A Chebyshev Spectral Method with Null Space Approach for Boundary-Value Problems of Euler-Bernoulli Beam
We proposed a Chebyshev spectral method with a null space approach for investigating the boundary-value problem of a nonprismatic Euler-Bernoulli beam with generalized boundary or interface conditions. It is shown here that, with few vital improvements, a Chebyshev spectral collocation approach can...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Shock and Vibration |
| Online Access: | http://dx.doi.org/10.1155/2018/2487697 |
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| author | C. P. Hsu C. F. Hung J. Y. Liao |
| author_facet | C. P. Hsu C. F. Hung J. Y. Liao |
| author_sort | C. P. Hsu |
| collection | DOAJ |
| description | We proposed a Chebyshev spectral method with a null space approach for investigating the boundary-value problem of a nonprismatic Euler-Bernoulli beam with generalized boundary or interface conditions. It is shown here that, with few vital improvements, a Chebyshev spectral collocation approach can be systematically applied to modeling nonprismatic Euler-Bernoulli beams with eigenvalue embedded tip-massed boundary conditions as well as the jump conditions that appear at the stepped interfaces. This study also presents a numerical stable asymptotic modal solution for the higher-order modes of a partially clamped beam and show that the proposed approach validates the robust higher-order modal solutions. Through a sequence of four increasingly complicated examples, using the proposed approach with higher-order modes, generalized boundary conditions, and interface jump conditions of nonprismatic beams, the results are in excellent agreement with those reported in the literature using various other approaches. |
| format | Article |
| id | doaj-art-973a14f31d99459786b4f9a5e5ca32eb |
| institution | Kabale University |
| issn | 1070-9622 1875-9203 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Shock and Vibration |
| spelling | doaj-art-973a14f31d99459786b4f9a5e5ca32eb2025-02-03T01:26:35ZengWileyShock and Vibration1070-96221875-92032018-01-01201810.1155/2018/24876972487697A Chebyshev Spectral Method with Null Space Approach for Boundary-Value Problems of Euler-Bernoulli BeamC. P. Hsu0C. F. Hung1J. Y. Liao2Department of Engineering Science and Ocean Engineering, National Taiwan University, No. 1, Sec. 4, Roosevelt Rd., Taipei, TaiwanDepartment of Engineering Science and Ocean Engineering, National Taiwan University, No. 1, Sec. 4, Roosevelt Rd., Taipei, TaiwanNational Chung Shang Institute of Science and Technology, PB 90008-6-16, Longtang, Taoyuan, TaiwanWe proposed a Chebyshev spectral method with a null space approach for investigating the boundary-value problem of a nonprismatic Euler-Bernoulli beam with generalized boundary or interface conditions. It is shown here that, with few vital improvements, a Chebyshev spectral collocation approach can be systematically applied to modeling nonprismatic Euler-Bernoulli beams with eigenvalue embedded tip-massed boundary conditions as well as the jump conditions that appear at the stepped interfaces. This study also presents a numerical stable asymptotic modal solution for the higher-order modes of a partially clamped beam and show that the proposed approach validates the robust higher-order modal solutions. Through a sequence of four increasingly complicated examples, using the proposed approach with higher-order modes, generalized boundary conditions, and interface jump conditions of nonprismatic beams, the results are in excellent agreement with those reported in the literature using various other approaches.http://dx.doi.org/10.1155/2018/2487697 |
| spellingShingle | C. P. Hsu C. F. Hung J. Y. Liao A Chebyshev Spectral Method with Null Space Approach for Boundary-Value Problems of Euler-Bernoulli Beam Shock and Vibration |
| title | A Chebyshev Spectral Method with Null Space Approach for Boundary-Value Problems of Euler-Bernoulli Beam |
| title_full | A Chebyshev Spectral Method with Null Space Approach for Boundary-Value Problems of Euler-Bernoulli Beam |
| title_fullStr | A Chebyshev Spectral Method with Null Space Approach for Boundary-Value Problems of Euler-Bernoulli Beam |
| title_full_unstemmed | A Chebyshev Spectral Method with Null Space Approach for Boundary-Value Problems of Euler-Bernoulli Beam |
| title_short | A Chebyshev Spectral Method with Null Space Approach for Boundary-Value Problems of Euler-Bernoulli Beam |
| title_sort | chebyshev spectral method with null space approach for boundary value problems of euler bernoulli beam |
| url | http://dx.doi.org/10.1155/2018/2487697 |
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