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Abstract

Versatile examples are essential in any engineering vibration course. However, most examples in current textbooks, especially those of multi-degree-of-freedom systems, are based on mass–spring systems. The system of spring-supported beams is explored in this report with the purpose of developing examples. Firstly, a method using the stiffness influence coefficient is illustrated in order to establish a vibration equation for a beam with three discrete masses. This is followed by a method using the flexibility influence coefficient. Then we analyze a general case, with an arbitrary number of springs and masses, using the energy method. Finally, a reduced case with repeated natural frequencies is explored.

Keywords

beam vibration equation repeated natural frequency flexibility influence coefficient stiffness influence coefficient

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References

Silva

C. W. D.

, Vibration: Fundamentals and Practice (University of British Columbia, Vancouver, 2006).

Thomson

W. T.

Dahleh

M. D.

, Theory of Vibration with Applications (Prentice-Hall, Englewood, NJ, 1997).

Tongue

B. H.

, Principles of Vibration (Oxford University Press, Oxford, 2002).

Rao

S. S.

, Mechanical Vibrations, 4th edn (Prentice-Hall, Englewood, NJ, 2003).

Blake

, Handbook of Mechanics, Materials, and Structures (Wiley, New York, 1985), pp. 258–260.

Antia

H. M.

, Numerical Methods for Scientists and Engineers (Birkhäuser, Basel, 2002), pp. 131–137.

Donaldson

B. K.

, Introduction to Structural Dynamics, Cambridge Aerospace Series (Cambridge University Press, Cambridge, 2006), pp. 279–289.

Chen

K. F.

Jiao

Q. Y.

, ‘Distinction of natural frequencies of chain structure vibration systems’, Journal of the Beijing Agricultural Engineering University, 15(2) (1995), 24–28.

Chen

K. F.

Jiao

Q. Y.

, ‘On the repeated natural frequencies for torsional vibration of shafts’, Applied Mathematics and Mechanics, 20(11) (1999), 1279–1285.

10.

Chen

K. F.

Wang

Y. G.

Zhou

, ‘Few-degree-of-freedom systems with repeated natural frequencies’, Int. J. Mech. Enging. Educ., 37(1) (2009), 67–77.

11.

Chen

K. F.

Jiao

, ‘A parsimonious mass–spring system capable of being tuned for arbitrary repeated natural frequencies’, Mechanics Research Communications, 36(1) (2009), 149–153.