Topological Three-Dimensional Metamaterial Based on Parametric Curves for Aerospace Vibration Control

The control of mechanical vibrations in mechanical and biomechanical systems represents an advanced research area that explores the integration of smart metamaterials and adaptive structural architectures to optimize the dynamic response of complex systems. Among the most promising approaches is the use of piezoelectric materials coupled with electrical shunt circuits, enabling active and semi-passive vibration control through electromechanical coupling. Piezoelectric metamaterials can convert mechanical strain into electrical energy and vice versa, allowing structural vibrations to be attenuated through energy dissipation mechanisms implemented in external electrical circuits. These systems are widely investigated for their potential to reduce resonance amplitudes, increase structural damping, and enhance the stability of engineered systems subjected to dynamic loads. In the context of aerospace engineering, vibration control is particularly critical due to the presence of multiple excitation sources, including aerodynamic turbulence, propulsion systems, structural coupling, and launch-induced loads. Conventional vibration mitigation strategies often rely on passive dampers or structural reinforcement; however, these methods may increase structural weight or offer limited adaptability to varying operational conditions. Recent advances in mechanical metamaterials have opened new possibilities for vibration control through the design of geometrically structured materials capable of manipulating the propagation of mechanical waves. In particular, topological metamaterials provide unique advantages due to their ability to support vibration modes that are robust against structural imperfections and local defects. These properties emerge from the topological characteristics of the system rather than solely from the intrinsic properties of the materials used. The proposed concept introduces a three-dimensional topological metamaterial architecture based on interlaced parametric curves, forming a spatial lattice capable of controlling the propagation of mechanical vibrations. Parametric curves provide a powerful mathematical framework for defining complex geometrical structures with high precision and flexibility. By varying parameters that define curvature, periodicity, and spatial orientation, it becomes possible to design structural networks that influence stiffness distribution, wave propagation, and energy dissipation within the material. Such parametric geometries can generate phononic band gaps, frequency intervals in which vibrational energy cannot propagate through the structure. This property allows the metamaterial to act as a mechanical filter, selectively attenuating vibration modes associated with undesirable resonances in aerospace structures. The analysis and optimization of these structures can be performed using advanced computational methods, particularly the Finite Element Method (FEM), which enables detailed simulation of coupled electromechanical and structural phenomena. Finite element models allow the investigation of modal characteristics, wave propagation behavior, stress distribution, and the interaction between piezoelectric components and their associated electrical shunt circuits. By integrating parametric geometric design, piezoelectric metamaterials, and numerical modeling techniques, the proposed framework provides a versatile platform for the development of lightweight, high-performance structures capable of adaptive vibration control. The architecture is particularly suitable for fabrication using additive manufacturing technologies, such as metallic 3D printing or advanced composite processing, enabling the production of intricate geometries that would be impractical with conventional manufacturing techniques. Potential aerospace applications include vibration suppression in aircraft wings, satellite structures, launch vehicle components, turbine systems, and precision instrumentation platforms. Additionally, the same conceptual framework may extend to biomechanical systems and smart structural materials used in robotics and biomedical engineering. This work presents the conceptual foundations of the proposed metamaterial architecture, emphasizing the role of parametric geometry, topological mechanics, and smart material integration in the design of next-generation vibration control systems.