DESCRIPTIONS IN EXISTING TEXTBOOKS ON MODAL ANALYSIS AND POSSIBLE MEASURES FOR IMPROVEMENT

Abstract

 Modal analysis is one of the key concepts in earthquake engineering. According to the author’s latest analysis, the descriptions in existing textbooks on modal analysis are not necessarily complete and do not give comprehensive understanding of the concept. In this article, the descriptions in existing textbooks are analysed and possible measures for improvement are discussed, especially focusing on two points: 1) Is the solution 𝜆 of the characteristic equation is always real and positive? 2) Is modal analysis applicable when the characteristic equation results in repeated eigenvalues? In terms of the former point, the answer could be described as “the solution 𝜆 of the characteristic equation is always real and positive because the mass matrix and the stiffness matrix are symmetric and positive definite,” however, the author could find only two text books that involve this conclusion, namely, Kondoh (1993) and Chopra (2012). Detailed explanations were only included in Kondoh (1993). In terms of the latter point, the answer could be described as “modal analysis is applicable even when the characteristic equation results in repeated eigenvalues,” however, the author could find only one text book that addresses this issue, namely, Chopra (2012). In addition, Chopra’s (2012) description does not involve detailed equations. Based on these observations, the author proposed possible measures for improving the descriptions on modal analysis with the aim of providing more comprehensive explanations on the subject for students and engineers.