Multiple Tuned Mass Damper Design for the Mitigation of Cantilever Beam Response

This study introduces an advanced framework for the design and optimization of multiple tuned mass dampers (MTMDs) to mitigate dynamic responses in cantilever beams subjected to both deterministic and stochastic excitations. Conventional methods, including single tuned mass dampers and uniformly distributed MTMD systems, often lack the capacity to effectively manage complex multimodal vibrations and unpredictable dynamic loads encountered in real-world scenarios. To address these limitations, this research employs the differential evolution algorithm to optimize the spatial distribution of mass, stiffness, and damping parameters. This optimization enhances the system’s ability to control translational and rotational responses across multiple vibrational modes with high precision. A primary innovation of this study is the incorporation of stochastic modeling based on the Laplace distribution, providing a more realistic representation of environmental disturbances compared to traditional Gaussian models. Additionally, the integration of the critical excitation method ensures the system’s robustness under extreme dynamic conditions, such as those caused by resonance or high-magnitude loads. The results indicate that the optimized MTMD system achieves significant reductions in displacement, acceleration, and rotational motion across a range of dynamic scenarios, including harmonic vibrations, seismic events, and wind-induced disturbances. The MTMD configuration is particularly effective in controlling higher-order modes and managing broad-spectrum excitations, areas where traditional systems typically underperform. The proposed MTMD framework provides a scientifically robust, adaptable, and scalable solution for structural vibration control. Its capability to address diverse dynamic conditions makes it particularly suitable for applications in high-rise buildings, bridges, and offshore platforms. By combining advanced optimization techniques with innovative modeling approaches, this research establishes a new benchmark for efficient and practical structural vibration mitigation.