Exploiting the internal resonance in shunted circuit-based vibration suppression

A Master of Science thesis in Mechanical Engineering by Khaled Al-Souqi entitled, “Exploiting the internal resonance in shunted circuit-based vibration suppression”, submitted in September 2024. Thesis advisor is Dr. Samir Emam. Soft copy is available (Thesis, Completion Certificate, Approval Signatures, and AUS Archives Consent Form).

Abstract

Vibration reduction is an essential component of structural engineering that guarantees the functionality and endurance of numerous mechanical and architectural systems during design and maintenance. The field has been significantly improved in recent years with the introduction of piezoelectric materials, which provide novel solutions for regulating and mitigating vibrations. This thesis presents an approach to enhance vibration attenuation in cantilever structures by integrating piezoelectric patches and a shunt circuit, thereby advancing the field of vibration control in cantilever structures. The thesis begins with an introduction that provides a thorough overview of the classifications of vibration control and the importance attributed to vibration attenuation techniques. A comprehensive literature review aims to analyze previous studies and their methodologies in piezoelectric material vibration control is provided. A mathematical model that governs the dynamics of a cantilever beam combined with a piezoelectric transducer and a shunted circuit is developed. The model's initial emphasis is on the single-mode vibration occurring within a linear structure. The major innovation of this study is the systemic integration of a nonlinear electrical component that is introduced to activate the two-to-one internal resonance. The internal resonance is a nonlinear phenomenon that has demonstrated the potential to enhance the suppression of vibrations significantly. In order to attain optimal attenuation efficiency, the mathematical model is numerically simulated using MATLAB. This process includes modifying the shunt circuit's electrical parameters and tuning the absorber's frequencies with the structure’s natural frequency. Moreover, the model is extended to account for the nonlinearity of the host structure to examine the robustness of the proposed model. The main outcome of this study is a development in the domain of vibration control, providing a solution for engineering applications that require vibration attenuation that is both more effective and adaptable.