A Unified Solution for the Vibration Analysis of Lattice Sandwich Beams with General Elastic Supports
Free vibration analyses of lattice sandwich beams with general elastic supports have rarely been discussed in this field’s literature. In this paper, a unified method is proposed to study the free vibration characteristics of lattice sandwich beams under various boundary conditions. The proposed met...
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| Format: | Article |
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MDPI AG
2021-10-01
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| Series: | Applied Sciences |
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| Online Access: | https://www.mdpi.com/2076-3417/11/19/9141 |
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| author | Yeqing Jin Ruiping Yang Hengxu Liu Haiwei Xu Hailong Chen |
| author_facet | Yeqing Jin Ruiping Yang Hengxu Liu Haiwei Xu Hailong Chen |
| author_sort | Yeqing Jin |
| collection | DOAJ |
| description | Free vibration analyses of lattice sandwich beams with general elastic supports have rarely been discussed in this field’s literature. In this paper, a unified method is proposed to study the free vibration characteristics of lattice sandwich beams under various boundary conditions. The proposed method is to convert the three truss cores of lattice sandwich beams into an equivalent homogeneous layer and introduce two different types of constraint springs to simulate the general elastic support boundary at both ends of lattice sandwich beams. By changing the rigidity of the boundary restraint spring, various boundary conditions can be easily obtained without modifying the solving algorithm and solving process. In order to overcome all the discontinuities or jumps associated with the elastic boundary support conditions, the displacement function of lattice sandwich beams is usually obtained as an improved Fourier cosine series along with four sine terms. On this basis, the unknown series coefficients of the displacement function are treated as the generalized coordinates and solved using the Rayleigh–Ritz method. The correctness of the present method is verified through comparison with existing literature. The calculation results of the present method are highly accurate, indicating that the present method is suitable for analyzing the vibration characteristics of lattice sandwich beams with general elastic supports. In addition, the effects of beam length, panel thickness, core height, radius and truss inclination on the natural frequencies of lattice sandwich beams with arbitrary boundary conditions have been discussed in this paper. |
| first_indexed | 2024-03-10T07:05:24Z |
| format | Article |
| id | doaj.art-0c827b381e3f4f419347b94202ab6742 |
| institution | Directory Open Access Journal |
| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-03-10T07:05:24Z |
| publishDate | 2021-10-01 |
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| series | Applied Sciences |
| spelling | doaj.art-0c827b381e3f4f419347b94202ab67422023-11-22T15:48:21ZengMDPI AGApplied Sciences2076-34172021-10-011119914110.3390/app11199141A Unified Solution for the Vibration Analysis of Lattice Sandwich Beams with General Elastic SupportsYeqing Jin0Ruiping Yang1Hengxu Liu2Haiwei Xu3Hailong Chen4Yantai Research Institute and Graduate School, Harbin Engineering University, Yantai 264006, ChinaYantai Research Institute and Graduate School, Harbin Engineering University, Yantai 264006, ChinaYantai Research Institute and Graduate School, Harbin Engineering University, Yantai 264006, ChinaCollege of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, ChinaYantai Research Institute and Graduate School, Harbin Engineering University, Yantai 264006, ChinaFree vibration analyses of lattice sandwich beams with general elastic supports have rarely been discussed in this field’s literature. In this paper, a unified method is proposed to study the free vibration characteristics of lattice sandwich beams under various boundary conditions. The proposed method is to convert the three truss cores of lattice sandwich beams into an equivalent homogeneous layer and introduce two different types of constraint springs to simulate the general elastic support boundary at both ends of lattice sandwich beams. By changing the rigidity of the boundary restraint spring, various boundary conditions can be easily obtained without modifying the solving algorithm and solving process. In order to overcome all the discontinuities or jumps associated with the elastic boundary support conditions, the displacement function of lattice sandwich beams is usually obtained as an improved Fourier cosine series along with four sine terms. On this basis, the unknown series coefficients of the displacement function are treated as the generalized coordinates and solved using the Rayleigh–Ritz method. The correctness of the present method is verified through comparison with existing literature. The calculation results of the present method are highly accurate, indicating that the present method is suitable for analyzing the vibration characteristics of lattice sandwich beams with general elastic supports. In addition, the effects of beam length, panel thickness, core height, radius and truss inclination on the natural frequencies of lattice sandwich beams with arbitrary boundary conditions have been discussed in this paper.https://www.mdpi.com/2076-3417/11/19/9141free vibrationlattice sandwich beamsgeneral elastic supportsimproved Fourier series methodRayleigh-Ritz method |
| spellingShingle | Yeqing Jin Ruiping Yang Hengxu Liu Haiwei Xu Hailong Chen A Unified Solution for the Vibration Analysis of Lattice Sandwich Beams with General Elastic Supports Applied Sciences free vibration lattice sandwich beams general elastic supports improved Fourier series method Rayleigh-Ritz method |
| title | A Unified Solution for the Vibration Analysis of Lattice Sandwich Beams with General Elastic Supports |
| title_full | A Unified Solution for the Vibration Analysis of Lattice Sandwich Beams with General Elastic Supports |
| title_fullStr | A Unified Solution for the Vibration Analysis of Lattice Sandwich Beams with General Elastic Supports |
| title_full_unstemmed | A Unified Solution for the Vibration Analysis of Lattice Sandwich Beams with General Elastic Supports |
| title_short | A Unified Solution for the Vibration Analysis of Lattice Sandwich Beams with General Elastic Supports |
| title_sort | unified solution for the vibration analysis of lattice sandwich beams with general elastic supports |
| topic | free vibration lattice sandwich beams general elastic supports improved Fourier series method Rayleigh-Ritz method |
| url | https://www.mdpi.com/2076-3417/11/19/9141 |
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