{"title":"Long-Wave Flexural Vibrations and Deformation of a Small-Size Beam Considering Surface Effects","authors":"G. I. Mikhasev","doi":"10.1134/s0021894424020184","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>A small-size elastic isotropic beam-strip loaded by variable body and surface forces is considered. On the front surfaces, surface shear stresses and inertia are taken into account within the framework of the Gurtin–Murdoch surface elasticity theory. Asymptotically correct equations describing the long-wavelength bending deformation of micro- and nano-beams taking into account shears and surface effects are derived by asymptotic integration of the two-dimensional elasticity equations over the strip thickness. The influence of surface stresses and inertia on the lower spectrum of natural vibrations of metal micro- and nano-beams is studied. It is shown that surface inertia has the same effect on the frequency spectrum of natural flexural vibrations as surface stresses.</p>","PeriodicalId":608,"journal":{"name":"Journal of Applied Mechanics and Technical Physics","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied Mechanics and Technical Physics","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1134/s0021894424020184","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MECHANICS","Score":null,"Total":0}
引用次数: 0
Abstract
A small-size elastic isotropic beam-strip loaded by variable body and surface forces is considered. On the front surfaces, surface shear stresses and inertia are taken into account within the framework of the Gurtin–Murdoch surface elasticity theory. Asymptotically correct equations describing the long-wavelength bending deformation of micro- and nano-beams taking into account shears and surface effects are derived by asymptotic integration of the two-dimensional elasticity equations over the strip thickness. The influence of surface stresses and inertia on the lower spectrum of natural vibrations of metal micro- and nano-beams is studied. It is shown that surface inertia has the same effect on the frequency spectrum of natural flexural vibrations as surface stresses.
期刊介绍：
Journal of Applied Mechanics and Technical Physics is a journal published in collaboration with the Siberian Branch of the Russian Academy of Sciences. The Journal presents papers on fluid mechanics and applied physics. Each issue contains valuable contributions on hypersonic flows; boundary layer theory; turbulence and hydrodynamic stability; free boundary flows; plasma physics; shock waves; explosives and detonation processes; combustion theory; multiphase flows; heat and mass transfer; composite materials and thermal properties of new materials, plasticity, creep, and failure.
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