Analyzing the Effect of Rotary Inertia and Elastic Constraints on a Beam Supported by a Wrinkle Elastic Foundation: A Numerical Investigation
This article presents a modal analysis of an elastically constrained Rayleigh beam that is placed on an elastic Winkler foundation. The study of beams plays a crucial role in building construction, providing essential support and stability to the structure. The objective of this investigation is to...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-06-01
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| Series: | Buildings |
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| Online Access: | https://www.mdpi.com/2075-5309/13/6/1457 |
| _version_ | 1797595656293974016 |
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| author | Gulnaz Kanwal Rab Nawaz Naveed Ahmed |
| author_facet | Gulnaz Kanwal Rab Nawaz Naveed Ahmed |
| author_sort | Gulnaz Kanwal |
| collection | DOAJ |
| description | This article presents a modal analysis of an elastically constrained Rayleigh beam that is placed on an elastic Winkler foundation. The study of beams plays a crucial role in building construction, providing essential support and stability to the structure. The objective of this investigation is to examine how the vibrational frequencies of the Rayleigh beam are affected by the elastic foundation parameter and the rotational inertia. The results obtained from analytical and numerical methods are presented and compared with the configuration of the Euler–Bernoulli beam. The analytic approach employs the technique of separation of variable and root finding, while the numerical approach involves using the Galerkin finite element method to calculate the eigenfrequencies and mode functions. The study explains the dispersive behavior of natural frequencies and mode shapes for the initial modes of frequency. The article provides an accurate and efficient numerical scheme for both Rayleigh and Euler–Bernoulli beams, which demonstrate excellent agreement with analytical results. It is important to note that this scheme has the highest accuracy for eigenfrequencies and eigenmodes compared to other existing tools for these types of problems. The study reveals that Rayleigh beam eigenvalues depend on geometry, rotational inertia minimally affects the fundamental frequency mode, and linear spring stiffness has a more significant impact on vibration frequencies and mode shapes than rotary spring stiffness. Further, the finite element scheme used provides the most accurate results for obtaining mode shapes of beam structures. The numerical scheme developed is suitable for calculating optimal solutions for complex beam structures with multi-parameter foundations. |
| first_indexed | 2024-03-11T02:39:27Z |
| format | Article |
| id | doaj.art-152c0df91e214c28b80badce771fe455 |
| institution | Directory Open Access Journal |
| issn | 2075-5309 |
| language | English |
| last_indexed | 2024-03-11T02:39:27Z |
| publishDate | 2023-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Buildings |
| spelling | doaj.art-152c0df91e214c28b80badce771fe4552023-11-18T09:38:32ZengMDPI AGBuildings2075-53092023-06-01136145710.3390/buildings13061457Analyzing the Effect of Rotary Inertia and Elastic Constraints on a Beam Supported by a Wrinkle Elastic Foundation: A Numerical InvestigationGulnaz Kanwal0Rab Nawaz1Naveed Ahmed2Department of Mathematics, COMSATS University Islamabad, Park Road, Tarlai Kalan, Islamabad 45550, PakistanDepartment of Mathematics, COMSATS University Islamabad, Park Road, Tarlai Kalan, Islamabad 45550, PakistanCentre for Applied Mathematics and Bioinformatics, Department of Mathematics and Natural Sciences, Gulf University for Science and Technology, Hawally 32093, KuwaitThis article presents a modal analysis of an elastically constrained Rayleigh beam that is placed on an elastic Winkler foundation. The study of beams plays a crucial role in building construction, providing essential support and stability to the structure. The objective of this investigation is to examine how the vibrational frequencies of the Rayleigh beam are affected by the elastic foundation parameter and the rotational inertia. The results obtained from analytical and numerical methods are presented and compared with the configuration of the Euler–Bernoulli beam. The analytic approach employs the technique of separation of variable and root finding, while the numerical approach involves using the Galerkin finite element method to calculate the eigenfrequencies and mode functions. The study explains the dispersive behavior of natural frequencies and mode shapes for the initial modes of frequency. The article provides an accurate and efficient numerical scheme for both Rayleigh and Euler–Bernoulli beams, which demonstrate excellent agreement with analytical results. It is important to note that this scheme has the highest accuracy for eigenfrequencies and eigenmodes compared to other existing tools for these types of problems. The study reveals that Rayleigh beam eigenvalues depend on geometry, rotational inertia minimally affects the fundamental frequency mode, and linear spring stiffness has a more significant impact on vibration frequencies and mode shapes than rotary spring stiffness. Further, the finite element scheme used provides the most accurate results for obtaining mode shapes of beam structures. The numerical scheme developed is suitable for calculating optimal solutions for complex beam structures with multi-parameter foundations.https://www.mdpi.com/2075-5309/13/6/1457Rayleigh beamEuler–Bernoulli beamWinkler foundationnatural frequenciesfinite element method |
| spellingShingle | Gulnaz Kanwal Rab Nawaz Naveed Ahmed Analyzing the Effect of Rotary Inertia and Elastic Constraints on a Beam Supported by a Wrinkle Elastic Foundation: A Numerical Investigation Buildings Rayleigh beam Euler–Bernoulli beam Winkler foundation natural frequencies finite element method |
| title | Analyzing the Effect of Rotary Inertia and Elastic Constraints on a Beam Supported by a Wrinkle Elastic Foundation: A Numerical Investigation |
| title_full | Analyzing the Effect of Rotary Inertia and Elastic Constraints on a Beam Supported by a Wrinkle Elastic Foundation: A Numerical Investigation |
| title_fullStr | Analyzing the Effect of Rotary Inertia and Elastic Constraints on a Beam Supported by a Wrinkle Elastic Foundation: A Numerical Investigation |
| title_full_unstemmed | Analyzing the Effect of Rotary Inertia and Elastic Constraints on a Beam Supported by a Wrinkle Elastic Foundation: A Numerical Investigation |
| title_short | Analyzing the Effect of Rotary Inertia and Elastic Constraints on a Beam Supported by a Wrinkle Elastic Foundation: A Numerical Investigation |
| title_sort | analyzing the effect of rotary inertia and elastic constraints on a beam supported by a wrinkle elastic foundation a numerical investigation |
| topic | Rayleigh beam Euler–Bernoulli beam Winkler foundation natural frequencies finite element method |
| url | https://www.mdpi.com/2075-5309/13/6/1457 |
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