# Novelty in Intelligent Controlled Oscillations in Smart Structures
###### Abstract
The methods and control techniques used were described in detail in [32]. This work has important applications because the problem of reducing oscillations is a common problem for both civil and mechanical engineers [32]. These applications can be used in airplanes, metal bridges, and large metal structures. Structures are stressed by dynamic loads such as wind and earthquake loading [32]. This paper outlines and explains the various methods and control techniques used to address this issue. This research is highly relevant because it addresses the shared challenge of oscillation. The applications of the outlined methods are broad, potentially benefiting areas such as airplane design, metal bridges, and large metal structures, all of which are subjected to dynamic stresses from wind and seismic activity. The development of effective strategies to control these vibrations is essential for the stability and durability of these structures. When materials are subjected to an electric field, they can experience distortion, a phenomenon that holds significance for engineers working on the development and application of advanced smart materials. By employing appropriate control techniques, these smart materials can play a vital role in minimizing oscillations, which is a crucial concern in various engineering fields. This issue is especially relevant for both civil and mechanical engineers, who frequently grapple with the challenge of reducing vibrations caused by dynamic forces such as earthquakes and wind. These structures are often exposed to dynamic loading conditions, including those imposed by wind and seismic activity, which can induce vibrations that compromise their stability and integrity. Therefore, it is essential to develop and implement effective control techniques for reducing vibration. The findings of this study could lead to advancements in the design and maintenance of structures that are more resilient to dynamic stresses, ultimately enhancing their safety, performance, and longevity. This study plays a crucial role in advancing the reduction in oscillations, which is an area of significant concern in engineering. This research begins with a comprehensive modeling process utilizing the finite element method as the foundational approach. The equations used for this modeling are meticulously detailed, specifically in Equations (1)-(10), providing a thorough understanding of the application of the finite element method in this context. Subsequently, this study introduces equations pertinent to control theory, which is an essential aspect of managing and reducing oscillations. A key focus is placed on the derivation of the transfer function, which is fundamental in control theory to understand how systems respond to various inputs. This derivation is presented in detail to ensure clarity in the development and application of the transfer function. The analysis within the study was multifaceted, employing both state-space domain and frequency domain analyses. The state-space domain analysis is elaborated upon through Equations (10) to (14), offering insights into the system's behavior in the time domain representation. Additionally, frequency domain analysis is thoroughly explored in Equations (15)-(33), providing an in-depth examination of how the system responds to different frequencies. By combining these analytical approaches, this study offers a comprehensive strategy to address and mitigate oscillations in various engineering applications.