The equation of free transverse vibration of beams with two sections of partially distributed mass is derived and its exact solution has been obtained. Experimental data for a cantilever beam are given to verify the computational results. Using a cantilever beam as an example, some interesting features of changes of natural frequencies with mass length and position are described. The method is finally generalized for the case of beams with multiple spans of distributed mass.

1.
Chan
K. T.
,
Leung
T. P.
, and
Wong
W. O.
,
1996
, “
Free Vibration of Simply Supported Beams Partially Loaded with Distributed Mass
,”
Journal of Sound and Vibration
, Vol.
191
, No.
4
, pp.
590
597
.
2.
Chan
K. T.
, and
Zhang
J. Z.
,
1995
, “
Free Vibration of a Cantilever Tube Partially Filled with Liquid
,”
Journal of Sound and Vibration
, Vol.
182
, No.
2
, pp.
185
190
.
3.
Chan, K. T., and Wang, X. Q., 1997, “Free Vibration of Timoshenko Beam Partially Loaded with Distributed Mass,” Journal of Sound and Vibration, revised version under review.
4.
Chen, Y., 1963, “On the Vibration of Beams or Rods Carrying a Concentrated Mass,” ASME Journal of Applied Mechanics, June 1963, pp. 310–311.
5.
Cranch, E. T., and Adler, A. A., 1956, “Bending Vibrations of Variable Section Beams,” ASME Journal of Applied Mechanics, March 1956, pp. 103–108.
6.
Goel, R. P., 1973, “Vibrations of a Beam Carrying a Concentrated Mass,” ASME Journal of Applied Mechanics, September 1973, pp. 821–822.
7.
Goel
R. P.
,
1976
, “
Transverse Vibrations of Tapered Beams
,”
Journal of Sound and Vibration
, Vol.
47
, No.
1
, pp.
1
7
.
8.
Kirchhoff, G., 1879, “Monatsberichte der K. Preuss. Akademie der Wissenschaften,” Berlin, Germany, Transversalschwingungen eiens Stakes von veranderlichen Querschnitt.
9.
Wang, H. C., 1967, “Generalized Hypergeometric Function Solutions on the Transverse Vibration of a Class of Nonuniform Beams,” ASME Journal of Applied Mechanics, September 1967, pp. 702–708.
This content is only available via PDF.
You do not currently have access to this content.