Analysis of a beam-column system under varying axial forces of elliptic type: The exact solution of Lamé's equation

International Journal of Solids and Structures

Volumn 41, Issue 8, 2004, Pages 2155-2163

  Elías Zúniga, Alex ^a  

^a SCHOOL OF ENGINEERING AND SCIENCES   (Mexico)

Author keywords

Buckling; Elastic stability; Euler load; Jacobi elliptic functions; Lateral vibration

Indexed keywords

COLUMNS (STRUCTURAL); VIBRATIONS (MECHANICAL);

AXIAL PULSATING FORCE; VIBRATIONAL FREQUENCY;

BEAMS AND GIRDERS;

BEAM; BUCKLING;

EID: 1542287366     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijsolstr.2003.11.036     Document Type: Article

References (13)

1. Byrd P.F. Friedman M.D. Handbook of Elliptic Integrals for Engineers and Physicists 1953 Springer-Verlag
2. Erdélyi A. Higher Transcendental Functions (Bateman Manuscript Project) vol. 3 1955 McGraw-Hill New York
3. Greene P.B. Kofman L. Linde A. Starobinsky A.A. Structure of resonance in preheating after inflation Physical Review D 56 10 1997 6175-6192
4. Hsu C.S. Some simple exact periodic responses for a nonlinear system under parametric excitation Journal of Applied Mechanics 1974 1135-1137
5. Klötter A. Kotowski A. Ueber die stabilitaet von loesungen Hillscher differtialgleichungen mit drei unabhaengigen parametran Zeitschrift für Angewandte Mathematik und Mechanik 23 1943 149
6. Lubkin S. Stoker J.J. Stability of columns and strings under periodically varying forces Quarterly of Applied Mathematics I 3 1943 215-236
7. Magnus W. Winkler S. Hill's Equation 1979 Dover Publications New York, NY
8. Nayfeh A.H. Mook D.T. Non-linear Oscillations 1973 John Wiley New York
9. O'Neil P.V. Advanced Engineering Mathematics third ed. 1991 Wadsworth, Inc
10. Porter B. The stability of systems governed by a special form of Hill's equation International Journal of Mechanical Sciences 4 1962 313-321
11. Rand R.H. On the stability of Hill's equation with four independent parameters Journal of Applied Mechanics 1969 885-886
12. Rand, R.H., 2001. Lecture Notes on Nonlinear Vibrations, a free on-line book available at
13. Stoker J.J. Nonlinear Vibrations 1950 Wiley-Interscience New York