Energy based multi-objective optimization for threedimensional buildings incorporating tuned mass dampers

Abstract

Designing a structure is a very critical part of the construction. Engineers must consider both static and dynamic loads such as wind, impact loads, and, most importantly, earthquakes, which represent the most critical and unpredictable type of dynamic loads, since they generate significant accelerations, displacements, and velocities that can threaten structural safety and serviceability. As technology progresses and structural systems become more polished, seismic design rules continue to evolve, reflecting new information and performance expectations. Excessive vibrations generated by earthquakes can lead to discomfort for people there, damage to structural and nonstructural materials, and even loss of operation. Therefore, understanding and managing the dynamic reaction of a building has become a major concern in earthquake engineering. The challenge becomes more pronounced for flexible and tall buildings, which tend to be subjected to significant lateral displacements and experience high floor accelerations under seismic stresses. Traditional strengthening methods, such as adding shear walls, bracing, or increasing member dimensions, improve stiffness, but they fail to address acceleration-related concerns. In a few instances, greater stiffness might even push the natural frequencies of the structure closer to prominent earthquake frequencies, leading to magnified vibrations. Past earthquake events have shown that medium and large ground motions can cause significant damage by causing excessive inter-story drift and accelerations, emphasizing the need for more efficient vibration mitigation techniques beyond standard design approaches. Vibration control technologies have become key elements of modern seismic design, seeking to reduce structural demand without relying basically on stiffness or strength gains. Structural control can be achieved through many methods, including passive, active, semi-active, and hybrid systems, each with different operating principles. Passive control systems are particularly popular because of their durability, simplicity, and independence from external power sources. They act by absorbing, decreasing, or dispersing the kinetic energy into the structure. In this context, the purpose of vibration control is to minimize structural deformation to promote comfort for occupants and protect nonstructural components. As buildings get more complex and adaptable, attaining these goals together becomes challenging, making vibration control devices essential elements of performance-based earthquake xxix engineering. Among passive systems, the Tuned Mass Damper (TMD) has emerged as one of the most effective and generally accepted options. TMD consists of an auxiliary mass coupled to the main structure by a spring and damper. When adjusted to the dominant frequency of the building, the TMD vibrates out of phase with the structure, absorbing and distributing a portion of seismic energy. The efficiency of a TMD depends significantly on three parameters: mass ratio, frequency ratio, and damping ratio. To develop an effective TMD, one needs to pick these characteristics properly. Traditional tuning formulas provide approximate solutions but often fall short under realistic seismic excitations, particularly when dealing with multi-directional ground motion or complex 3D structures. As a result, optimization techniques have become essential tools for achieving high-performance TMD designs. Modern optimization algorithms, such as Particle Swarm Optimization (PSO), Differential Evaluation (DE), Genetic Algorithms (GA), and Harmony Search (HS), enable engineers to explore a wide design range and evaluate multiple performance objectives. Instead of relying solely on displacement or acceleration reduction, recent research emphasizes energy-based performance measures, such as minimizing total structure energy, which provide an indication of the energy transfer mechanism from the main structure to the TMD. This thesis presents an energy-based optimization study of a TMD system implemented in a three-dimensional (3D) shear building model subjected to bi-directional ground motion. While conventional TMD design approaches mainly target displacement or acceleration reduction, recent research has shown the importance of understanding how energy flows through a structure during an earthquake. Energy-based design provides a deeper interpretation of structural behavior and can potentially lead to more efficient vibration control strategies. However, only a limited number of studies have focused on the total structure energy as an optimization objective, and most applications still rely on two-dimensional models with single-direction excitation. This creates a gap in the literature regarding energy-based, multi-objective TMD optimization of realistic 3D systems. This study aims to address this gap by developing a full 3D shear building model with a two-directional TMD equipped in the roof level. The building consists of five stories, idealized using lumped-mass, stiffness, and damping matrices; as a result, it is a 15 degree-of-freedom (DOF) structure model. The TMD, by neglecting the torsional behavior, contributes two additional DOF in the x and y direction. Leading to a combined system of 17 DOF. The structure is analyzed under bi-directional earthquake records, specifically El Centro (1940) and Tarzana (1994). The dynamic response is obtained using the Newmark-Beta method, and the energy components are traced throughout the analysis. Optimization is performed in MATLAB formulated by simultaneously minimizing top floor displacement in both directions x and y, and total structural energy. Advanced metaheuristic algorithms, especially the Non‑Dominated Sorting Genetic Algorithm III (NSGA‑III) and the Multi‑Objective Grey Wolf Optimizer (MOGWO), are applied to effectively explore the design space and identify Pareto‑optimal solutions. The ultimate optimal TMD configuration is selected from the Pareto front based on a normalized ideal‑point approach, ensuring a fair trade‑off xxx between competing performance objectives., and results demonstrate that the TMD significantly enhances seismic performance. The reduction in top-floor displacement reaches approximately 47% in the x direction and 38% in the y direction under the El Centro record, while under the Tarzana record, it is reduced by 23% in the x direction and 28% in the y direction. While the total structure energy has been decreased to around 63% under El Centro and 45% under the Tarzana record.