Modal Decomposition Method for Structural Analysis

The implementation of modal decomposition method for structural analysis in MATLAB can effectively handle multi-degree-of-freedom problems. This approach solves complex vibration problems by decomposing the system's vibration modes into several fundamental modes. These fundamental modes, known as natural vibration modes, represent intrinsic properties of the structural system. The motion equations for these natural modes can be solved using a special mathematical formulation called the eigenvalue problem, typically implemented through MATLAB's built-in eig() function or specialized matrix decomposition algorithms. Once we obtain these natural vibration modes and their corresponding natural frequencies, we can reconstruct the system's complete vibration behavior through linear combination. This method includes automatic visualization functionality that generates vibration mode plots using MATLAB's plotting commands, providing intuitive graphical representation of structural vibration patterns for enhanced analytical clarity.