Scholarlink

<p>In the low-frequency range of the spectrum, we construct the asymptotics of the frequencies and modes of eigenvibrations of an isotropic and homogeneous elastic junction of thin cylindrical vertical rods and a horizontal plate.The junction surface is free of external loads everywhere except for the rigidly clamped edge of the plate.Several types of vibrations are identified, accompanied by bending deformations of the plate and/or the rods.The justification of the asymptotic formulas is based on an&#xa0;asymptotically sharp anisotropic weighted Korn inequality, a classical lemma on “almost eigenvalues,” and a convergence theorem for normalized eigenvalues.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Deformation of a Thin Elastic Plate with a Fixed Edge and Attached Rods. Part 2: The Spectral Problem

  • 期刊论文

  • 发表日期：

    2025年7月23日

查看全文
  • S. A. Nazarov

摘要

In the low-frequency range of the spectrum, we construct the asymptotics of the frequencies and modes of eigenvibrations of an isotropic and homogeneous elastic junction of thin cylindrical vertical rods and a horizontal plate.The junction surface is free of external loads everywhere except for the rigidly clamped edge of the plate.Several types of vibrations are identified, accompanied by bending deformations of the plate and/or the rods.The justification of the asymptotic formulas is based on an asymptotically sharp anisotropic weighted Korn inequality, a classical lemma on “almost eigenvalues,” and a convergence theorem for normalized eigenvalues.