Natural frequencies of a beam-mass system in transverse vibration: Rayleigh estimation versus eigenanalysis solutions

International Journal of Mechanical Sciences

Volumn 45, Issue 6-7, 2003, Pages 981-993

  Low, K H ^a  

^a NANYANG TECHNOLOGICAL UNIVERSITY   (Singapore)

Author keywords

Beam mass system; Eigenanalysis; Euler Bernoulli beam; Frequency equation; Rayleigh's method; Transverse vibration

Indexed keywords

BOUNDARY CONDITIONS; EIGENVALUES AND EIGENFUNCTIONS; LOADING; NATURAL FREQUENCIES; VIBRATIONS (MECHANICAL);

BEAM-MASS SYSTEMS; TRANSVERSE VIBRATIONS;

BEAMS AND GIRDERS;

EID: 0242405931     PISSN: 00207403     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijmecsci.2003.09.009     Document Type: Article

References (36)

1. Chen Yu. On the vibration of beams or rods carrying a concentrated mass. Journal of Applied Mechanics. 30:1963;310-311.
2. Pan H.H. Transverse vibration of an Euler beam carrying a system of heavy bodies. Journal of Applied Mechanics. 32:1965;434-437.
3. Chintakindi L., Rao A. Method of calculation of frequencies of partially fixed beams carrying masses. Journal of the Acoustical Society of America. 40:1966;367-371.
4. Srinath L.S., Das Y.C. Vibrations of beams carrying mass. Journal of Applied Mechanics Series E. 34:1967;784-785.
5. Stanišić M.M., Hardin J.C. On the response of beams to an arbitrary number of concentrated moving masses. Journal of the Franklin Institute. 287:1969;115-123.
6. Goel R.P. Vibrations of a beam carrying a concentrated mass. Journal of Applied Mechanics. 40:1973;821-822.
7. Goel R.P. Free vibrations of a beam-mass system with elastically restrained ends. Journal of Sound and Vibration. 47:1976;9-14.
8. Lau J.H. Fundamental frequency of a constrained beam. Journal of Sound and Vibration. 78:1981;154-157.
9. Stephen N.G. Comment on "A note on the vibrations of restrained beams and rods with point masses" Journal of Sound and Vibration. 100(1):1985;149-150.
10. Gurgoze M. On the vibrations of restrained beams and rods with heavy masses. Journal of Sound and Vibration. 100(4):1985;588-589.
11. Laura P.A.A., Cortinez V.H. Optimization of eigenvalues in the case of vibrating beams with point masses. Journal of Sound and Vibration. 108(2):1986;346-348.
12. Gurgoze M., Batan H. A note on the vibrations of a restrained cantilever beam carrying a heavy tip body. Journal of Sound and Vibration. 106(3):1986;533-536.
13. Liu W.H., Wu W.J.-.R., Huang C.-.C. Free vibration of beams with elastically restrained edges and intermediate concentrated masses. Journal of Sound and Vibration. 122:1988;193-207.
14. De Rosa M.A., Franciosi C., Maurizi M.J. On the dynamic behaviour of slender beams with elastic ends carrying a concentrated mass. Computers and Structures. 58:1996;1145-1159.
15. Özkaya E., Pakdemirli M., Öz H.R. Non-linear vibrations of a beam-mass system under different boundary conditions. Journal of Sound and Vibration. 199:1997;679-696.
16. Low K.H. On the eigenfrequencies for mass loaded beams under classical boundary conditions. Journal of Sound and Vibration. 215:1998;381-389.
17. Low K.H. Comparisons of experimental and numerical frequencies for classical beams carrying a mass in span. International Journal of Mechanical Sciences. 41:1999;1515-1531.
18. Liu W.H., Yeh F.H. Free vibration of a restrained-uniform beam with intermediate masses. Journal of Sound and Vibration. 117(3):1987;555-570.
19. Liu W.H., Huang C.-.C. Vibrations of a concentrated beam carrying a heavy tip body. Journal of Sound and Vibration. 123(l):1988;15-29.
20. Maurizi M.J., Bellés P.M. Natural frequencies of the beam-mass system: comparison of the two fundamental theories of beam vibrations. Journal of Sound and Vibration. 150:1991;330-334.
21. Low K.H., Lim T.M., Chai G.B. Experimental and analytical investigations of vibration frequencies for centerloaded beams. Computers and Structures. 48:1993;1157-1162.
22. Low K.H. Closed-form formulas for fundamental vibration frequency of beams under off-centre load. Journal of Sound and Vibration. 201:1997;528-533.
23. Low K.H., Dubey R.N. A note on the fundamental shape function and frequency of beams under off-center load. Journal of Sound and Vibration. 202:1997;134-138.
24. Low K.H., Dubey R.N., Chai G.B. Experimental investigation and shape functions for lateral vibration of axially constrained beams with a concentrated mass at the centre. Journal of Sound and Vibration. 202:1997;446-451.
25. Özkaya E., Pakdemirli M. Non-linear vibrations of a beam-mass system with both ends clamped. Journal of Sound and Vibration. 221:1999;491-503.
26. Naguleswaran S. Lateral vibration of a uniform Euler-Bernoulli beam carrying a particle at an intermediate point. Journal of Sound and Vibration. 227(l):1999;205-214.
27. Dimaragonas A.D. Vibration for engineers. 1992;Prentice Hall, Englewood Cliffs, NJ.
28. Rao S.S. Mechanical vibrations. 3rd ed. 1995;Addison-Wesley, Reading, MA.
29. Heal K.M., Hansen M.L., Rickard K.M. Maple V: learning guide. 1996;Springer, New York.
30. Low K.H. A modified Dunkerley formula for eigenfrequencies of beams carrying concentrated masses. International Journal of Mechanical Sciences. 42:2000;1287-1305.
31. Low K.H. On the methods to derive frequency equations of beams carrying multiple masses. International Journal of Mechanical Sciences. 43:2001;871-881.
32. Low K.H. Further note on the methods to derive frequency equations of beams carrying multiple masses. International Journal of Mechanical Sciences. 44:2002;447-449.
33. James M.L., et al. Vibration of mechanical and structural systems with microcomputer applications. 1993;HarperCollins College Publishers, New York.
34. Low K.H. A reliable algorithm for solving frequency equations involving transcendental functions. Journal of Sound and Vibration. 161:1993;369-377.
35. Gilat A. MATLAB: an introduction with applications. 2004;Wiley, New York.
36. Math Works. User's Guide 2002 Symbolic math toolbox: for use with MATLAB, Version 3. Massachusetts: The MathWorks, Inc.