type2 更穩定、可控性更佳。分析附加兩種 PMTLD 系統的主結構頻率響應曲線，顯示 type1 模型在抑制結構振動的表現更好。進而使用狀態空間方法(State Space Procedure, SSP)迭代求解type1模型液體晃動與單自由度主結構的互制行為，驗證參數設計的成效。此外，透過 921 地震歷時模擬，展示了 type1 模型在真實地震下對結構振動控制的可靠性。

This study systematically investigates the effects of different porous media configurations in a Porous Media Tuned Liquid Damper (PMTLD) on the fluid dynamic characteristics using a mathematical analytical approach. The study also examines the effectiveness of PMTLD in controlling structural vibration behavior. Based on the assumption that the flow field satisfies the Shallow Water Equations (SWE) under the conditions of inviscid, irrotational, and incompressible flow, potential flow theory is applied to establish mathematical models for two different configurations of porous media within a rectangular water tank. In the first configuration (type1), the porous media is installed near the free liquid surface, while in the second configuration (type2), the porous media is placed at the bottom of the container. The flow field is divided into simple subdomains, and the velocity potential components for each subdomain are solved using the method of separation of variables. The coupling of the flow field is handled by applying the continuity conditions for velocity and pressure at the interfaces between subdomains, along with the free surface motion equation. The study further derives and solves for the undetermined coefficients, investigating the effects of porous media parameters on sloshing mode frequencies, free surface profiles, and base shear forces. Using the resulting dynamic characteristics of the flow field, an equivalent mechanical model for the PMTLD system is constructed. Following the optimization design concept proposed by J. P. Den Hartog, the design focuses on parameters such as modal frequency, modal mass, and modal damping ratio to enhance the robustness of the PMTLD system. The study finds that, with other parameters fixed, the type1 model offers more stable modal damping ratios and better controllability compared to type2. Analysis of the frequency response curves for structures with the two types of PMTLD systems shows that the type1 model performs better in suppressing structural vibrations. Additionally, the state-space procedure (SSP) is used to iteratively solve the coupled behavior between sloshing in the type1 model and a single-degree-of-freedom (SDOF) main structure, verifying the effectiveness of the parameter design. Moreover, simulations of the 921 Chi-Chi earthquake demonstrate the reliability of the type1 model in controlling structural vibrations under real earthquake conditions.