The dynamic and static response of a nonuniform beam with nonhomogeneous elastic boundary conditions is studied by generalizing the method of Mindlin-Goodman and utilizing the exact solutions of general elastically restrained non-uniform beams given by Lee and Kuo. A general form of change of dependent variable is introduced and the shifting functions expressed in terms of the four fundamental solutions of the system, instead of the fifth degree polynomials taken by Mindlin-Goodman, are selected. The physical meanings of these shifting polynomial functions are explored. Finally, the limiting cases are discussed and examples are given to illustrate the analysis.
Issue Section:
Research Papers
1.
Berry
I. G.
Nagdhi
P. M.
1956
, “On the Vibration of Elastic Bodies Having Time-Dependent Boundary Conditions
,” Quarterly of Applied Mathematics
, Vol. 14
, No. 1
, pp. 43
–50
.2.
Edstrom
C. R.
1981
, “The Vibrating Beam With Nonhomogeneous Boundary Conditions
,” ASME Journal of Applied Mechanics
, Vol. 48
, pp. 669
–670
.3.
Gou, P. F., and Karim-Panahi, K., 1988, “Beam With Time Dependent Boundary Conditions, Closed Form (series) Solution Versus Response Spectrum Method,” Dynamics and Seismic Issues in Primary and Secondary Systems: ASME Pressure Vessels and Piping Conference, PVP V137, pp. 33–44.
4.
Grant
D. A.
1983
, “Beam Vibrations With Time-Dependent Boundary Conditions
,” Journal of Sound and Vibration
, Vol. 89
, No. 4
, pp. 519
–522
.5.
Herrmann
G.
1955
, “Forced Motions of Timoshenko Beams
,” ASME Journal of Applied Mechanics
, Vol. 22
, pp. 53
–56
.6.
Lee
S. Y.
Ke
H. Y.
Kuo
Y. H.
1990
, “Analysis of Non-Uniform Beam Vibration
,” Journal of Sound and Vibration
, Vol. 142
, No. 1
, pp. 15
–29
.7.
Lee
S. Y.
Kuo
Y. H.
1992
, “Exact Solutions for the Analysis of General Elastically Restrained Nonuniform Beams
,” ASME Journal of Applied Mechanics
, Vol. 59
, No. 2
, pp. 205
–212
.8.
Lee
S. Y.
Lin
S. M.
1996
, “Dynamic Analysis of Nonuniform Beams With Time Dependent Elastic Boundary Conditions
,” ASME Journal of Applied Mechanics
, Vol. 63
, pp. 474
–478
.9.
Mindlin
R. D.
Goodman
L. E.
1950
, “Beam Vibrations With Time-Dependent Boundary Conditions
,” ASME Journal of Applied Mechanics
, Vol. 17
, pp. 377
–380
.10.
Nothmann
G. A.
1948
, “Vibration of a Cantilever Beam With Prescribed End Motion
,” ASME Journal of Applied Mechanics
, Vol. 15
, pp. 327
–334
.11.
Paz, M., 1980, Structural Dynamics: Theory and Computation, Van Nostrand Reinhold, New York, pp. 232–234.
12.
Sloss
J. M.
Sadek
I.
Bruch
J. C.
1986
, “A Reduction Method for Nonhomogeneous Boundary Conditions
,” ASME Journal of Applied Mechanics
, Vol. 53
, pp. 404
–411
.13.
Yen
T. C.
Kao
S.
1959
, “Vibration of Beam-Mass System With Time-Dependent Boundary Conditions
,” ASME Journal of Applied Mechanics
, Vol. 26
, pp. 353
–356
.
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