Exploring damped and undamped frequencies in beam structures with viscoelastic supports using GFEM and state-space formulation
This study introduces a novel analytical and numerical framework for determining the damped and undamped frequencies of elastically restrained Euler–Bernoulli (EB) and shear beams (SB) supported by two-parameter (visco-Winkler) and three-parameter (visco-Pasternak) viscoelastic foundations (VF). The...
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| Language: | English |
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Elsevier
2025-01-01
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| Series: | Alexandria Engineering Journal |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110016824011360 |
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| author | Gulnaz Kanwal Hani Alahmadi Rab Nawaz Tayyab Nawaz |
| author_facet | Gulnaz Kanwal Hani Alahmadi Rab Nawaz Tayyab Nawaz |
| author_sort | Gulnaz Kanwal |
| collection | DOAJ |
| description | This study introduces a novel analytical and numerical framework for determining the damped and undamped frequencies of elastically restrained Euler–Bernoulli (EB) and shear beams (SB) supported by two-parameter (visco-Winkler) and three-parameter (visco-Pasternak) viscoelastic foundations (VF). The scientific novelty lies in extending the classical separation of variables approach and coupling it with eigenvalue-based dispersion relations to derive an innovative spatial matrix formulation for displacements, slopes, and their derivatives. This method provides enhanced accuracy and robustness, especially in modeling complex vibrational behavior in the presence of damping and shear effects, a challenge often encountered in conventional studies. The research further integrates the Galerkin finite element method (GFEM) to offer a shear locking-free solution, demonstrating convergence to exact results, and thereby addressing critical limitations in previous methods. Additionally, the study introduces the application of state-space formulations combined with the Runge–Kutta method (RK4) to precisely analyze the response of damped systems, which adds significant value in exploring complex beam dynamics. Through a comprehensive comparison of analytical and finite element methods (FEM), the findings are validated and visualized under varying damping conditions, providing practical insights for the design and optimization of structures with viscoelastic supports. The contributions of this work include not only a deeper understanding of the interaction between damping, foundation stiffness, and structural dynamics but also the development of a versatile and scalable approach that broadens the applicability of beam models in advanced engineering applications. |
| format | Article |
| id | doaj-art-3c9667e4758e41b29e00d00d27db599d |
| institution | Kabale University |
| issn | 1110-0168 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Alexandria Engineering Journal |
| spelling | doaj-art-3c9667e4758e41b29e00d00d27db599d2025-01-18T05:03:32ZengElsevierAlexandria Engineering Journal1110-01682025-01-011115877Exploring damped and undamped frequencies in beam structures with viscoelastic supports using GFEM and state-space formulationGulnaz Kanwal0Hani Alahmadi1Rab Nawaz2Tayyab Nawaz3Department of Mathematics, COMSATS University Islamabad, Park Road, Tarlai Kalan, 45550, Islamabad, PakistanDepartment of Mathematics, College of Science, Jouf University, P.0. Box 2014, Sakaka, Saudi Arabia; Corresponding author.Department of Mathematics, COMSATS University Islamabad, Park Road, Tarlai Kalan, 45550, Islamabad, Pakistan; Center for Applied Mathematics and Bioinformatics (CAMB), Gulf University for Science and Technology, 32093 Hawally, KuwaitDepartment of Mathematics, University of Illinois at Urbana Champaign, 1409 W Green St, Urbana, IL 61801, USAThis study introduces a novel analytical and numerical framework for determining the damped and undamped frequencies of elastically restrained Euler–Bernoulli (EB) and shear beams (SB) supported by two-parameter (visco-Winkler) and three-parameter (visco-Pasternak) viscoelastic foundations (VF). The scientific novelty lies in extending the classical separation of variables approach and coupling it with eigenvalue-based dispersion relations to derive an innovative spatial matrix formulation for displacements, slopes, and their derivatives. This method provides enhanced accuracy and robustness, especially in modeling complex vibrational behavior in the presence of damping and shear effects, a challenge often encountered in conventional studies. The research further integrates the Galerkin finite element method (GFEM) to offer a shear locking-free solution, demonstrating convergence to exact results, and thereby addressing critical limitations in previous methods. Additionally, the study introduces the application of state-space formulations combined with the Runge–Kutta method (RK4) to precisely analyze the response of damped systems, which adds significant value in exploring complex beam dynamics. Through a comprehensive comparison of analytical and finite element methods (FEM), the findings are validated and visualized under varying damping conditions, providing practical insights for the design and optimization of structures with viscoelastic supports. The contributions of this work include not only a deeper understanding of the interaction between damping, foundation stiffness, and structural dynamics but also the development of a versatile and scalable approach that broadens the applicability of beam models in advanced engineering applications.http://www.sciencedirect.com/science/article/pii/S1110016824011360Shear beamVisco-Pasternak foundationVisco-Winkler foundationUndamped and damped frequenciesGalerkin finite element methodRK4 |
| spellingShingle | Gulnaz Kanwal Hani Alahmadi Rab Nawaz Tayyab Nawaz Exploring damped and undamped frequencies in beam structures with viscoelastic supports using GFEM and state-space formulation Alexandria Engineering Journal Shear beam Visco-Pasternak foundation Visco-Winkler foundation Undamped and damped frequencies Galerkin finite element method RK4 |
| title | Exploring damped and undamped frequencies in beam structures with viscoelastic supports using GFEM and state-space formulation |
| title_full | Exploring damped and undamped frequencies in beam structures with viscoelastic supports using GFEM and state-space formulation |
| title_fullStr | Exploring damped and undamped frequencies in beam structures with viscoelastic supports using GFEM and state-space formulation |
| title_full_unstemmed | Exploring damped and undamped frequencies in beam structures with viscoelastic supports using GFEM and state-space formulation |
| title_short | Exploring damped and undamped frequencies in beam structures with viscoelastic supports using GFEM and state-space formulation |
| title_sort | exploring damped and undamped frequencies in beam structures with viscoelastic supports using gfem and state space formulation |
| topic | Shear beam Visco-Pasternak foundation Visco-Winkler foundation Undamped and damped frequencies Galerkin finite element method RK4 |
| url | http://www.sciencedirect.com/science/article/pii/S1110016824011360 |
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