{"title":"可压缩流体中多孔弹性夹层板的有效边界条件","authors":"F. G. Leppington","doi":"10.1098/rspa.1990.0019","DOIUrl":null,"url":null,"abstract":"The transmission of sound through a sandwich panel, consisting of a honeycomb cellular structure bounded by two thin elastic plates, is considerably reduced at a certain frequency if one (or both) of the plates is perforated so as to link a significant number of the cells to the exterior fluid. This effect occurs at or near the Helmholtz resonance frequency for the cells, with the acoustic wavelength large compared with the cell dimensions. An analysis is given for the problem of plane waves incident upon a plane sandwich plate of infinite extent, using matched expansions, for the cases of acoustically hard or acoustically transparent cell walls. The compound panel is shown to be acoustically equivalent to that of a hypothetical surface with different normal velocities on either side and effective boundary conditions are derived, with generalizations to deal with more complicated structures, finite plates and more general incident fields.","PeriodicalId":20605,"journal":{"name":"Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences","volume":"16 1","pages":"385 - 399"},"PeriodicalIF":0.0000,"publicationDate":"1990-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"17","resultStr":"{\"title\":\"The effective boundary conditions for a perforated elastic sandwich panel in a compressible fluid\",\"authors\":\"F. G. Leppington\",\"doi\":\"10.1098/rspa.1990.0019\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The transmission of sound through a sandwich panel, consisting of a honeycomb cellular structure bounded by two thin elastic plates, is considerably reduced at a certain frequency if one (or both) of the plates is perforated so as to link a significant number of the cells to the exterior fluid. This effect occurs at or near the Helmholtz resonance frequency for the cells, with the acoustic wavelength large compared with the cell dimensions. An analysis is given for the problem of plane waves incident upon a plane sandwich plate of infinite extent, using matched expansions, for the cases of acoustically hard or acoustically transparent cell walls. The compound panel is shown to be acoustically equivalent to that of a hypothetical surface with different normal velocities on either side and effective boundary conditions are derived, with generalizations to deal with more complicated structures, finite plates and more general incident fields.\",\"PeriodicalId\":20605,\"journal\":{\"name\":\"Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences\",\"volume\":\"16 1\",\"pages\":\"385 - 399\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1990-02-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"17\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1098/rspa.1990.0019\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1098/rspa.1990.0019","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The effective boundary conditions for a perforated elastic sandwich panel in a compressible fluid
The transmission of sound through a sandwich panel, consisting of a honeycomb cellular structure bounded by two thin elastic plates, is considerably reduced at a certain frequency if one (or both) of the plates is perforated so as to link a significant number of the cells to the exterior fluid. This effect occurs at or near the Helmholtz resonance frequency for the cells, with the acoustic wavelength large compared with the cell dimensions. An analysis is given for the problem of plane waves incident upon a plane sandwich plate of infinite extent, using matched expansions, for the cases of acoustically hard or acoustically transparent cell walls. The compound panel is shown to be acoustically equivalent to that of a hypothetical surface with different normal velocities on either side and effective boundary conditions are derived, with generalizations to deal with more complicated structures, finite plates and more general incident fields.