Natural angular frequencies and eigenmodes of orthotropic rectangular parallelepiped with sliding boundary conditions for all faces
Natural angular frequencies and natural vibration modes of the three-dimensional orthotropic rectangular parallelepiped that is not made of layers are investigated. The natural angular frequencies and eigenmodes are calculated as the eigenvalues and eigenvectors of the frequency equation that is der...
| Main Authors: | , |
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| Format: | Article |
| Language: | Japanese |
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The Japan Society of Mechanical Engineers
2023-05-01
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| Series: | Nihon Kikai Gakkai ronbunshu |
| Subjects: | |
| Online Access: | https://www.jstage.jst.go.jp/article/transjsme/89/921/89_22-00112/_pdf/-char/en |
| _version_ | 1797817372739895296 |
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| author | Hiroshi TANABE Shinji TAMURA |
| author_facet | Hiroshi TANABE Shinji TAMURA |
| author_sort | Hiroshi TANABE |
| collection | DOAJ |
| description | Natural angular frequencies and natural vibration modes of the three-dimensional orthotropic rectangular parallelepiped that is not made of layers are investigated. The natural angular frequencies and eigenmodes are calculated as the eigenvalues and eigenvectors of the frequency equation that is derived from the relationship between stress and strain in the x-, y- and z-axes, the equations of motion and the admissible functions of displacements. In the numerical examples, we investigate a three-dimensional orthotropic material and an isotropic material. In the relationship between the dimensions and the natural angular frequencies, there are three ranges where the natural angular frequencies vary linearly, they are almost constant and the intermediate range between them regardless the type of the materials. In the case of the three-dimensional orthotropic material, two natural angular frequencies were almost the same only in the range where the natural angular frequencies vary linearly. All eigenmodes are changed in the intermediate range and are unchanged in the other ranges regardless the type of the materials. In the case of the isotropic material, there is always only one dominant component of eigenvectors, while in the case of the three-dimensional orthotropic material, there are sometimes two. |
| first_indexed | 2024-03-13T08:53:33Z |
| format | Article |
| id | doaj.art-a9be503ed7f44f57880035d372d38651 |
| institution | Directory Open Access Journal |
| issn | 2187-9761 |
| language | Japanese |
| last_indexed | 2024-03-13T08:53:33Z |
| publishDate | 2023-05-01 |
| publisher | The Japan Society of Mechanical Engineers |
| record_format | Article |
| series | Nihon Kikai Gakkai ronbunshu |
| spelling | doaj.art-a9be503ed7f44f57880035d372d386512023-05-29T07:33:06ZjpnThe Japan Society of Mechanical EngineersNihon Kikai Gakkai ronbunshu2187-97612023-05-018992122-0011222-0011210.1299/transjsme.22-00112transjsmeNatural angular frequencies and eigenmodes of orthotropic rectangular parallelepiped with sliding boundary conditions for all facesHiroshi TANABE0Shinji TAMURA1Graduate School of Natural Science and Technology, Shimane UniversityInterdisciplinary Faculty of Science and Engineering, Shimane UniversityNatural angular frequencies and natural vibration modes of the three-dimensional orthotropic rectangular parallelepiped that is not made of layers are investigated. The natural angular frequencies and eigenmodes are calculated as the eigenvalues and eigenvectors of the frequency equation that is derived from the relationship between stress and strain in the x-, y- and z-axes, the equations of motion and the admissible functions of displacements. In the numerical examples, we investigate a three-dimensional orthotropic material and an isotropic material. In the relationship between the dimensions and the natural angular frequencies, there are three ranges where the natural angular frequencies vary linearly, they are almost constant and the intermediate range between them regardless the type of the materials. In the case of the three-dimensional orthotropic material, two natural angular frequencies were almost the same only in the range where the natural angular frequencies vary linearly. All eigenmodes are changed in the intermediate range and are unchanged in the other ranges regardless the type of the materials. In the case of the isotropic material, there is always only one dominant component of eigenvectors, while in the case of the three-dimensional orthotropic material, there are sometimes two.https://www.jstage.jst.go.jp/article/transjsme/89/921/89_22-00112/_pdf/-char/encontinuous systemanisotropyorthotropynatural angular frequencyeigenmode |
| spellingShingle | Hiroshi TANABE Shinji TAMURA Natural angular frequencies and eigenmodes of orthotropic rectangular parallelepiped with sliding boundary conditions for all faces Nihon Kikai Gakkai ronbunshu continuous system anisotropy orthotropy natural angular frequency eigenmode |
| title | Natural angular frequencies and eigenmodes of orthotropic rectangular parallelepiped with sliding boundary conditions for all faces |
| title_full | Natural angular frequencies and eigenmodes of orthotropic rectangular parallelepiped with sliding boundary conditions for all faces |
| title_fullStr | Natural angular frequencies and eigenmodes of orthotropic rectangular parallelepiped with sliding boundary conditions for all faces |
| title_full_unstemmed | Natural angular frequencies and eigenmodes of orthotropic rectangular parallelepiped with sliding boundary conditions for all faces |
| title_short | Natural angular frequencies and eigenmodes of orthotropic rectangular parallelepiped with sliding boundary conditions for all faces |
| title_sort | natural angular frequencies and eigenmodes of orthotropic rectangular parallelepiped with sliding boundary conditions for all faces |
| topic | continuous system anisotropy orthotropy natural angular frequency eigenmode |
| url | https://www.jstage.jst.go.jp/article/transjsme/89/921/89_22-00112/_pdf/-char/en |
| work_keys_str_mv | AT hiroshitanabe naturalangularfrequenciesandeigenmodesoforthotropicrectangularparallelepipedwithslidingboundaryconditionsforallfaces AT shinjitamura naturalangularfrequenciesandeigenmodesoforthotropicrectangularparallelepipedwithslidingboundaryconditionsforallfaces |