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Finite element modal analysis of two-dimensional heterogeneous elastic structures with variable material parameters | ||
| Journal of Mathematical Modeling | ||
| مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 19 شهریور 1405 اصل مقاله (3.32 M) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22124/jmm.2026.33701.3096 | ||
| نویسندگان | ||
| Hamzah Bakhti* ؛ Najat Magouh | ||
| M2CS, STIS Research Center, ENSAM, Mohammed V University in Rabat, 10100, Rabat, Morocco | ||
| چکیده | ||
| The finite element method is used for the modal analysis of two-dimensional composite elastic structures with space-dependent material parameters. The scope is limited to two-dimensional, linear, isotropic, perfectly bonded composites under plane strain. The numerical examples represent multilayer and particle-reinforced composites with explicitly resolved particle regions, while the formulation also permits smoothly varying coefficients for functionally graded materials. The study combines variable-material modeling and finite element modal analysis within a unified framework. The elastodynamic problem is formulated in weak form, and the properties of the associated variable-coefficient elasticity operator are established under standard assumptions. The dynamic model is then approximated using finite elements to study the effects of geometric and material properties on the natural frequencies and mode shapes. A mesh-refinement study confirms convergence of the first six frequencies and stability of the associated mode shapes. A global bending-frequency consistency check is performed against the Euler--Bernoulli solution for a homogeneous clamped--clamped layer, while the heterogeneous cases are treated as parametric applications. For the prescribed multilayer configurations, the computed frequencies increase with the stiffness or thickness ratio and decrease with the density ratio. For the particle-reinforced composite, the two-dimensional particle area fraction produces a non-monotonic frequency response, which is interpreted qualitatively in terms of the stiffness--inertia balance. These findings demonstrate the ability of the proposed model to capture the main modal features of heterogeneous elastic structures. | ||
| کلیدواژهها | ||
| Finite element method؛ modal analysis؛ heterogeneous elastic structures؛ composite materials؛ natural frequencies and vibration modes | ||
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آمار تعداد مشاهده مقاله: 8 تعداد دریافت فایل اصل مقاله: 4 |
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