Abstract
A uniform cantilever beam of varying orientation with a tip mass at the free end can be used as a basic model of many practical structures such as flexible robot arm or antenna mast. The aim of the study described here is to investigate the influence of the orientation effect on the natural frequency of the cantilever beam carrying a tip mass. An analytic solution is obtained by using the Adomian decomposition method. The accuracy of the Adomian decomposition method with a varying number of terms in the series is investigated by comparing its results with those generated by the finite element method.
1.
Handoo
, K. L.
, and Sundararajan
, V.
, 1971, “Parametric Instability of a Cantilever Column With End Mass
,” J. Sound Vib.
0022-460X, 18
(1
), pp. 45
–53.
2.
To
, W. S.
, 1982, “Vibration of Cantilever Beam With a Base Excitation and Tip Mass
,” J. Sound Vib.
0022-460X, 83
, pp. 445
–460
.3.
Goel
, R. P.
, 1973, “Vibration of a Beam Carrying Concentrated Mass
,” ASME J. Appl. Mech.
0021-8936, 40
, pp. 813
–815
.4.
Laura
, P. A. A.
, and Cortinez
, V. H.
, 1986, “Optimization of Eigenvalues in the Case of Vibrating Beams With Point Masses
,” J. Sound Vib.
0022-460X, 108
, pp. 346
–348
.5.
Laura
, P. A. A.
, and Gutierrez
, R. H.
, 1986, “Vibrations of an Elastically Restrained Cantilever Beam of Varying Cross Section With Tip Masses of Finite Length
,” J. Sound Vib.
0022-460X, 108
, pp. 123
–131
.6.
Naguleswaran
, S.
, 2002, “Transverse Vibrations of a Euler-Bernoulli Uniform Beam Carrying Several Particles
,” Int. J. Mech. Sci.
0020-7403, 44
, pp. 2463
–2478.
7.
Gökdağ
, H.
, and Kopmaz
, O.
, 2005, “Coupled Bending and Torsional Vibration of a Beam With In-Span and Tip Attachments
,” J. Sound Vib.
0022-460X, 287
(3
), pp. 591
–610
8.
Adomian
, G.
, 1988, “A Review of the Decomposition Method in Applied Mathematics
,” J. Math. Anal. Appl.
0022-247X, 135
(2
), pp. 501
–544
.9.
Adomian
, G.
, 1985, “On the Solution of Algebraic by the Decomposition Method
,” J. Math. Anal. Appl.
0022-247X, 105
(1
), pp. 141
–166
.10.
Adomian
, G.
, 1988, Nonlinear Stochastic System Theory and Application to Physics
, Kluwer Academic
, Dordrecht
.11.
Adomian
, G.
, and Rach
, R.
, 1986, “On Composite Nonlinearties and the Decomposition Method
,” J. Math. Anal. Appl.
0022-247X, 113
(2
), pp. 504
–509
.12.
Wazwaz
, A. M.
, 2001, “Analytic Treatment for Variable Coefficient Fourth-Order Parabolic Partial Differential Equations
,” Appl. Math. Comput.
0096-3003, 123
, pp. 219
–227
.13.
Yaman
, M.
, and Sen
, S.
, 2004, “The Analysis of the Orientation Effect of Nonlinear Flexible Systems on Performance of the Pendulum Absorber
,” Int. J. Non-Linear Mech.
0020-7462, 39
(5
), pp. 741
–752
.14.
Laura
, P. A. A.
, Pombo
, J. L.
, and Susemihl
, E. A
, 1974, “A Note on the Vibration of a Clamped-Free Beam With a Mass at the Free End
,” J. Sound Vib.
0022-460X 37
(2), pp. 161
–168
.15.
Cherruault
, Y.
, 1989, “Convergence of Adomian’s Method
,” Kybernetik
0023-5946, 18
, pp. 31
–38
.Copyright © 2007
by American Society of Mechanical Engineers
You do not currently have access to this content.
