MATLAB Implementation of Transfer Matrix Method for Rotor Dynamics

The transfer matrix method serves as a powerful analytical approach for programming rotor dynamic analysis, specifically implementing the methodology described on page 30 of Zhong Yie's "Rotor Dynamics". This method leverages fundamental linear algebra principles and matrix operations to compute oscillation and vibration characteristics of mechanical systems. In rotor dynamics applications, the transfer matrix method enables comprehensive analysis of vibration modes, natural frequencies, and identification of potential instabilities or critical speeds during operation. The implementation involves constructing a transfer matrix that mathematically relates input forces and displacements to output forces and displacements at each rotor segment. For the specific analysis referenced from page 30 of Zhong Yie's "Rotor Dynamics", the MATLAB implementation typically follows these computational steps: First, define the rotor system's physical parameters and boundary conditions using structured arrays. Second, assemble elemental transfer matrices for each rotor section using state-space formulations. The core algorithm involves recursive matrix multiplication across rotor segments, with key functions handling eigenvalue extraction for natural frequency calculation and stability assessment. The code implementation would include functions for: - System parameter initialization (mass, stiffness, damping matrices) - Transfer matrix assembly using state vector propagation - Eigenvalue solver implementation for frequency extraction - Critical speed identification through determinant root-finding This methodological approach provides a versatile framework for rotor dynamics analysis, demonstrating practical application of matrix operations and numerical methods in mechanical system modeling. The page 30 example from Zhong Yie's text illustrates fundamental implementation techniques that can be extended to more complex rotor configurations through modular code design.