Rotor Dynamics Major Assignment: Critical Speed Calculation for Dual-Rotor System

This is my major assignment in rotor dynamics. The primary objective was to develop a MATLAB program to calculate critical speeds for dual-rotor systems. To achieve this, I implemented the transfer matrix method, a powerful mathematical approach for analyzing dynamic systems. The transfer matrix technique is particularly useful for describing transitional system behavior and finds applications in control systems, signal processing, and mechanical vibrations. In the code implementation, I structured the solution using state vectors and transfer matrices to represent the rotor's dynamic characteristics at different stations. The algorithm involved assembling system matrices by multiplying individual element transfer matrices (accounting for mass, stiffness, and damping properties), followed by solving the eigenvalue problem to determine critical speeds where resonance occurs. Key MATLAB functions employed included matrix multiplication operations, eigenvalue solvers (eig function), and custom-developed functions for constructing rotor segment transfer matrices. The implementation handled boundary conditions by applying appropriate constraints at bearing locations and rotor ends. During the coding process, I encountered challenges in handling complex eigenvalue solutions and ensuring numerical stability for large matrix operations. Through systematic debugging and validation with theoretical cases, I successfully completed the program. This assignment significantly enhanced my understanding of rotor dynamics principles and practical implementation of transfer matrix methods for engineering applications.