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Zagadnienia własne belki na stochastycznym podłożu Własowa
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Abstrakty
Dynamic eigenproblem of a beam resting on Vlasov's foundation has been analyzed by the Finite Element Method. While the beam properties were applied deterministic, the respective sub-soil parameters were assumed as random variables. Two specific cases of the stochastic description of the foundation of the beam were analyzed: one-dimensional, spatial random field of the sub-soil Young modulus as well as specific cross-correlations of Young modulus and Poisson ratio. The stochastic analysis was carried out using Monte Carlo simulation techniques. Six natural frequencies and modes were obtained by numerical eigenproblem solution in the deterministic example. An analysis of the effect of changes in the coefficient of variation of Young modulus and Poisson ratio on the first four natural frequencies was carried out for various cross-correlation assumptions. Characteristic decrease of mean values of the natural frequencies and respective increase of their standard deviations with the increase of the coefficient of variation of sub-soil Young modulus was observed. Respective variation coefficients of the natural frequencies were calculated too. Following earlier research on stochastic description of soil parameters, a negative correlation between Young modulus and Poisson ratio was assumed. Two extreme cases of cross-correlations of the Young modulus and Poisson ratios were analyzed in the numerical analyses: full (negative) correlation and lack of correlation.
Przeanalizowano zagadnienie własne belki spoczywającej na podłożu Własowa. W sformułowaniu modelu obliczeniowego wykorzystano MES. Przyjęto, że własności materiałowe belki są deterministyczne, podczas gdy parametry materiałowe podłoża gruntowego mają charakter stochastyczny i zostały opisane jako zmienne losowe. W pracy rozważono dwa szczegółowe przypadki losowego opisu podłoża gruntowego: jednowymiarowe pole losowe Younga oraz szczególne przypadki wzajemnej korelacji modułu Younga i liczby Poisson'a. Szczegółową analizę stochastyczną przeprowadzono wykorzystując techniki symulacyjne Metody Monte Carlo. W analizie deterministycznej obliczono sześć pierwszych częstości i postaci drgań własnych. Przeprowadzono analizę wpływu zmian współczynników zmienności modułu Younga i liczby Poissona na cztery częstości drgań własnych dla różnych przypadków założonej korelacji wzajemnej analizowanych parametrów podłoża. Zaobserwowano charakterystyczne zmniejszanie się wartości oczekiwanej i wzrost odpowiednich odchyleń standardowych częstości drgań własnych ze wzrostem współczynnika zmienności modułu Younga gruntu. Wyznaczono także odpowiednie współczynniki zmienności częstości drgań własnych. W nawiązaniu do wcześniejszych badań, przyjęto ujemną korelację między modułem Younga a współczynnikiem Poisson'a. Przeanalizowano dwa skrajne przypadki korelacji wzajemnej modułu Younga i liczby Poissona: pełną (ujemną) korelację oraz całkowity brak korelacji.
Czasopismo
Rocznik
Tom
Strony
447--477
Opis fizyczny
Bibliogr. 58 poz., il.
Twórcy
autor
autor
- Opole University of Technology, Faculty of Civil Engineering, Opole, Poland, b.kaleta@po.opole.pl
Bibliografia
- 1. B. N. ALEMDAR, P. GÜLKAN, Beams on generalized foundations: supplementary element matrices, Engineering Structures, 19, 11, 910-920, 1997.
- 2. E. E. ALONSO, R. J. KRIZEK, Stochastic formulation of soil properties, Proceedings of Int. Conf.; "Applications of Statistics and Probability in Soil and Structural Engineering", Aachen 1975.
- 3. Y. AYVAZ, A. DALOGLU, Earthquake analysis of beams resting on elastic foundations by using a modified Vlasov model, J. of Sound and Vibration, 200, 3, 315-325, 1997.
- 4. Y. AWAZ, O. ÖZGAN, Application of modified Vlasov model to free vibration analysis of beams resting on elastic foundation, J. of Sound and Vibration, 255, l, 111-127, 2002.
- 5. K. J. BATHE, Finite Element Procedures in Engineering Analysis, Prentice-Hall, I Englewood Cliffs, New Jersey 1982.
- 6. J. R. BENJAMIN, C. A. CORNELL, Probability, statistics and decision for civil engineers, McGraw-Hill, New York 1970.
- 7. W. BRZĄKAŁA, Soil properties as random variables [in Polish], Archives of Civil Engineering, 28, 4, 599-606, 1981.
