The moving web is widely used to make printing and packaging products, flexible electronics, cloths, etc. The impact of the variable density on printing web dynamic behavior is considered. The density changes in the form of sine half-wave in the lateral direction. Based on the D'Alembert's principle, the transverse vibration differential equation of moving printing web with variable density is established and is discretized by using the differential quadrature method (DQM). The complex characteristic equation is derived. The impacts of the density coefficient and the dimensionless speed on the web stability and vibration characteristics are discussed. The results show that it is feasible to use the DQM to analyze the problem of transverse vibration of printing web with varying density; the tension ratio and the density coefficient have important impacts on the stability of moving printing web. This study provides theoretical guidance and basis for optimizing the structure of printing press and improving the stable working speed of printing press and web.

References

References
1.
Luo
,
A. C. J.
,
2011
, “
A Theory for Nonlinear Soft Webs
,”
Commun. Nonlinear Sci. Numer. Simul.
,
16
(
4
), pp.
2184
2199
.
2.
Beisel
,
J. A.
, and
Good
,
J. K.
,
2010
, “
The Instability of Webs in Transport
,”
ASME J. Appl. Mech.
,
78
(
1
), p.
011001
.
3.
Marynowski
,
K.
, and
Kapitaniak
,
T.
,
2002
, “
Kelvin–Voigt Versus Bürgers Internal Damping in Modeling of Axially Moving Viscoelastic web
,”
Int. J. Nonlinear Mech.
,
37
(
7
), pp.
1147
1161
.
4.
Filipich
,
C. P.
, and
Rosales
,
M. B.
,
2007
, “
Vibration of Non-Homogeneous Rectangular Membranes With Arbitrary Interfaces
,”
J. Sound Vib.
,
305
(
4–5
), pp.
582
595
.
5.
Yang
,
X. D.
,
Zhang
,
W.
,
Chen
,
L. Q.
, and Yao, M. H.,
2012
, “
Dynamical Analysis of Axially Moving Plate by Finite Difference Method
,”
Nonlinear Dyn.
,
67
(
2
), pp.
997
1006
.
6.
Gajbhiye
,
S. C.
,
Upadhyay
,
S. H.
, and
Harsha
,
S. P.
,
2012
, “
Free Vibration Analysis of Flat Thin Membrane
,”
Int. J. Eng. Sci. Technol.
,
4
(
8
), pp.
3942
3948
.http://www.ijest.info/docs/IJEST12-04-08-015.pdf
7.
Wu
,
J. M.
,
Lei
,
W. J.
,
Wu
,
Q. M.
, Wang, Y., and Ma, L. E.,
2014
, “
Transverse Vibration Characteristics and Stability of a Moving Membrane With Elastic Supports
,”
J. Low Freq. Noise, Vib. Act. Control
,
33
(
1
), pp.
65
78
.
8.
Farokhi
,
H.
,
Ghayesh
,
M. H.
, and
Hussain
,
S.
,
2016
, “
Three-Dimensional Nonlinear Global Dynamics of Axially Moving Viscoelastic Beams
,”
ASME J. Vib. Acoust.
,
138
(
1
), p.
011007
.
9.
Yao
,
G.
, and
Zhang
,
Y. M.
,
2016
, “
Dynamics and Stability of an Axially Moving Plate Interacting With Surrounding Airflow
,”
Meccanica
,
51
(
9
), pp.
2111
2119
.
10.
Huang
,
J. L.
, and
Zhu
,
W. D.
,
2017
, “
A New Incremental Harmonic Balance Method With Two Time Scales for Quasi-Periodic Motions of an Axially Moving Beam With Internal Resonance Under Single-Tone External Excitation
,”
ASME J. Vib. Acoust.
,
139
(
2
), p.
021010
.
11.
Wu
,
J. M.
,
Wu
,
Q. M.
,
Ma
,
L. E.
, and Liu, L. L.,
2010
, “
Parameter Vibration and Dynamic Stability of the Printing Paper Web With Variable Speed
,”
J. Low Freq. Noise, Vib. Active Control
,
29
(
4
), pp.
281
291
.
12.
Malookani
,
R. A.
, and
Horssen
,
W. T. V.
,
2016
, “
On Parametric Stability of a Nonconstant Axially Moving String Near Resonances
,”
ASME J. Vib. Acoust.
,
139
(
1
), p.
011005
.
13.
Sasajima
,
M.
,
Kakudate
,
T.
, and
Narita
,
Y.
,
2002
, “
Vibration Behavior and Simplified Design of Thick Rectangular Plates With Variable Thickness
,”
ASME J. Vib. Acoust.
,
124
(
2
), pp.
302
309
.
14.
Chakraverty
,
S.
,
Jindal
,
R.
, and
Agarwal
,
V. K.
,
2007
, “
Vibration of Nonhomogeneous Orthotropic Elliptic and Circular Plates With Variable Thickness
,”
ASME J. Vib. Acoust.
,
129
(
2
), pp.
256
259
.
15.
Gupta
,
A. K.
, and
Khanna
,
A.
,
2007
, “
Vibration of Visco-Elastic Rectangular Plate With Linearly Thickness Variations in Both Directions
,”
J. Sound Vib.
,
301
(
3–5
), pp.
450
457
.
16.
Kaur
,
H.
, and
Gupta
,
A. K.
,
2014
, “
Comparative Study of Effect of Thermal Gradient on Free Vibrations of Clamped Visco-Elastic Rectangular Plates With Linear and Parabolic Thickness Variations in Both Directions
,” Acta Technica CSAV,
59
(
2
), pp.
199
214
.
17.
Hirano
,
T.
,
Kim
,
H.
, and
Tanaka
,
Y.
,
2008
, “
Study of the Effect of Thermal Gradient on Free Vibration of Clamped Visco-Elastic Rectangular Plates With Linearly Thickness Variation in Both Directions
,”
Meccanica
,
43
(
4
), pp.
449
458
.
18.
Zhou
,
Y. F.
, and
Wang
,
Z. M.
,
2014
, “
Application of the Differential Quadrature Method to Free Vibration of Viscoelastic Thin Plate With Linear Thickness Variation
,”
Meccanica
,
49
(
12
), pp.
2817
2828
.
19.
Lal
,
R.
, and
Rani
,
R.
,
2015
, “
Axisymmetric Vibrations of Composite Annular Sandwich Plates of Quadratically Varying Thickness by Harmonic Differential Quadrature Method
,”
Acta Mech.
,
226
(
6
), pp.
1993
2012
.
20.
Buchanan
,
G. R.
,
2005
, “
Vibration of Circular Membranes With Linearly Varying Density Along a Diameter
,”
J. Sound Vib.
,
280
(
1–2
), pp.
407
414
.
21.
Ma
,
L. E.
,
Wu
,
J. M.
,
Mei
,
X. S.
,
Wang
,
Y.
, and
Li
,
Z.
,
2013
, “
Active Vibration Control of Moving web With Varying Density
,”
J. Low Freq. Noise, Vib. Act. Control
,
32
(
4
), pp.
323
334
.
22.
Bert
,
C. W.
, and
Malik
,
M.
,
1996
, “
Differential Quadrature Method in Computational Mechanics: A Review
,”
ASME Appl. Mech. Rev.
,
49
(
1
), pp.
1
28
.
23.
Hou
,
Z. Y.
, and
Wang
,
Z. M.
,
2005
, “
The Transverse Vibration and Stability Analysis of an Axially Moving Membrane
,”
J. Xi'an Univ. Technol.
,
21
(
4
), pp.
402
404
.
You do not currently have access to this content.