Abstract
This chapter recalls the main aspects of structural dynamics which will be used in the subsequent chapters, with a particular emphasis on control. The chapter begins with the eigenvalue problem of a discrete system (mode shapes and natural frequencies), discusses the modal decomposition, including in the presence of rigid body modes, and introduces the dynamic flexibility matrix. Systems with collocated actuators and sensors are treated with special attention for their remarkable property of alternating poles and zeros; the relation between the transmission zeros (anti-resonances) and the natural frequencies of the constrained system is highlighted. The vibration of the Euler–Bernoulli beam is briefly discussed as an example of distributed system. Next, the chapter discusses the reduction methods: Guyan and Craig–Bampton. The chapter concludes with a short list of references and a set of problems.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
\(Q_i=1/2\xi _i\) is often called the quality factor of mode i .
References
Bathe KJ, Wilson EL (1976) Numerical methods in finite element analysis. Prentice-Hall, Englewood Cliffs
Cannon RH (1967) Dynamics of physical systems. McGraw-Hill, New York
Clough RW, Penzien J (1975) Dynamics of structures. McGraw-Hill, New York
Craig RR (1981) Structural dynamics. Wiley, New York
Craig RR, Bampton MCC (1968) Coupling of substructures for dynamic analyses. AIAA J 6(7):1313–1319
Gawronski WK (2004) Advanced structural dynamics and active control of structures. Springer, Berlin
Geradin M, Rixen D (1993) Mechanical vibrations. Theory and application to structural dynamics, Wiley, New York
Hughes PC (1972) Attitude dynamics of three-axis stabilized satellite with a large flexible solar array. J Astronaut Sci 20:166–189
Hughes PC (1974) Dynamics of flexible space vehicles with active attitude control. Celest Mech J 9:21–39
Hughes TJR (1987) The finite element method. Linear static and dynamic finite element analysis, Prentice-Hall, Englewood Cliffs
Inman DJ (1989) Vibration, with control, measurement, and stability. Prentice-Hall, Englewood Cliffs
Meirovitch L (1980) Computational methods in structural dynamics. Sijthoff & Noordhoff, The Netherlands
Modi VJ (1974) Attitude dynamics of satellites with flexible appendages - a brief review. AIAA J Spacec Rocket 11:743–751
Preumont A (2013) Twelve lectures on structural dynamics. Springer, Berlin
Zienkiewicz OC, Taylor RL (1989) The finite element method, vol 2, 4th edn. McGraw-Hill, New York
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this chapter
Cite this chapter
Preumont, A. (2018). Some Concepts in Structural Dynamics. In: Vibration Control of Active Structures. Solid Mechanics and Its Applications, vol 246. Springer, Cham. https://doi.org/10.1007/978-3-319-72296-2_2
Download citation
DOI: https://doi.org/10.1007/978-3-319-72296-2_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-72295-5
Online ISBN: 978-3-319-72296-2
eBook Packages: EngineeringEngineering (R0)