Eine Plattform für die Wissenschaft: Bauingenieurwesen, Architektur und Urbanistik
Eine Plattform für die Wissenschaft: Bauingenieurwesen, Architektur und Urbanistik
Dynamic Analysis of a Vertically Loaded Rigid Disc in a Functionally Graded Transversely Isotropic Half-Space
https://orcid.org/http://orcid.org/0000-0002-1760-9838
In this paper, a theoretical formulation for the interaction of a rigid disc embedded in a transversely isotropic functionally graded (TIFG) half-space under a time-harmonic vertical vibration is presented. The medium is considered linear elastic, and the exponential variation of properties along the depth is assumed to model the effect of elastic non-homogeneities. The use of potential function accompanied by the integral transform method is applied to handle the equations of motion of the media and formulate the vertical vibration behavior. The governing system of equations of motion for this class of problems can be uncoupled into a solely fourth-order partial differential equation. With the aid of integral transforms, a relaxed treatment of the mixed-boundary value problem is formulated as dual integral equations, which, in turn, is reduced to a Fredholm integral equation of the second kind. The dynamic contact pressure under the disc and the impedance function are analytically evaluated. Due to the complicated integrand functions, the integrals are evaluated numerically, and the results are presented graphically, while the numerical solutions represent the effect of material inhomogeneity through the medium for different frequencies. The numerical scheme which considers the presence of singularities is discussed, and the semi-infinite integral is evaluated using the residue theory. In addition, the cut-off frequency is found explicitly, which gives an alternative solution with a good approximation using a static formulation. Also, the results of the present study might serve as good benchmarks for numerical methods and experimental investigations that consider soil-structure-interaction problems.
Dynamic Analysis of a Vertically Loaded Rigid Disc in a Functionally Graded Transversely Isotropic Half-Space
https://orcid.org/http://orcid.org/0000-0002-1760-9838
In this paper, a theoretical formulation for the interaction of a rigid disc embedded in a transversely isotropic functionally graded (TIFG) half-space under a time-harmonic vertical vibration is presented. The medium is considered linear elastic, and the exponential variation of properties along the depth is assumed to model the effect of elastic non-homogeneities. The use of potential function accompanied by the integral transform method is applied to handle the equations of motion of the media and formulate the vertical vibration behavior. The governing system of equations of motion for this class of problems can be uncoupled into a solely fourth-order partial differential equation. With the aid of integral transforms, a relaxed treatment of the mixed-boundary value problem is formulated as dual integral equations, which, in turn, is reduced to a Fredholm integral equation of the second kind. The dynamic contact pressure under the disc and the impedance function are analytically evaluated. Due to the complicated integrand functions, the integrals are evaluated numerically, and the results are presented graphically, while the numerical solutions represent the effect of material inhomogeneity through the medium for different frequencies. The numerical scheme which considers the presence of singularities is discussed, and the semi-infinite integral is evaluated using the residue theory. In addition, the cut-off frequency is found explicitly, which gives an alternative solution with a good approximation using a static formulation. Also, the results of the present study might serve as good benchmarks for numerical methods and experimental investigations that consider soil-structure-interaction problems.
Dynamic Analysis of a Vertically Loaded Rigid Disc in a Functionally Graded Transversely Isotropic Half-Space
https://orcid.org/http://orcid.org/0000-0002-1760-9838
In this paper, a theoretical formulation for the interaction of a rigid disc embedded in a transversely isotropic functionally graded (TIFG) half-space under a time-harmonic vertical vibration is presented. The medium is considered linear elastic, and the exponential variation of properties along the depth is assumed to model the effect of elastic non-homogeneities. The use of potential function accompanied by the integral transform method is applied to handle the equations of motion of the media and formulate the vertical vibration behavior. The governing system of equations of motion for this class of problems can be uncoupled into a solely fourth-order partial differential equation. With the aid of integral transforms, a relaxed treatment of the mixed-boundary value problem is formulated as dual integral equations, which, in turn, is reduced to a Fredholm integral equation of the second kind. The dynamic contact pressure under the disc and the impedance function are analytically evaluated. Due to the complicated integrand functions, the integrals are evaluated numerically, and the results are presented graphically, while the numerical solutions represent the effect of material inhomogeneity through the medium for different frequencies. The numerical scheme which considers the presence of singularities is discussed, and the semi-infinite integral is evaluated using the residue theory. In addition, the cut-off frequency is found explicitly, which gives an alternative solution with a good approximation using a static formulation. Also, the results of the present study might serve as good benchmarks for numerical methods and experimental investigations that consider soil-structure-interaction problems.
Dynamic Analysis of a Vertically Loaded Rigid Disc in a Functionally Graded Transversely Isotropic Half-Space
Transp. Infrastruct. Geotech.
Kalantari, Maziar (Autor:in) / Khaji, Naser (Autor:in) / Eskandari-Ghadi, Morteza (Autor:in) / Keawsawasvong, Suraparb (Autor:in)
Transportation Infrastructure Geotechnology ; 10 ; 660-684
01.08.2023
25 pages
Aufsatz (Zeitschrift)
Elektronische Ressource
Englisch
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