压电层合板理论作为三维问题的渐近逼近

Q3 Mathematics

Pmm Journal of Applied Mathematics and Mechanics Pub Date : 2017-01-01 DOI:10.1016/j.jappmathmech.2017.07.006

I.D. Kochetkov, N.N. Rogacheva

{"title":"压电层合板理论作为三维问题的渐近逼近","authors":"I.D. Kochetkov, N.N. Rogacheva","doi":"10.1016/j.jappmathmech.2017.07.006","DOIUrl":null,"url":null,"abstract":"<div><p><span>A theory of laminated plates, whose central plane coincides with the symmetry plane of the plate, has been constructed by the </span>asymptotic method of reducing the three-dimensional equations of piezoelectricity to the two-dimensional equations of piezoelectric plates without the use of any hypotheses. The plate contains both elastic and piezoelectric layers. The constructed theory is compared with the theories of other authors. As an example, a numerical calculation has been carried out of the piezoelectric state of a circular three-layer plate performing induced harmonic vibrations.</p></div>","PeriodicalId":49686,"journal":{"name":"Pmm Journal of Applied Mathematics and Mechanics","volume":"81 1","pages":"Pages 52-65"},"PeriodicalIF":0.0000,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.jappmathmech.2017.07.006","citationCount":"1","resultStr":"{\"title\":\"Theory of piezoelectric laminated plates as an asymptotic approximation of the three-dimensional problem\",\"authors\":\"I.D. Kochetkov, N.N. Rogacheva\",\"doi\":\"10.1016/j.jappmathmech.2017.07.006\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p><span>A theory of laminated plates, whose central plane coincides with the symmetry plane of the plate, has been constructed by the </span>asymptotic method of reducing the three-dimensional equations of piezoelectricity to the two-dimensional equations of piezoelectric plates without the use of any hypotheses. The plate contains both elastic and piezoelectric layers. The constructed theory is compared with the theories of other authors. As an example, a numerical calculation has been carried out of the piezoelectric state of a circular three-layer plate performing induced harmonic vibrations.</p></div>\",\"PeriodicalId\":49686,\"journal\":{\"name\":\"Pmm Journal of Applied Mathematics and Mechanics\",\"volume\":\"81 1\",\"pages\":\"Pages 52-65\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2017-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/j.jappmathmech.2017.07.006\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Pmm Journal of Applied Mathematics and Mechanics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0021892817300424\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Pmm Journal of Applied Mathematics and Mechanics","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0021892817300424","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}

引用次数: 1

摘要

在不使用任何假设的情况下，采用将三维压电方程简化为二维压电板方程的渐近方法，建立了中心平面与板的对称平面重合的层合板理论。该板包含弹性层和压电层。将所构建的理论与其他作者的理论进行了比较。作为实例，对三层圆板的压电态进行了诱发谐波振动的数值计算。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Theory of piezoelectric laminated plates as an asymptotic approximation of the three-dimensional problem

A theory of laminated plates, whose central plane coincides with the symmetry plane of the plate, has been constructed by the asymptotic method of reducing the three-dimensional equations of piezoelectricity to the two-dimensional equations of piezoelectric plates without the use of any hypotheses. The plate contains both elastic and piezoelectric layers. The constructed theory is compared with the theories of other authors. As an example, a numerical calculation has been carried out of the piezoelectric state of a circular three-layer plate performing induced harmonic vibrations.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Pmm Journal of Applied Mathematics and Mechanics 物理-力学

CiteScore

0.70

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： This journal is a cover to cover translation of the Russian journal Prikladnaya Matematika i Mekhanika, published by the Russian Academy of Sciences and reflecting all the major achievements of the Russian School of Mechanics.The journal is concerned with high-level mathematical investigations of modern physical and mechanical problems and reports current progress in this field. Special emphasis is placed on aeronautics and space science and such subjects as continuum mechanics, theory of elasticity, and mathematics of space flight guidance and control.