Electronic Thesis and Dissertation Repository

Thesis Format

Monograph

Degree

Master of Engineering Science

Program

Mechanical and Materials Engineering

Supervisor

Asokanthan, Samuel F.

2nd Supervisor

Tutunea-Fatan, O. R.

Joint Supervisor

Abstract

The present research is concerned with structural optimization of cylindrical and hemispherical resonators (CRs & HRs) employing computational tools. Additionally, it focuses on obtaining a reduced-order model (ROM) for HR, that accurately represents its dynamic behavior. The optimization process primarily focuses on achieving a prescribed frequency spacing around the Dominant flexural frequency (DFF) of a resonator and minimizing the computational frequency split present at DFF. Techniques such as widening the boundary value range of the input parameters via Single as well as Multi-Objective approaches have been exploited to achieve the research objectives. The results demonstrate that the frequency separation around the DFF can be increased, and the frequency split at the DFF can be reduced using the structural optimization methods available within the computational tool. Further, a ROM of HR derived computationally from the full-order model (FOM) is demonstrated to adequately capture the HR dynamics.

Summary for Lay Audience

Cylindrical Resonators (CRs) and Hemispherical Resonators (HRs), respectively, are made of cylindrical and hemispherical shell structures that have the ability to resonate efficiently at their own characteristic frequencies. These devices form the basis of vibratory gyroscopes which are used in applications such as navigation of mobile platforms and provision of autopilot and control of aircraft, ships, and land vehicles. In the present research, the structure of the CRs and HRs are improved using computational tools. A full-order model (FOM) of a structure closely represents its physical characteristics, and the corresponding dynamic behavior while the reduced-order model (ROM) is a simplified version of FOM that adequately depicts the dynamic behavior of the full-order structure. This study aims to establish a detailed and systematic procedure for obtaining a ROM from a FOM with appropriate validation. The CRs and HRs can resonate at any of their natural frequencies, however, the resonant behavior at one of the frequencies, known as Dominant Flexural Frequency (DFF) is considered as the most important natural frequency for vibratory gyroscope applications. For precise operation of a gyroscope, the resonator is subjected to a sinusoidal excitation at DFF and it is important for the energy to not transfer to other neighboring modes other than the DFF. Hence, it is crucial to have a moderate frequency separation around the DFF and this study focuses on achieving pre-determined frequency separations. When the computational analysis is performed on the CR and HR structures, the two modes of DFF have slightly different frequency values. Ideally, these values should be equal and this research focuses on designing structures to minimize this discrepancy in frequency. Several computational techniques have been experimented for achieving the research objectives. The ROM for the HR is developed in a computational environment using fundamentals of dynamics and suitable mathematical operations. The ROM is developed by extracting the dominant characteristics of the model, while giving less importance to less significant model characteristics. The research outcomes demonstrated that it is feasible to successfully increase the frequency separation around DFF and minimize the frequency split of a structure using computational tools and techniques. Additionally, the research results indicate that the ROM designed for the HR can accurately represent the FOM of HRs.

Download

Available for download on Wednesday, December 31, 2025

Share

COinS