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- W4302307788 abstract "The dynamic elasticity problem for rectangular domain is presented in this paper. The conditions of the second main elasticity problem are given at the lateral sides. It is necessary to find the wave field of the rectangular domain under steady state loading. The integral Fourier transform was applied to the formulated boundary value problem and reduced it to a one dimensional vector boundary problem. The last one was solved with the method based on matrix differential calculations which was successfully applied earlier to solve the analogous static problem [1, 2]. As a result, the non-homogeneous one-dimensional boundary problem was derived and solved with the help of Green’s matrix-function apparatus [3]. The wave field is constructed as a superposition of the homogeneous and non-homogeneous solutions and contains the unknown derivative of the displacements. To find this unknown displacement the singular integral equation is derived and solved with the help of the orthogonal polynomial method. Application of the inverse integral Fourier transform finalized the construction of the stated problem solution. The analysis of wave field of the rectangular domain depending on different loading types, frequency values and domain’s size was done." @default.
- W4302307788 created "2022-10-06" @default.
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- W4302307788 date "2022-10-07" @default.
- W4302307788 modified "2023-09-27" @default.
- W4302307788 title "Dynamic Mixed Problem of Elasticity for a Rectangular Domain" @default.
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- W4302307788 doi "https://doi.org/10.1007/978-3-031-15758-5_20" @default.
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