Abstract
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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Gladwell GML (2004) Inverse Problems in Vibration. 2nd edn. Springer, Dordrecht (1986, 1st edn, Martinus Nijhoff Publishers, Dordrecht)
Gladwell GML (1991) Qualitative properties of finite element models I: Sturm-Liouville systems. Q J Mech Appl Math 44(2):249–265
Golub GH, Boley D (1977) Inverse Eigenvalue Problems for Band Matrices. In: Watson GA (ed) Numerical analysis. Springer, Heidelberg, New York, pp 23–31
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)
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)
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)
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)
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)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2019 Springer Nature Singapore Pte Ltd. and Peking University Press
About this chapter
Cite this chapter
Wang, D., Wang, Q., He, B. (2019). Qualitative Properties of Vibration and Static Deformation Associated with Discrete Systems of Strings and Bars. In: Qualitative Theory in Structural Mechanics. Springer, Singapore. https://doi.org/10.1007/978-981-13-1376-9_3
Download citation
DOI: https://doi.org/10.1007/978-981-13-1376-9_3
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-13-1375-2
Online ISBN: 978-981-13-1376-9
eBook Packages: EngineeringEngineering (R0)