Modal Analyses by Eigenvector and Ritz Vector Methods

This paper delves into the practical implications of two modal dynamic analysis methods: eigenvector modal analysis and Ritz vector modal analysis.Eigenvector modal analysis, a staple in engineering practice, provides crucial insights into the dynamic behaviours of structures during free vibrations and forms the basis for modal superposition dynamic response analysis.Ritz vector modal analysis, primarily used for modal superposition dynamic response analysis, is examined for its unique characteristics and advantages.We emphasize the practical relevance of mode shapes and participation factors and demonstrate the load dependent nature of participation factors.The intricacies of Ritz analysis are explored, particularly highlighting its load dependent nature and the non-orthogonality of mode shapes for the applied loads.The essential steps and formulas for conducting Ritz analysis are presented, and practical recommendations for its uses in modal superposition dynamic response analysis are offered.We conclude by assessing the efficacy of Ritz vector modal analysis in modal superposition dynamic response analysis, underscoring its efficiency and potential benefits for engineering applications.