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Titlebook: Vibrations of Shells and Rods; Khanh Chau Le Book 1999 Springer-Verlag Berlin Heidelberg 1999 asymptotic methods.elasticity.knowledge.mate

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发表于 2025-3-21 18:44:44 | 显示全部楼层 |阅读模式
书目名称Vibrations of Shells and Rods
编辑Khanh Chau Le
视频videohttp://file.papertrans.cn/983/982800/982800.mp4
概述For engineers and advanced students wishing to understand the mathematical point-of-view of vibrations of one- and two-dimensional structures * Develops theories of low- and high-frequency vibrations.
图书封面Titlebook: Vibrations of Shells and Rods;  Khanh Chau Le Book 1999 Springer-Verlag Berlin Heidelberg 1999 asymptotic methods.elasticity.knowledge.mate
描述We live in a world of vibrations and waves, without which there would not be sound, light, radio, television, communication etc. That is why the study of vibrations and waves is so important in many branches of physics and me­ chanics. This book is devoted to the study of small mechanical vibrations of shells and rods, which are made of elastic or piezoelectric materials. But even in this very special field there are already many excellent books and mono­ graphs written since the monumental work by Rayleigh [47]. The peculiarity of the present book is that we regard the equations of shells and rods as two- and one-dimensional approximate equations which can be derived from the three-dimensional theory by using the variational-asymptotic method. The latter has been invented especially for those variational problems which contain small parameters. It turns out that for vibrations of shells and rods there are many situations in which such small parameters exist. Thus, the application of the variational-asymptotic method enables one to derive not only the classical two- and one-dimensional theories of low-frequency vibra­ tions of shells and rods, but also the theories of high-frequenc
出版日期Book 1999
关键词asymptotic methods; elasticity; knowledge; materials; mechanics; shells; vibration
版次1
doihttps://doi.org/10.1007/978-3-642-59911-8
isbn_softcover978-3-642-64179-4
isbn_ebook978-3-642-59911-8
copyrightSpringer-Verlag Berlin Heidelberg 1999
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发表于 2025-3-22 00:02:17 | 显示全部楼层
Piezoelectric shellsby electrodes, and the time-dependent voltage, ϕ.(.), be specified on them. The problem is to construct a two-dimensional theory of piezoceramic shells that enables one to determine their resonant vibrations in a wide range of frequencies.
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Elastic shells called an elastic shell, the surface . its middle surface, and . its thickness. A plate is the special case of the shell, whose middle surface is plane. The shell is said to be thin if . is much smaller than the characteristic sizes as well as the radius of curvature of the middle surface
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Preliminariesare denoted . .... In a chosen fixed cartesian co-ordinate system a point . corresponds to a triple (., ., .), with . being its i-th co-ordinate. The translation space of ., is denoted by ν it is a three-dimensional vector space. Elements of ν are called (spatial) vectors and are denoted with boldfa
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Elastic shells three-dimensional Euclidean space ɛ, bounded by a smooth closed curve ∂. (in the case of closed surfaces ∂. = ∅). The surface is described by a vector equation.=.(.,.),.where . is a smooth vector-value function of two variables ., .. At each point of the middle surface we restore the segment of len
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