Frequencies of beams carrying multiple masses: Rayleigh estimation versus eigenanalysis solutions

Journal of Sound and Vibration

Volumn 268, Issue 4, 2003, Pages 843-853

  Low, K H ^a  

^a NANYANG TECHNOLOGICAL UNIVERSITY   (Singapore)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; BEAMS AND GIRDERS; DIFFERENTIAL EQUATIONS; EIGENVALUES AND EIGENFUNCTIONS; ERROR ANALYSIS; PARAMETER ESTIMATION; VIBRATION MEASUREMENT;

TRIGONOMETRIC FUNCTIONS;

ACOUSTIC VARIABLES MEASUREMENT;

EID: 0344033631     PISSN: 0022460X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-460X(03)00282-7     Document Type: Article

References (32)

1. Y. Chen, On the vibration of beams or rods carrying a concentrated mass, Journal of Applied Mechanics 30 (1963) 310-311.
2. H.H. Pan, Transverse vibration of an Euler beam carrying a system of heavy bodies, Journal of Applied Mechanics 32 (1965) 434-437.
3. C.L. Amba-Rao, Method of calculation of frequencies of partially fixed beams carrying masses, Journal of the Acoustical Society of America 40 (1966) 367-371.
4. L.S. Srinath, Y.C. Das, Vibrations of beams carrying mass, Journal of Applied Mechanics Series E 34 (1967) 784-785.
5. M.M. Stanišić, J.C. Hardin, On the response of beams to an arbitrary number of concentrated moving masses, Journal of the Franklin Institute 287 (1969) 115-123.
6. R.P. Goel, Vibrations of a beam carrying a concentrated mass, Journal of Applied Mechanics 40 (1973) 821-822.
7. M. Gurgoze, A note on the vibrations of restrained beams and rods with point masses, Journal of Sound and Vibration 96 (1984) 461-468.
8. N.G. Stephen, 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.
9. M. Gurgoze, On the vibrations of restrained beams and rods with heavy masses, Journal of Sound and Vibration 100 (4) (1985) 588-589.
10. P.A.A. Laura, V.H. Cortinez, Optimization of eigenvalues in the case of vibrating beams with point masses, Journal of Sound and Vibration 108 (2) (1986) 346-348.
11. M. Gurgoze, H. Batan, 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.
12. W.H. Liu, W.J.-R. Wu, C.-C. Huang, Free vibration of beams with elastically restrained edges and intermediate concentrated masse, Journal of Sound and Vibration 122 (1988) 193-207.
13. M.A. De Rosa, C. Franciosi, M.J. Maurizi, On the dynamic behaviour of slender beams with elastic ends carrying a concentrated mass, Computers and Structures 58 (1996) 1145-1159.
14. E. Özkaya, M. Pakdemirli, H.R. Öz, Non-linear vibrations of a beam-mass system under different boundary conditions, Journal of Sound and Vibration 199 (1997) 679-696.
15. K.H. Low, On the eigenfrequencies for mass loaded beams under classical boundary conditions, Journal of Sound and Vibration 215 (1998) 381-389.
16. K.H. Low, Comparisons of experimental and numerical frequencies for classical beams carrying a mass in span, International Journal of Mechanical Sciences 41 (1999) 1515-1531.
17. W.H. Liu, F.H. Yeh, Free vibration of a restrained-uniform beam with intermediate masses, Journal of Sound and Vibration 117 (3) (1987) 555-570.
18. W.H. Liu, C.-C. Huang, Vibrations of a concentrated beam carrying a heavy tip body, Journal of Sound and Vibration 123 (1) (1988) 15-29.
19. M.J. Maurizi, P.M. Bellés, 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.
20. E. Özkaya, M. Pakdemirli, Non-linear vibrations of a beam-mass system with both ends clamped, Journal of Sound and Vibration 221 (1999) 491-503.
21. K.H. Low, T.M. Lim, G.B. Chai, Experimental and analytical investigations of vibration frequencies for center-loaded beams, Computers and Structures 48 (1993) 1157-1162.
22. K.H. Low, Closed-form formulas for fundamental vibration frequency of beams under off-centre load, Journal of Sound and Vibration 201 (1997) 528-533.
23. K.H. Low, R.N. Dubey, 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. K.H. Low, R.N. Dubey, G.B. Chai, 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. K.H. Low, A modified Dunkerley formula for eigenfrequencies of beams carrying concentrated masses, International Journal of Mechanical Sciences 42 (2000) 1287-1305.
26. K.H. Low, On the methods to derive frequency equations of beams carrying multiple masses, International Journal of Mechanical Sciences 43 (2001) 871-881.
27. K.H. Low, Reply to Comments on "On the methods to derive frequency equations of beams carrying multiple masses", International Journal of Mechanical Sciences 44 (2002) 447-449.
28. L. Meirovitch, Elements of Vibration Analysis, McGraw-Hill, New York, 1986.
29. S.S. Rao, Mechanical Vibrations, 3rd edition, Addison-Wesley, Reading, MA, 1995.
30. K.M. Heal, M.L. Hansen, K.M. Rickard, Maple V: Learning Guide, Springer, New York, 1996.
31. M.L. James, et al., Vibration of Mechanical and Structural Systems with Microcomputer Applications, HarperCollins College Publishers, New York, 1993.
32. K.H. Low, A reliable algorithm for solving frequency equations involving transcendental functions, Journal of Sound and Vibration 161 (1993) 369-377.