Five Algorithms for Dynamic Analysis: Implementation Methods and MATLAB Code

This article introduces five distinct algorithms for dynamic analysis that enable the computation of required results in structural dynamics. The algorithms covered include the Modal Superposition Method (which decomposes system response using natural modes), Newmark Integration Algorithm (an implicit time integration scheme for dynamic equations), and Central Difference Algorithm (an explicit method for time-domain analysis), among others. For detailed implementation insights, refer to the accompanying MATLAB m-file codes that demonstrate practical application scenarios. The m-files contain key function implementations such as eigenvalue decomposition for modal analysis, iterative solution procedures for Newmark-beta method, and explicit time-stepping formulations for central differences. These algorithms may yield varying results across different application scenarios, requiring careful selection based on specific problem characteristics like stability requirements, computational efficiency, and accuracy needs.