Abstract This paper considers the classical methods of surface damping of bending vibrations of thin-walled structures and a promising integral version of a damping coating consisting of two layers of a material with pronounced viscoelastic properties separated by a thin reinforcing layer of a high modulus material. A finite element with 14 degrees of freedom for modeling an elongated plate with the specified damping coating has been developed with consideration of the transverse compression of damping layers under high-frequency vibrations of the plate. The generalized problem of complex eigenvalues in the lower part of the spectrum of complex modes and frequencies of free vibrations of a damped plate is solved by the subspace iteration method taking into account the frequency dependence of the dynamic elastic moduli of the material. The damping properties of the plate are determined from the imaginary parts of the complex eigenfrequencies and the relative energy dissipation at resonance.

中文翻译：

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具有整体阻尼涂层的细长板的复杂特征频率和阻尼特性

摘要 本文考虑了薄壁结构弯曲振动的经典表面阻尼方法和有前途的阻尼涂层的整体版本，该阻尼涂层由两层具有显着粘弹性的材料组成，由高模量材料的薄增强层隔开。已经开发了一个具有 14 个自由度的有限元，用于模拟具有指定阻尼涂层的细长板，并考虑了在板的高频振动下阻尼层的横向压缩。考虑到材料的动态弹性模量的频率依赖性，通过子空间迭代方法解决了阻尼板的复模态谱和自由振动频率的下半部分复特征值的广义问题。