- 8. W. BRZĄKAŁA, W. PUŁA, A probabilistic analysis of foundation settlements, Computers and Geotechnics, 18, 4, 291-309, 1996.
- 9. W. Q. CHEN, F. C. Lü, Z. G. BIAN, A mixed method for bending and free vibration of beams resting on a Pasternak elastic foundation, Applied Mathematical Modelling, 28, 877-890, 2004.
- 10. Y. F. CHENG, C. P. PANTELIDES, Dynamic Timoshenko beams-columns on elastic media, J. of Structures Engineering ASCE, 114, 1988.
- 11. T. CHMIELEWSKI, H. NOWAK, Structural mechanics [in Polish], WNT, Warszawa 1996.
- 12. T. CHMIELEWSKI, P. GÓRSKI, B. KALETA, Exercises in structural mechanics [in Polish], WNT, Warszawa 2002.
- 13. T. CHMIELEWSKI, Z. ZEMBATY, Fundamentals of structural dynamics [in Polish], Arkady, Warszawa 1998.
- 14. J. D. COLLINS, W.T. THOMSON, The eingenvalue problem for structural systems with statistical properties, AIAA Journal, 7, 4, 1969.
- 15. A. M. DE ROSA, Free vibration of Timoshenko beams on two-parameter elastic foundation, Computers & Structures, 57, 151-156, 1995.
- 16. A. DER KIUREGHIAN, J.-D. KE., The stochastic finite element method in structural reliability, Probabilistic Engineering Mechanics, 3, 2, 83-91, 1988.
- 17. Z. DING, A general solution to vibrations of beams on variable Winkler elastic foundation, Computers & Structures, 47, 83-90, 1993.
- 18. M. EISENBERGER, J. BIELAK, Remarks on two papers dealing with the response of beams on two-parameter elastic foundations, Short Communications, Earthquake Engineering and Structural Dynamics, 18, 1077-1078, 1989.
- 19. M. EISENBERGER, Vibration frequencies in beams fn variable one- and two-parameter elastic foundations, J. of Sound and Vibration, 176, 5, 577-584, 1994.
- 20. J. L. W. FAVRE, Statistics, reliability theory and safety factors, Panel discussion. Proc. of 7th ICSMFE Conf., Brighton, 4, 98-99, 1979.
- 21. M. M. FILONIENKO-BORODICH, A very simple model of an elastic foundation capable of spreading the load [in Russian], Transzheldorizdat, 53, Moscow 1945.
- 22. R. L. Fox, M. P. KAPOOR, Rates of conge of eigenvalues and eigenvectors, AIAA Journal, 6, 12, 2426-2429, 1968.
- 23. C. FRANCIOSI, A. MASI, Free vibrations of foundation beams on two-parameter elastic soil, Computers & Structures, 47, 419-426, 1993.
- 24. M. GRYCZMAŃSKI, Analytical and numerical subsoil models for soil-foundation interaction problems, Studia Geotechnica et Mechanica, 16, 3-4, 29-72, 1994.
- 25. R. JONES, J. XENOPHONTOS, The Vlasov foundation model, Int. J. Mech. Sci., 19, 317-323, 1977.
- 26. V. KOLÁŘ, I. NĚMEC, Modelling of soil-structure interaction, Academia, Prague 1989.
- 27. S. KUKLA, Free vibration of a beams supported on a stepped elastic foundation, J. of Sound and Vibration, 149, 259-265, 1991.
- 28. I. K. LEE, W. WHITE, O. G. INGLES, Geotechnical engineering, Pitman Publishing, Ltd., London 1983.
- 29. J. LIPIŃSKI, Machine foundations [in Polish], Arkady, Warszawa 1969.
- 30. G. G. MEYERHOF, Development of geotechnical limit state design, Proceedings of the International Symposium on Limit State Design in Geotechnical Engineering, Copenhagen, 1, 1-12, 1993.
- 31. G. G. MEYERHOF, Development of geotechnical limit state design, Canadian Geotechnical Journal, 32, 128-136, 1995.
- 32. W. MIRONOWICZ, P. ŚNIADY, Dynamics of machine foundation with random parameters, J. of Sound and Vibration, 112, l, 23-30, 1987.
- 33. W. MIRONOWICZ, M. ZOMBROŃ, Random vibration problems of embedded black foundations [in Polish], 46th Conf. KIL i W, PAN i KN, "Krynica 2000".
- 34. N. R. NAIDU, G. V. RAO, Vibration of initially stressed uniform beams on a two-parameter elastic foundation, Computers & Structures, 57, 941-943, 1995.
