各向异性板的面导纳特性研究

目前在工程上各向异性结构中的振动问题和振动能量传递的问题越来越多,然而对各向异性结构导纳的研究还不充分,对各向异性板面导纳的研究也还处于萌芽状态.面导纳不仅反映结构的振动特性还能反映能量传递的特性,因此面导纳比点导纳在工程上更加贴合实际.论文根据理论公式获得了一般各向异性板面导纳的理论解,并与有限元模型的数值解对比发现两者有较好的一致性.作者采用有限元方法深入研究了各向异性板的弹性常数、板的尺寸大小及边界条件等对面导纳及其点导纳和面导纳差异值的影响,力求给工程测量和实际运用提供指导.研究发现增加激励面积、减小结构刚度及阻尼系数会使点、面导纳差异变大,剪切模量对板振动特性的影响远小于弹性模量,一般各向异性板模型退化为正交各向异性板模型会使点、面导纳差异变大,加大板的面积及增加阻尼系数有利于缩减导纳的波动范围,边界条件对板减振性能的影响较小.

Study of Surface Mobility of Anisotropic Plates

The surface mobility of anisotropic plates with different materials, geometric properties and boundary conditions is studied. Surface mobility, which reflects the characteristics of not only the vibration but also the power transmission of structures, is more practical than point mobility in engineering. There are more and more problems about structural vibration and vibration power transmission of anisotropic materials in engineering; however, research on the surface mobility of such structures is insufficient. In this study, according to the theoretical formula, the surface mobility of the orthotropic plate is obtained and compared with the numerical solution of the finite element model. It is found that the two solutions are in good agreement. In this paper, the finite element method is used to study the influence of elastic constants, size of the plate and boundary conditions on the surface mobility and the difference between the point mobility and the surface mobility of the anisotropic plate. It is found that increasing the excitation area and reducing the structural stiffness and the damping coefficient of the structure will make the difference between the point mobility and the surface mobility larger. The influence of shear modulus on the vibration characteristics of the plate is far less than that of elastic modulus. Reducing the model of the anisotropic plate to the model of an orthotropic plate but keeping both shear modulus and elastic modulus unchanged will also make the difference between the point mobility and the surface mobility larger. Increasing the size and the damping coefficient of the plate can reduce the range of mobility fluctuation, and the boundary conditions have little influence on the vibration reduction performance of the plate. These results can be applied to the investigation of the vibration power transmission of anisotropic plate-like structures in civil engineering, aeronautical engineering and mechanical engineering.