Qualitative Properties of Vibration and Static Deformation Associated with Discrete Systems of Strings and Bars

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


In this chapter, we will study qualitative properties of natural frequencies and mode shapes of discrete models of second-order continuous systems, such as strings in lateral vibration, bars in longitudinal vibration, and shafts in torsional vibration. We will also discuss qualitative properties of static deformation associated with some of these discrete systems.


  1. 1.
    Gladwell GML (2004) Inverse Problems in Vibration. 2nd edn. Springer, Dordrecht (1986, 1st edn, Martinus Nijhoff Publishers, Dordrecht)Google Scholar
  2. 2.
    Gladwell GML (1991) Qualitative properties of finite element models I: Sturm-Liouville systems. Q J Mech Appl Math 44(2):249–265CrossRefGoogle Scholar
  3. 3.
    Golub GH, Boley D (1977) Inverse Eigenvalue Problems for Band Matrices. In: Watson GA (ed) Numerical analysis. Springer, Heidelberg, New York, pp 23–31Google Scholar
  4. 4.
    Tian X, Dai H (2007) Inverse vibration problem for the discrete system of a rod. J Shandong Inst Light Ind (Nat Sci Ed) 21(1):4–7 (in Chinese)Google Scholar
  5. 5.
    Wang QS, Wang DJ (1987) Construction of the discrete system for the rod by partial natural modes and frequencies data. J Vib Eng 1:83–87 (in Chinese)Google Scholar
  6. 6.
    Wang QS, Wang DJ, He BC (1992) Qualitative properties of frequencies and modes of discrete system of continuous second-order systems. J Vib Shock 11(3):7–12 (in Chinese)Google Scholar
  7. 7.
    Wang QS, Wang DJ (1997) Qualitative properties of frequencies and modes and inverse modes problems of discrete systems for a rod on the elastic bases. J. AQTC (Nat Sci Ed) 3(2):19–25 (in Chinese)Google Scholar
  8. 8.
    Wang QS, Wang DJ (2014) Supplementary proof of some oscillation property for discrete systems of rod and beam having rigid modes. Chin Q Mech 35(2):262–269 (in Chinese)Google Scholar

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

Personalised recommendations