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Oscillatory Matrices and Kernels as Well as Properties of Eigenpairs

  • Dajun WangEmail author
  • Qishen Wang
  • Beichang (Bert) He
Chapter

Abstract

The theory of oscillatory matrices and kernels forms the mathematical foundation for the study of qualitative properties of natural frequencies and mode shapes of bars and beams. This chapter provides an introduction to the theory. The content is drawn largely from the monograph, Oscillation Matrices and Kernels and Small Vibrations of Mechanical Systems, written by creators of the theory, Gantmacher and Krein; but Sect. 2.11 and most of Sect. 2.10 are the original work by authors of this book as well as their collaborators Zijun Zheng and Pu Chen.

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Copyright information

© Springer Nature Singapore Pte Ltd. and Peking University Press 2019

Authors and Affiliations

  1. 1.Department of Mechanics and Engineering SciencePeking UniversityBeijingChina
  2. 2.School of Physics and Electrical EngineeringAnqing Normal UniversityAnqingChina
  3. 3.HBC ConsultingSeattleUSA
  4. 4.State Key Laboratory for Turbulence and Complex SystemsPeking UniversityBeijingChina

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