MATLAB Implementation for Structural Dynamic Analysis

Structural dynamic analysis serves as a critical methodology in engineering for investigating structural response characteristics under dynamic loading conditions. MATLAB, with its robust numerical computation capabilities and comprehensive toolbox ecosystem, stands as an ideal platform for implementing such analyses.

The MATLAB implementation typically involves these key procedural steps: First, establishing the structural mechanical model through discretization via the finite element method. Subsequently, constructing the mass matrix, stiffness matrix, and damping matrix—these three matrices form the core components describing structural dynamic properties. For free vibration analysis, solving eigenvalue problems yields natural frequencies and mode shapes using MATLAB's eig() function. For forced vibration analysis, time-domain integration methods (e.g., Newmark-β algorithm implementation) or frequency-domain analysis techniques compute structural responses under dynamic loads through differential equation solvers like ode45.

MATLAB's advantage lies in its built-in functions and tools that streamline these computational processes. The eig() function handles eigenvalue problems efficiently, while the ode suite (ode45, ode15s) facilitates transient analysis with adaptive step-size control. Furthermore, MATLAB's graphical capabilities enable intuitive visualization of mode shape animations and time-history response curves through plot() and animation functions, significantly aiding result interpretation and validation.

For complex engineering scenarios, MATLAB's symbolic computation toolbox (Symbolic Math Toolbox) supports theoretical derivations, and the Parallel Computing Toolbox accelerates large-scale problem solving through multicore or cluster-based processing. By strategically leveraging these functionalities, engineers and researchers can efficiently execute complete analytical workflows from theoretical modeling to result visualization.