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Dynamic Responses of Two Beams Connected by a Spring-Mass Device

Published online by Cambridge University Press:  16 October 2012

H.- P. Lin  and
D. Yang
H.- P. Lin*
Affiliation:
Department of Mechanical and Automation Engineering, Da-Yeh University, Changhua, Taiwan 51591, R.O.C
D. Yang
Affiliation:
School of Automobile Engineering, Harbin Institute of Technology at Weihai, Shandong, China, P.R.O.C
*
*Corresponding author (linhp@mail.dyu.edu.tw)
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Abstract

This paper deals with the transverse free vibrations of a system in which two beams are coupled with a spring-mass device. The dynamics of this system are coupled through the motion of the mass. The entire system is modeled as two two-span beams and each span of the continuous beams is assumed to obey the Euler-Bernoulli beam theory. Considering the compatibility requirements across each spring con-nection position, the eigensolutions (natural frequencies and mode shapes) of this system can be obtained for different boundary conditions. Some numerical results and experimental validations are presented to demonstrate the method proposed in this article.

Keywords

Beam structuresSpring-mass systemEigensolutionsNatural frequenciesMode shapes
Type
Articles
Information
Journal of Mechanics , Volume 29 , Issue 1 , March 2013 , pp. 143 - 155
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2012

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References

REFERENCES

1. Gürgöze, M. “On the Eigenfrequencies of a Cantilever Beams with Attached Tip Mass and a Spring-Mass System,” Journal of Sound and Vibration, 190, pp. 149–162 (1996).Google Scholar
2. Rossi, R. E, Laura, P. A. and Larrondo, H., “Free Vibration of Timoshenko Beams Carrying Elastically Mounted, Concentrated Masses,” Journal of Sound and Vibration, 165, pp. 209–223 (1993).Google Scholar
3. Nicholson, J. W. and Bergman, L. A., “Free Vibration of Combined Dynamical System,” Journal of Engineering Mechanics, 112, pp. 1–13 (1986).CrossRefGoogle Scholar
4. Jen, M. U. and Magrab, E. B., “Natural Frequencies and Mode Shapes of Beams Carrying a Two-Degree-of-Freedom Spring-Mass System,” Journal of Vibration and Acoustics, 115, pp. 202–209 (1993).Google Scholar
5. Wu, J. S. and Chou, H. M., “Free Vibration Analysis of a Cantilever Beam Carrying Any Number of Elastically Mounted Point Masses with the Analytical-and Numerical-Combined Method,” Journal of Sound and Vibration, 213, pp. 317–332 (1998).Google Scholar
6. Gürgöze, M. “On the Alternative Formulations of the Frequency Equation of a Bernoulli-Euler Beam to Which Several Spring-Mass Systems are Attached In-Span,” Journal of Sound and Vibration, 217, pp. 585–595 (1998).Google Scholar
7. Wu, J. S. and Chou, H. M., “A New Approach for Determining the Natural Frequencies and Mode Shapes of a Uniform Beam Carrying Any Number of Sprung Masses,” Journal of Sound and Vibration, 220, pp. 451–468 (1999).CrossRefGoogle Scholar
8. Cha, P. D., “Natural Frequencies of a Linear Elastica Carrying Any Number of Sprung Masses,” Journal of Sound and Vibration, 247, pp. 185–194 (2001).Google Scholar
9. Bambill, D. V. and Rossit, C. A., “Forced Vibrations of a Beam Elastically Restrained Against Rotation and Carrying a Spring-Mass System,” Ocean Engineering, 29, pp. 605–626 (2002).CrossRefGoogle Scholar
10. Kukla, S., Przybylski, J. and Tomski, L., “Longitudinal Vibrations of Rods Coupled by Translational Springs,” Journal of Sound and Vibration, 185, pp. 712–722 (1995).CrossRefGoogle Scholar
11. Gürgöze, M., “Alternative Formulations of the Frequency Equation of Longitudinally Vibrating Rods Coupled by a Double Spring-Mass System,” Journal of Sound and Vibration, 208, pp. 331–338 (1997).Google Scholar
12. Mermertas, V. and Gürgöze, M., “Longitudinal Vibrations of Rods Coupled by a Double Spring-Mass System,” Journal of Sound and Vibration, 202, pp. 748–755 (1997).Google Scholar
13. Inceoğlu, S. and Gürgöze, M., “Longitudinal Vibrations of Rods Coupled by Several Spring-Mass Systems,” Journal of Sound and Vibration, 234, pp. 895–905 (2000).Google Scholar
14. Gürgöze, M., Erdogan, D. and Inceoğlu, S., “Bending Vibration of Beams Coupled by a Double Spring-Mass System,” Journal of Sound and Vibration, 243, pp. 361–369 (2001).Google Scholar
15. Inceoğlu, S. and Gürgöze, M., “Bending Vibrations of Beams Coupled by Several Double Spring-Mass Systems,” Journal of Sound and Vibration, 243, pp. 370–379 (2001).Google Scholar
16. Lin, H. P. and Chang, S. C., “Free Vibration Analysis of Multi-Span Beams with Intermediate Flexible Constraint,” Journal of Sound and Vibration, 281, pp. 155–169 (2005).Google Scholar
17. Lin, H. P., “Dynamic Responses of Beams with a Flexible Support Under a Constant Speed Moving Load,” Journal of Mechanics, 24, pp. 195–204 (2008).Google Scholar