Chao Zhou, Zhuofan Ni, Xinran Zheng, Bo Wang, Rui Li
{"title":"辛解框架下矩形夹芯板的新基准自由振动解","authors":"Chao Zhou, Zhuofan Ni, Xinran Zheng, Bo Wang, Rui Li","doi":"10.1177/10996362221106780","DOIUrl":null,"url":null,"abstract":"In this paper, the first attempt is made to obtain some new analytic free vibration solutions of rectangular sandwich panels within the symplectic solution framework, which are difficult to tackle within the conventional analytic solution framework. The sandwich panels with honeycomb and truss cores are first treated as equivalent thick plates. The governing dual equation is then established within the Hamiltonian system. Subsequently, the original problem is converted into two subproblems whose analytic solutions are acquired by applying the variable separation and symplectic eigen expansion. The superposition yields the final analytic free vibration solution, with the emerging coefficients determined according to the equivalence between the original problem and the superposition. The natural frequency and mode shape solutions by the present symplectic superposition method are quantitatively shown via numerical and graphical results, respectively, and are all well validated by consistency with classical solutions, experimental results, or the numerical solutions by the refined finite element modeling. Besides providing the new results that can serve as benchmarks, the effects of the size parameters on the natural frequencies of the sandwich panels are also analyzed. Since the developed method gives up the assumption of any trial solutions and follows a rigorous derivation to yield new analytic solutions, it provides opportunities for solving more intricate problems of sandwich panels and shells.","PeriodicalId":17215,"journal":{"name":"Journal of Sandwich Structures & Materials","volume":null,"pages":null},"PeriodicalIF":3.5000,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"On new benchmark free vibration solutions of rectangular sandwich panels within the symplectic solution framework\",\"authors\":\"Chao Zhou, Zhuofan Ni, Xinran Zheng, Bo Wang, Rui Li\",\"doi\":\"10.1177/10996362221106780\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, the first attempt is made to obtain some new analytic free vibration solutions of rectangular sandwich panels within the symplectic solution framework, which are difficult to tackle within the conventional analytic solution framework. The sandwich panels with honeycomb and truss cores are first treated as equivalent thick plates. The governing dual equation is then established within the Hamiltonian system. Subsequently, the original problem is converted into two subproblems whose analytic solutions are acquired by applying the variable separation and symplectic eigen expansion. The superposition yields the final analytic free vibration solution, with the emerging coefficients determined according to the equivalence between the original problem and the superposition. The natural frequency and mode shape solutions by the present symplectic superposition method are quantitatively shown via numerical and graphical results, respectively, and are all well validated by consistency with classical solutions, experimental results, or the numerical solutions by the refined finite element modeling. Besides providing the new results that can serve as benchmarks, the effects of the size parameters on the natural frequencies of the sandwich panels are also analyzed. Since the developed method gives up the assumption of any trial solutions and follows a rigorous derivation to yield new analytic solutions, it provides opportunities for solving more intricate problems of sandwich panels and shells.\",\"PeriodicalId\":17215,\"journal\":{\"name\":\"Journal of Sandwich Structures & Materials\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":3.5000,\"publicationDate\":\"2022-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Sandwich Structures & Materials\",\"FirstCategoryId\":\"88\",\"ListUrlMain\":\"https://doi.org/10.1177/10996362221106780\",\"RegionNum\":3,\"RegionCategory\":\"材料科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"ENGINEERING, MECHANICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Sandwich Structures & Materials","FirstCategoryId":"88","ListUrlMain":"https://doi.org/10.1177/10996362221106780","RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, MECHANICAL","Score":null,"Total":0}
On new benchmark free vibration solutions of rectangular sandwich panels within the symplectic solution framework
In this paper, the first attempt is made to obtain some new analytic free vibration solutions of rectangular sandwich panels within the symplectic solution framework, which are difficult to tackle within the conventional analytic solution framework. The sandwich panels with honeycomb and truss cores are first treated as equivalent thick plates. The governing dual equation is then established within the Hamiltonian system. Subsequently, the original problem is converted into two subproblems whose analytic solutions are acquired by applying the variable separation and symplectic eigen expansion. The superposition yields the final analytic free vibration solution, with the emerging coefficients determined according to the equivalence between the original problem and the superposition. The natural frequency and mode shape solutions by the present symplectic superposition method are quantitatively shown via numerical and graphical results, respectively, and are all well validated by consistency with classical solutions, experimental results, or the numerical solutions by the refined finite element modeling. Besides providing the new results that can serve as benchmarks, the effects of the size parameters on the natural frequencies of the sandwich panels are also analyzed. Since the developed method gives up the assumption of any trial solutions and follows a rigorous derivation to yield new analytic solutions, it provides opportunities for solving more intricate problems of sandwich panels and shells.
期刊介绍:
The Journal of Sandwich Structures and Materials is an international peer reviewed journal that provides a means of communication to fellow engineers and scientists by providing an archival record of developments in the science, technology, and professional practices of sandwich construction throughout the world. This journal is a member of the Committee on Publication Ethics (COPE).