Lie group theory and analytical solutions for the axially accelerating string problem

Journal of Sound and Vibration

Volumn 230, Issue 4, 2000, Pages 729-742

  Ozkaya E ^a   Pakdemirli, M ^a  

^a CELAL BAYAR UNIVERSITY   (Turkey)

Author keywords

[No Author keywords available]

Indexed keywords

ACCELERATION; APPROXIMATION THEORY; MATHEMATICAL TRANSFORMATIONS; NUMERICAL METHODS; PARTIAL DIFFERENTIAL EQUATIONS; VELOCITY;

ARBITRARY VELOCITY FUNCTION; AXIALLY ACCELERATING STRING PROBLEM; LIE GROUP THEORY; TIME DEPENDENT VELOCITY; TRANSVERSE VIBRATIONS;

VIBRATIONS (MECHANICAL);

EID: 0033741086     PISSN: 0022460X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jsvi.1999.2651     Document Type: Article

References (13)

1. MIRANKER W. L. The wave equation in a medium in motion. IBM Journal of Research and Development. 4:1960;36-42.
2. MOTE C. D. Jr. Stability of systems transporting accelerating axially moving materials. Transactions of the American Society of Mechanical Engineers, Journal of Dynamic Systems, Measurements and Control. 97:1975;96-98.
3. PAKDEMİRLİ M., ULSOY A. G., CERANO Ǧ A. Transverse vibration of an axially accelerating string. Journal of Sound and Vibration. 169:1994;179-196.
4. PAKDEMİRLİ M., BATAN H. Dynamic stability of a constantly accelerating string. Journal of Sound and Vibration. 168:1993;371-378.
5. WICKERT J. A. Transient vibration of gyroscopic systems with unsteady superposed motion. Journal of Sound and Vibration. 195:1996;797-807.
6. PAKDEMİRLİ M., ULSOY A. G. Stability of an axially accelerating string. Journal of Sound and Vibration. 203:1997;815-832.
7. x ). Journal of Mathematical Physics. 32:1991;2988-2995.
8. IBRAGIMOV N. H., TORRISI M. A simple method for group analysis and its application to a model of detonation. Journal of Mathematical Physics. 33:1992;3931-3939.
9. IBRAGIMOV N. H. CRCHandbook of Lie Group Analysis of Differential Equations. 1995;CRC Press, Boca Raton.
10. TORRISI M., TRACINA R., VALENTI A. A group analysis approach for a non-linear differential system arising in diffusion phenomena. Journal of Mathematical Physics. 37:1996;4758-4767.
11. YÜRÜSOY M., PAKDEMİRLİ M. Group classification of a non-Newtonian fluid model using classical approach and equivalence transformations. International Journal of Non-Linear Mechanics. 34:1999;341-346.
12. PAKDEMİRLİ M., YÜRÜSOY M. Similarity transformations for partial differential equations. SIAM Review. 40:1998;96-101.
13. BLUMAN G. W., KUMEI S. Symmetries and Differential Equations. 1989;Springer-Verlag, New York.