Analysis of the Spatial Vibration of Nonprismatic Arches by Means of Recurrence Relations for the Coefficients of the Chebyshev Series Expansion of the Solution
PBN-AR
Instytucja
Wydział Inżynierii Kształtowania Środowiska i Geodezji (Uniwersytet Przyrodniczy we Wrocławiu)
Informacje podstawowe
Główny język publikacji
angielski
Czasopismo
MATHEMATICAL PROBLEMS IN ENGINEERING (30pkt w roku publikacji)
ISSN
1024-123X
EISSN
Wydawca
HINDAWI PUBLISHING CORPORATION
DOI
URL
Rok publikacji
2018
Numer zeszytu
Article ID 1512825
Strony od-do
1-27
Numer tomu
Volume 2018
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(liczba autorów: 2)
Pozostali autorzy
+ 1
Open access
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Streszczenia
Język
angielski
Treść
The problem of spatial vibrations, both aperiodically forced and free vibrations, of an arch with an arbitrary distribution of material and geometric parameters is considered. Approximation with Chebyshev series was used to solve a conjugated system of partial differential equations describing the problem. The system of differential equations was solved using an algorithm generating a recursive infinite system of equations, developed by S. Paszkowski in “Numerical applications of Chebyshev polynomials” (in Polish), Warsaw PWN, 1975. Since the coefficients of the obtained system of equations are defined by closed analytical formulas they can be directly used to solve any nonprismatic arch, without it being necessary to solve again the considered problem. The algorithm is highly accurate; i.e., already at a small approximation base it yields results agreeing with exact analytical solutions (obviously for problems in the case of which such solutions can be derived). In order to demonstrate this the eigenfrequencies and eigenvectors obtained for a circular prismatic arch were compared with their precise values determined from the exact analytical solutions. The results yielded by the proposed method were also compared with the results obtained by other methods and by other authors. As an illustration, the proposed method was used to solve a more complex problem, i.e., the problem of the free and aperiodically forced vibrations of a nonprismatic arch with its axis described by a catenary curve. In the example the effect of the lack of cross-sectional symmetry of the arch on the form of the system’s spatial free and forced vibrations was analysed.
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System-identifier
PX-5c51aa11d5de62f432862eb3
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