Eigenvalue problem of a beam stochastic Vlasov foundation

Kaleta, B.; Zembaty, Z.

Artykuł - szczegóły

Tytuł artykułu

Eigenvalue problem of a beam stochastic Vlasov foundation

Autorzy

Kaleta B. , Zembaty Z.

Wybrane pełne teksty z tego czasopisma

Identyfikatory

Warianty tytułu

Zagadnienia własne belki na stochastycznym podłożu Własowa

Języki publikacji

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.

Słowa kluczowe

beams elastic foundation Vlasov soil stochastic eigenproblem Monte Carlo simulation

belka zagadnienie własne podłoże Własowa podłoże stochastyczne symulacja Monte Carlo

Wydawca

Komitet Inżynierii Lądowej i Wodnej PAN
Politechnika Warszawska, Wydział Inżynierii Lądowej

Czasopismo

Archives of Civil Engineering

Rocznik

2007

Tom

Vol. 53, nr 3

Strony

447--477

Opis fizyczny

Bibliogr. 58 poz., il.

Twórcy

autor

Kaleta B.

autor

Zembaty Z.

Opole University of Technology, Faculty of Civil Engineering, Opole, Poland, b.kaleta@po.opole.pl

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Bibliografia

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