Description of Plates with the Matrix Klein–Gordon Equation.
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| Title: | Description of Plates with the Matrix Klein–Gordon Equation. |
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| Authors: | Kniazeva, K. S.1 (AUTHOR) knyazevaks05@gmail.com, Shelest, E. L.1 (AUTHOR), Shanin, A. V.1 (AUTHOR) |
| Source: | Acoustical Physics. Oct2025, Vol. 71 Issue 5, p675-682. 8p. |
| Subjects: | Klein-Gordon equation, Structural plates, Vibration (Mechanics), Waveguides, Finite element method, Differential equations |
| Abstract: | The matrix Klein–Gordon equation (MKGE) describes waveguides with a discrete structure of their cross section. It may also be considered as a continuous waveguide model constructed by applying the waveguide finite element method. In this paper, the possibility of describing the bending vibrations of a thin plate with MKGE is studied. The problem is not trivial, as MKGE contains second-order time and coordinate derivatives, and bending vibrations are described by an equation with a fourth-order coordinate derivative. In this paper, matrix Klein–Gordon equations of different dimensions are derived for a plate. It is shown that a linear approximation of plate deformation over a cross section leads to overestimated plate stiffness values, but more complicated models give correct values. [ABSTRACT FROM AUTHOR] |
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| Database: | Engineering Source |
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| Abstract: | The matrix Klein–Gordon equation (MKGE) describes waveguides with a discrete structure of their cross section. It may also be considered as a continuous waveguide model constructed by applying the waveguide finite element method. In this paper, the possibility of describing the bending vibrations of a thin plate with MKGE is studied. The problem is not trivial, as MKGE contains second-order time and coordinate derivatives, and bending vibrations are described by an equation with a fourth-order coordinate derivative. In this paper, matrix Klein–Gordon equations of different dimensions are derived for a plate. It is shown that a linear approximation of plate deformation over a cross section leads to overestimated plate stiffness values, but more complicated models give correct values. [ABSTRACT FROM AUTHOR] |
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| ISSN: | 10637710 |
| DOI: | 10.1134/S1063771025600433 |
