The transverse vibrations of two translating strings interconnected by a Winkler elastic foundation, and subjected to axial loading are investigated. The system of governing partial differential equations of this gyroscopic system is cast in the first order canonical form. It is shown that the natural frequencies are composed of two infinite sets, representing in-phase and out-of-phase vibrations of the two strings. The effects of the axial tension ratios of the two continuous media, as well as the effects of the elastic foundation stiffness are investigated. In general, it is found that the natural frequencies increase with increasing elastic stiffness of the foundation. It is found that the elastic foundation does not alter the critical speed, but different mass and tension ratios do.
Volume Subject Area:
Dynamic Systems and Control
1.
Hwang
S.-J.
Perkins
N. C.
1992
, “Supercritical Stability of an Axially Moving Beam Part I: Model and Equilibrium Analysis
,” Journal of Sound and Vibration
, 154
, 381
–396
.2.
Wickert
J. A.
Mote
C. A.
1990
, “Classical Vibration Analysis of Axially-Moving Continua
,” ASME Journal of Applied Mechanics
, 57
(3)
, 738
–744
.3.
Meirovitch
L.
1974
, “A New Method of Solution of the Eigenvalue Problem for Gyroscopic Systems
,” AIAA Journal
, 12
, 1337
–1342
.4.
Hughes
P. C.
D’Eleuterio
G. M.
1986
, “Modal Parameter Analysis of Gyroscopic Continua
,” ASME Journal of Applied Mechanics
, 53
, 918
–924
.5.
Chung
C. H.
Tan
C. A.
1993
, “Transfer Function Formulation of Constrained Distributed Parameter Systems, Part II: Applications
,” ASME Journal of Applied Mechanics
, 60
, 1012
–1019
.6.
Bhat
R. B.
Xistris
G. D.
Sanker
T. S.
1982
, “Dynamic Behavior of a Moving Belt Supported on Elastic Foundation
,” ASME Journal of Mechanical Design
, 104
, 143
–147
.7.
Wickert
J. A.
1994
, “Response Solutions for the Vibration of a Traveling String on an Elastic Foundation
,” ASME Journal of Vibration and Acoustics
, 116
(1)
, 137
–139
.8.
Cheng
S. P.
Perkins
N. C.
1991
, “The Vibration and Stability of a Friction-Guided, Translating String
,” Journal of Sound and Vibration
, 144
, 281
–292
.9.
Perkins
N. C.
1990
, “Linear Dynamics of a Translating String on Elastic Foundation
,” Journal of Vibrations and Acoustics
, 112
, 2
–7
.10.
Parker
R. G
1999
, “Supercritical Speed Stability of the Trivial Equilibrium of an Axially Moving String on an Elastic Foundation
,” Journal of Sound and Vibration
, 221
, 205
–219
.11.
Tan
C. A.
Yang
B.
Mote
C. D.
1990
, “On the Vibration of Hydrodynamic Bearings
,” Journal of Vibration and Acoustics
, 112
, 337
–345
.12.
Tan
C. A.
Zhang
L.
1994
, “Dynamic Characteristics of a Constrained String Translating Across an Elastic Foundation
,” Journal of Vibration and Acoustics
, 116
, 318
–325
.13.
Chen
J. S.
1997
, “Natural frequencies and stability of of an axially-travelling string in contact with a stationary load system
,” Journal of Vibration and Acoustics
, 119
, pp. 152
–157
.14.
Chakraborty
G.
Mallik
A. K.
1999
, “Nonlinear Vibration of a Traveling Beam Having an Intermediate Guide
”, Nonlinear Dynamics
, 20
, pp. 247
–265
.15.
Riedel
C. H.
Tan
C. A.
1998
, “Dynamic Characteristics and Mode Localization of Elastically Constrained Axially Moving Strings and Beams
”, Journal of Sound and Vibration
, 215
, pp. 455
–473
.16.
Fung
R. F
Chou
J.-H
Kuo
Y. L
2002
, “Optimal Boundary Control of an Axially Moving Material System
,” ASME Journal of Dynamic Systems, Measurement, and Control
, 124
, 55
–61
.17.
Fung
R. F
Huang
J. S
Chen
Y. C
Yao
C. M
1998
, “Nonlinear Dynamic Analysis of the Viscoelastic String with a Harmonically Varying Transport Speed
,” Computers & Structures
, 66
(6)
, 777
–784
.18.
Cha
P. D.
2002
, “Eigenvalues of a Linear Elastica Carrying Lumped Masses, Springs and Viscous Dampers
,” Journal of Sound and Vibration
, 257
, 798
–808
.19.
Zen
G.
Mu¨ftu¨
S.
2006
, “Stability of an accelerating string subjected to frictional guiding forces
,” Journal of Sound and Vibration
, 289
, pp. 551
–576
.20.
Cabanska-Placzkiewicz
K.
1998
, “Free Vibration oh the System of Two Strings Coupled by a Viscoelastic Interlayer
,” Engineering Transactions
, 46
, 217
–227
.21.
Oniszczuk
Z.
2000
, “Transverse Vibrations of Elastically Connected Double-String Complex System, Part I: Free Vibrations
,” Journal of Sound and Vibration
, 232
, 355
–366
.22.
Oniszczuk
Z.
2000
, “Transverse Vibrations of Elastically Connected Double-String Complex System, Part I: Forced Vibrations
,” Journal of Sound and Vibration
, 232
, 367
–386
.23.
Oniszczuk
Z.
2002
, “Damped Vibration Analysis of a Two-Degree-of-Freedom Discrete System
,” Journal of Sound and Vibration
, 257
, 391
–403
.24.
Oniszczuk
Z.
2003
, “Damped Vibration Analysis of an Elastically Connected Complex Double-String System
,” Journal of Sound and Vibration
, 264
, 253
–271
.25.
Cheng
G.
Zu
J. W.
2003
, “Dynamic Analysis of an Optical Fiber Coupler in Telecommunications
,” Journal of Sound and Vibration
, 268
, 15
–31
.26.
Oniszczuk
Z.
2002
, “Free Transverse Vibrations of Elastically Connected Complex Beam-String System
,” Journal of Sound and Vibration
, 254
, 703
–715
.27.
Graff, K.F., 1975, Wave motion in elastic solids, Ohio State University Press.
28.
Meirovitch
L.
1975
, “A Modal Analysis for the Response of Linear Gyroscopic Systems
,” ASME Journal of Applied Mechanics
, 42
, 446
–450
.29.
Meirovitch, L., 1997, Principles and Techniques of Vibrations, Prentice Hall, NJ, U.S.A.
30.
He
S.
Rao
M. D.
1993
, “Vibration and Damping Analysis of Multi-Span Sandwich Beams with Arbitrarily Boundary Conditions
,” Journal of Sound and Vibration
, 164
, 125
–142
.31.
Gao
J. X
Cheng
L.
2005
, “Modeling and Control of power flow in a double-beam system
,” Thin-Walled Structures
, 43
, 751
–771
.32.
Sokolinsky
V. S.
Bermen
H. F. V.
Lavoie
J. A.
Nutt
S. R.
2004
, “Analytical and Experimental Study of Free Vibration Response f Soft-Core Sandwich Beams
,” Journal of Sandwich Structures and Materials
, 6
, 239
–261
.
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