Abstract
The focus of this chapter is qualitative properties of vibrational modes, static deformation, vibration control, etc. of repetitive structures. Types of repetitive structures covered here include structures with mirror symmetry (abbreviated as symmetric structures in subsequent discussion), rotationally periodic structures (also referred to as cyclic periodic or cyclic symmetric structures in the literature), linearly periodic structures (called linear periodic structures by some authors), chain structures (also known as linking or linked structures), and axisymmetric structures.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bao G (1982) Application of group theory in vibration analysis of shell structures with space rotating symmetry. J Shandong Inst Ind 12(1):14–26 (in Chinese)
Cai C, Wu F (1983) On the vibration of rotational periodic structures. Acta Scientiarum Naturalium Univ Sunyatseni 22(3):1–9
Cai C, Chung Y, Chan H (1990) Uncoupling of dynamic equations for periodic structures. J Sound Vibr 139(2):253–263
Cai CW, Liu JK, Chan HC (2002) Exact analysis of bi-periodic structures. World Scientific Publication, Singapore
Chan H, Cai C, Chung Y (1998) Exact analysis of structures with periodicity using U-transformation. World Scientific Publication, Singapore
Chen P (2002) A note on computation of rotationally periodic structures. Chin J Comp Mech 19(1):112–113 (in Chinese)
Chen WM, Wang DJ, Zhou CY et al (2001) The vibration control of repetitive structures. In: Proceedings of the Asia-Pacific vibration conference, vol III. Jilin Science & Technology Press, Changchun, pp 929–932
Chen WM, Sun DC, Wang DJ et al (2006) Reduction approaches for vibration control of repetitive structures. Appl Math Mech 27(5):575–582
Evensen DA (1976) Vibration analysis of multi-symmetric structures. AIAA J 14(4):446–453
Hu HY, Cheng DL (1988) Investigation on modal characteristics of cyclosymmetric structures. Chin J Appl Mech 5(3):1–8 (in Chinese)
Jin DK, Sun DC, Chen WM et al (2005) Static shape control of repetitive structures integrated with piezoelectric actuators. Smart Mater Struct 3:1410–1420
Thomas DL (1979) Dynamics of rotational periodic structure. Int J Num Methods Eng 1979(14):81–102
Timoshenko S (1955) Vibration problem in engineering, 3rd edn
Wang DJ, Wang CC (2000) Natural vibrations of repetitive structures. Chin J Mech 16(2):85–95
Wang DJ, Zhou CY, Rong J (2003) Free and forced vibration of repetitive structures. Int J Solids Struct 40:5477–5494
Wang DJ, Chen J, Wang HJ (2003) The feature of the dual tones of Chinese music bells. Mech Eng 25(4):12–16 (in Chinese)
Wang WL, Zhu NS, Xu JH (1990) Double compatible mode synthesis of symmetric structures with Cn group. J Aerospace Power 5(4):352–356 (in Chinese)
Zhang J, Wang WL, Chen XJ (1984) Natural mode analysis of N blades disc coupled system—modal synthesis of symmetry structure with CNV group. Acta Mech Solida Sin 5(4):469–481 (in Chinese)
Zhong W (1991) The eigen-value problem of the chain of identical substructures and the expansion method solution lasted on the eigen-vectors. Acta Mech Sin 23(1):72–81
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 of Repetitive Structures. In: Qualitative Theory in Structural Mechanics. Springer, Singapore. https://doi.org/10.1007/978-981-13-1376-9_7
Download citation
DOI: https://doi.org/10.1007/978-981-13-1376-9_7
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-13-1375-2
Online ISBN: 978-981-13-1376-9
eBook Packages: EngineeringEngineering (R0)