本文主要研究拘束阻尼層貼覆於移動樑上的動態行為。首先利用漢米爾頓原理與有限元素法推導軸向移動樑的運動方程式，其中包含轉動慣量、剪力變形與張力作功等效應。其次，心材的黏彈材料假設為不可壓縮，且楊氏係數與剪力模數以複數描述。最後軸向移動對系統產生阻尼效應，使運動方程式含有阻尼項。利用狀態空間方法求得移動樑的自然振動行為。
由結果可以得到阻尼層的厚度比增加，系統的自然頻率會成線性減少，損失因子則緩慢的增加。阻尼層材料的選擇也相當重要，黏彈材料的強度在適當範圍內可得到較好的阻尼效應。貼覆拘束阻尼的移動樑，自然頻率較未貼覆的低，相對地臨界速度也隨之降低。當軸向移動樑的速度到達臨界速度時，移動樑會產生發散不穩定。在拘束層方，拘束層材料的強度與樑主體相當時，可得到較好的減振效果。
在動態穩定方面，本文採用Bolotin 的法則來分析移動樑的動態穩定問題，並使用一次近似之方法來架構出不同幾何及材料性質下的動態不穩定區之圖形。

The objective of this dissertation is to study the vibration and damping of a traveling beam with a constrained layer damping. The discrete layer finite element method and the Hamilton’s principle are employed to derive the finite-element equations of motion for the traveling beam including transverse shear effects.
The middle layer is the linear viscoelastic material layer, assuming that viscoelastic material is almost incompressible. The extensional and shear moduli of the viscoelastic material are described by complex quantities. Complex-eigenvalued problem are solved by state-space method, and the frequencies and modal loss factor of the composite beam are extracted. The effects of stiffness and thickness of the viscoelastic and constrained layers on natural frequencies and modal loss factors of traveling beam are presented. It is shown that the viscoelastic material can reduce the natural frequencies and the critical speed of the traveling beam is decreased. Tension fluctuations are the dominant source of excitation in traveling
materials. The regions of dynamic instability are determined by Bolotin’s method and numerical results are shown that the constrained damping layer attached to beam tends to stabilize the traveling material. The effects of various parameters, such as types of viscoelastic material response and thickness, on dynamic stability are also investigated.

01. E. M. Kerwin Jr, 1959 Journal of the Acoustical Society of America 31,
952-962. Damping of flexural waves by a constrained viscoelastic layer.
02. D. Ross, E. E. Ungar and E. M. Kerwin Jr, 1959 Structural Damping:
Colloquium on Structural Damping, ASME Annual Meeting (J. E. Ruzicka,
editor). Damping of plate flexural vibrations by means of viscoelastic
03. R. A. Di Taranto, 1965 Journal of Applied Mechanics ASME Series E 87,
881-886. Theory of vibratory bending of elastic and viscoelastic layered
04. D. J. Mead and S. Markus, 1969 Journal of Sound and Vibration 10,
163-175. The forced vibrations of a three-layer damped sandwich beam
with arbitrary boundary conditions.
05. D. J. Mead and S. Markus, 1970 Journal of Sound and Vibration 12,
99-112. Loss factors and resonant frequencies of encastré damped
06. D. K. Rao, 1978 Journal of Mechanical Engineering Science 20, 271-282.
Frequency and loss factors of sandwich beams under various boundary
07. A. K. Lall, N. T. Asnani and B. C. Nakra, 1988 Journal of Sound and
Vibration 123, 247-259. Damping analysis of partially covered sandwich
beams.
08. J. M. Lifshitz and M. Leibowitz, 1987 International Journal of Solids and
Structures 23, 1027-1034. Optimal sandwich beam design for maximum
viscoelastic damping.
09. C. D. Johnson, D. A. Kieholz and L. C. Rogers, 1981 Shock and Vibration
Bulletin 51, 71-81. Finite element prediction of damping in beams with
constrained viscoelastic layers.
10. W. Imaino and J. C. Harrison, 1991 Journal of Sound and Vibration 149,
354-359. A comment on constrained layer damping structures with low
viscoelastic modulus.
11. C. Sun and J. M. Whitney, 1973 AIAA Journal 11, 178-183. Theories for
the dynamic response of laminated plates.
12. N. Alam and N. T. Asnani, 1987 Journal of Sound and Vibration 119,
347-362. Refined vibration and damping analysis of multi-layered
rectangular plated.
13. J. A Zapfe and G. A. Lesieutre, 1999 Computers and Structures 70,
647-666. A discrete layer beam finite element for the dynamic analysis of
composite sandwich beams with integral damping layers.
14. V. V. Bolotin, 1964 The Dynamic Stability of Elastic Systems. San
Francisco: Holden-Day.
