Simplest-expression integrals involving beam-column eigenmodes

• Autorzy: Colombo J. I. , Morales C. A.
• Języki publikacji: EN

Abstrakty

EN

Novel integrals, in their simplest form, involving beam-column eigenfunctions and derivatives are presented. All the integrals arise in computational stability analysis of frames. It is stressed that simpler results improve the accuracy of Rayleigh–Ritz-based approximate methods for buckling analysis of distributed structures.

Słowa kluczowe

EN

beam-column eigenfunctions; simplest-expression integrals; stability; buckling; Rayleigh-Ritz method

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Archives of Mechanics
• Rocznik: 2012
• Tom: Vol. 64, nr 5
• Strony: 529--535
• Opis fizyczny: Bibliogr. 17 poz.

Twórcy

autor

Colombo J. I.

autor

Morales C. A.

• Departamento de Ingeniería Estructural y Geotécnica Pontificia Universidad Católica de Chile Vicuńa Mackenna 4860, Santiago, Chile

Bibliografia

• 1. L. Meirovitch, M.K. Kwak, Rayleigh–Ritz based substructure synthesis for flexible multibody systems, AIAA Journal, 29, 1709–1719, 1991.
• 2. C.A. Morales, Rayleigh–Ritz based substructure synthesis for multiply supported structures, Journal of Vibration and Acoustics, 122, 2–6, 2000.
• 3. C.A. Morales, M.A. Ciaccia, Substructure synthesis method for buckling analysis In frames, Meccanica, 42, 601–607, 2007.
• 4. L. Meirovitch, M.K. Kwak, Convergence of the classical Rayleigh–Ritz method and the finite element method, AIAA Journal, 28, 1509–1516, 1990.
• 5. J.L. Maulbetsch, Buckling of compressed rectangular plates with built-in edges, J. Appl. Mech., 4, 59–62, 1937.
• 6. D. Young, Vibration of rectangular plates by Ritz method, J. Appl. Mech., 17, 448–453, 1950.
• 7. G.B. Warburton, Vibration of thin cylindrical shells, Journal of the Mechanical Engineering Sciences, 7, 399–407, 1965.
• 8. D.M. Egle, J.L. Sewall, An analysis of free vibration of orthogonally stiffened cylindrical shells with stiffeners treated as discrete elements, AIAA Journal, 6, 518–526, 1968.
• 9. C.B. Sharma, Calculation of natural frequencies of fixed-free circular cylindrical shells, Journal of Sound and Vibration, 35, 55–76, 1974.
• 10. C.A. Morales, Dynamic analysis of frames by a Rayleigh–Ritz based substructure synthesis method, Engineering Structures, 22, 1632–1640, 2000.
• 11. Y. Narita, A.W. Leissa, Frequencies and mode shapes of cantilevered laminated composite plates, Journal of Sound and Vibration, 154, 161–172, 1992.
• 12. R.B. Bath, Natural frequencies of rectangular plates using characteristic orthogonal poly-nomials in Rayleigh–Ritz method, Journal of Sound and Vibration, 102, 493–499, 1985.
• 13. C.A. Morales, Dynamic analysis of an L-shape structure by Rayleigh–Ritz substructure synthesis method, Meccanica, 44, 339–343, 2009.
• 14. R.D. Blevins, Formulas for Natural Frequency and Mode Shape, Van Nostrand Reinhold, California, 1979.
• 15. C.B. Sharma, Calculation of integrals involving characteristic beam functions, Journal of Sound and Vibration, 56, 475–480, 1978.
• 16. A.Y.T. Leung, Integration of beam functions, Computers and Structures, 29, 1087–1094, 1988.
• 17. C.A. Morales, J.F. Ramírez, Further simplest-expression integrals involving beam eigenfunctions and derivatives, Journal of Sound and Vibration, 253, 518–522, 2002.