- 35. G. PALCZAK, M. WITT, Static analysis of beams on stochastic two-parametric elastic foundation [in Polish], 20th Conf. KIL i W PAN i KN, "Krynica 1974".
- 36. P. L. PASTERNAK, On a new method of an elastic foundation by means of two foundation constants [in Russian], Gossizd. Lit. Stroit. Archit., Moscow 1954.
- 37. J. PRZEWŁÓCKI, Randomness in some soil mechanics problems [in Polish], Instytut Budownictwa Wodnego PAN, no.25, Gdańsk 1998.
- 38. W. PUŁA, M. WYJADŁOSKI, Effect of elastic parameters' rondom variability on shallow foundation settlements by finite layer methods, Studia Geotechnica et Mechanica, 21, 3-4, 87-119, 1999.
- 39. W. PUŁA, Application of reliability theory to asses safety of foundations [in Polish], Oficyna Wydawnicza Politechniki Wrocławskiej, Wrocław 2004.
- 40. R. RACKWITZ, Reviewing probabilistic soil modelling, Computers and Geotechnics, 25, 3-4, 199-223, 2000.
- 41. A. G. RAZAQPUR, K. R. SHAH, Exact analysis of beams on two-parameter elastic foundations, Int. J. Solids Structures, 27, 4, 435-454, 1991.
- 42. M. SHINOZUKA, Stochastic fields and their digital simulation, [In:] Schueller G.I. and Shinozuka M. [Eds.], Stochastic methods in structural dynamics, Martinus Nijhoff Publishers, Boston, Mass., 93-133, 1987.
- 43. M. SHINOZUKA, Basic issues in stochastic finite element analysis, [In:] ICASP-5 Proceedings, 5th International Conference on Applications of Statistics and Probability, [Ed.] N. Lind, University of Waterloo Press, Ontario, l, 507-520, Vancouver 1987.
- 44. M. SHINOZUKA, Stochastic fields and their digital simulation, [In:] Stochastic Methods in Structural Dynamics, SCHUËLLER G. I. and SHINOZUKA M., [Eds.] Nijhoff Publishers, Netherlands, 93-133, 1987.
- 45. E. SCHULTZE, Frequency distributions and correlations of soil properties, Proc. of the first Int. Conf. of Statistics and Probability in Soil and Structural Engineering (ICASP), P. Lumb [ed.], Hong-Kong University Press, Hong-Kong, 372-387, 1972.
- 46. P. ŚNIADY, Fundamentals of stochastic structural dynamics [in Polish], Oficyna Wydawnicza Pol. Wrocławskiej, 2000.
- 47. K. SOBCZYK, Stochastic differential equations with applications to physics and engineering, Kluwer, Dortrech, The Netherlands, 1991.
- 48. D. THAMBIRATNAM, Y. ZHUGE, Free vibration analysis of beams on elastic foundation, Computers & Structures, 60, 971-980, 1996.
- 49. W. WEAVER, Jr., P. R. JOHNSTON, Finite element for structural analysis, by Prentice-Hall, Inc. Englewood Cliffs, New Jersey, 1984.
- 50. E. WINKLER, Die Lehre von der Elastiziät und Festigkeit, Dominikus, 1867.
- 51. J. P. WOLF, Dynamic soil-structure interaction, Prentice-Hall, Englewood Cliffs, N. J., 1985.
- 52. A. J. YALSANGKAR, Vibration of beams on a two-parameter elastic Foundation, Proc. Eleventh Canadian congress of Applied Mechanics, University of Alberta Edmonton, 1987.
- 53. E. H. VANMARCKE, Probabilistic modelling of soil profiles, Journal of the Geotechnica Engineering Division, ASCE, 103, GT11, 1227-1246, 1977.
- 54. V. Z. VLASOV, N. N. LEONT'EV, Beams, plates and shells on elastic foundations, Israel Program for Scientific Translations, Jerusalem 1966.
- 55. T. YOKOYAMA, Vibration analysis of Timoshenko beam-columns on two-parameter elastic foundation, Computers & Structures, 61, 995-1007, 1996.
- 56. Z. ZEMBATY, Vibrations of bridge structure under kinematic wave excitations, Journal of Structural Engineering, ASCE, 123, 479-488, 1997.
- 57. Z. ZEMBATY, A. RUTENBERG, Spatial response spectra and site amplification effects, Engineering Structures, 24, 11, 1485-1496, 2002.
- 58. R. ZIELIŃSKI, Random number generators [in Polish], WNT, Warszawa 1970.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BTB2-0042-0051