15. R. M. Evan-Iwanowski, 1967 Resonance Oscillations in Mechanical
Systems. Amsterdam: Elsevier.
16. K. K. Stevens and R. M. Evan-Iwanowski, 1969 International Journal of
Solids and Structures 5, 755-765. Parametric resonance of viscoelastic
columns.
17. S. Dost and P. G. Glockner, 1982 International Journal of Solids and
Structures 18, 587-596. On the dynamic stability of viscoelastic perfect
columns.
18. G. Cederbaum and M. Mond, 1992 ASME Journal of Applied Mechanics
59, 16-19. Stability properties of a viscoelastic column under a periodic
force.
19. D. Touati and G. Cederbaum, 1994 International Journal of Solids and
Structures 31, 2367-2376. Dynamic stability of nonlinear viscoelastic
plates.
20. R. Barakat, 1967 Journal of the Acoustical Society of America 43, 533-539.
Transverse vibrations of a moving thin rod.
21. A. Simpson, 1973 Journal of Mechanical Engineering Science 15,
159-164. Transverse modes and frequencies of beams translating between
fixed end supports.
22. H. M. Nelson, 1979 Journal of Sound and Vibration 65, 381-389.
Transverse vibration of a moving strip.
23. A. G. Ulsoy, C. D. Mote Jr and R. Syzmani, 1978 Holz als Roh-und
Werkstoff 36, 273-280. Principal developments in band saw vibration and
stability research.
24. J. A. Wickert and C. D. Mote Jr, 1988 Shock and Vibration Digest 20, 3-13.
Current research on the vibration and stability of axially moving materials.
25. S. Chonan, Journal of Sound and Vibration 107, 155-165. Steady state
response of an lateral load.
26. E. J. Patula, 1976 Journal of Applied Mechanics ASME Series E 43,
475-479. Attenuation of concentrated loads in a thin moving elastic strip.
27. J. A. Wickert and C. D. Mote Jr, 1990 Journal of Applied Mechanics 57,
738-744. Classical vibration analysis of axially moving continua.
28. C. D. Mote Jr, 1966 Journal of Applied Mechanics 33, 463-464. On the
non-linear oscillation of an axially moving string.
29. A. L. Thurman and C. D. Mote Jr, 1969 Journal of Applied Mechanics 36,
83-91. Free, periodic, nonlinear oscillation of an axially moving strip.
30. J. A. Wickert, 1992 International Journal of Nonlinear Mechanics 27,
503-517. Nonlinear vibration of traveling tensioned beam.
31. W. F. Ames, S. Y. Lee and J. N. Zeiser, 1968 International Journal of
Non-linear Mechanics 3, 449-469. Non-linear vibration of a traveling
threadline.
32. W. L. Miranker, 1960 IBM Journal of Research and Development 4, 36-42.
The wave equation in medium in motion.
33. C. D. Mote Jr, 1975 Journal of Dynamic Systems, Measurement and
Control 97, 96-98. Stability of systems transporting accelerating axially
moving materials.
34. M. Pakdemirli, A. G. Ulsoy and A. Ceranoglu, 1994 Journal of Sound and
Vibration 169, 179-196. Transverse vibration of an axially accelerating
string.
35. M. Pakdemirli and H. Batan, 1993 Journal of Sound and Vibration 168,
371-378. Dynamic stability of a constantly accelerating strip.
36. S. Mahalingam, 1957 British Journal of Applied Physics 8, 145-148.
Transverse vibrations of power transmission chains.
37. C. D. Mote, 1965 Journal of The Franklin Institute 279, 430-444. A study
of bandsaw vibrations.
38. S. Naguleswaran and C. J. H. Williams, 1968 International Journal of
Mechanical Science 10, 239-250. Lateral vibrations of bandsaw blades,
pulley belts and the like.
39. K. W. Wang, 1991 ASME Machine Dynamics and Element Vibrations 36,
41-50. On the stability of chain drive systems under periodic sprocket
oscillations.
40. C. D. Mote, 1968 Journal of The Franklin Institute 285, 329-346.
Dynamic stability of an axially moving band.
41. M. Pakdemirli and A. G. Ulsoy, 1997 Journal of Sound and Vibration 203,
815-832. Stability analysis of an axially accelerating string.
42. A. D. Nashif, I. G. Jones and J. P. Henderson, 1985 Vibration Damping,
Chichester: John Wiley & Sons.
43. R. M. Lin and M. K. Lim, 1996 Journal of Acoustical Society of America
100, 3182-3191. Complex eigensensitivity-based characterization of
structures with viscoelastic damping.
44. E. M. Daya and M. Potier-Ferry, 2001 Computers and Structures 79,
533-541. A numerical method for nonlinear eigenvalue problems
application to vibrations of viscoelastic structures.