The classical methods of surface damping of bending vibrations of thin-walled structures and a promising integrated version with a damping coating consisting of two layers of a material with pronounced viscoelastic properties and an intermediate thin reinforcing layer of a high-modulus material are discussed. A four-layer finite element for an elongate plate with an integral damping coating is developed taking into account the lateral compression of the damping layers. A system of governing equations of the finite-element method is constructed for analyzing the dynamic response of the plate during its resonant vibrations. Iterative algorithms have been developed to take into account the amplitude dependence of the logarithmic decrements of vibrations of material of the damping layers when determining the damping properties of the plate and determining its vibration eigenmodes and eigenfrequencies with consideration of frequency dependence of the dynamic elastic moduli of the material. Numerical experiments were carried out to test the finite element developed and the iterative algorithms mentioned. The influence of aerodynamic resistance forces on the overall damping level of a cantilever plate with an integral damping coating is assessed.

中文翻译：

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带整体阻尼涂层的细长板共振的数值模拟

讨论了薄壁结构弯曲振动的经典表面阻尼方法和有前途的集成版本，阻尼涂层由两层具有显着粘弹性的材料和高模量材料的中间薄增强层组成。考虑到阻尼层的横向压缩，开发了一种用于带有整体阻尼涂层的细长板的四层有限元。构建了有限元方法的控制方程系统，用于分析板在共振期间的动态响应。在确定板的阻尼特性和确定其振动本征模式和本征频率时，已经开发了迭代算法来考虑阻尼层材料振动的对数衰减的幅度依赖性，同时考虑到板的动态弹性模量的频率依赖性。材料。进行了数值实验来测试所开发的有限元和提到的迭代算法。评估了空气动力阻力对具有整体阻尼涂层的悬臂板的整体阻尼水平的影响。进行了数值实验来测试所开发的有限元和提到的迭代算法。评估了空气动力阻力对具有整体阻尼涂层的悬臂板的整体阻尼水平的影响。进行了数值实验来测试所开发的有限元和提到的迭代算法。评估了空气动力阻力对具有整体阻尼涂层的悬臂板的整体阻尼水平的影响。