Dynamic Characteristic Analysis of Constrained Damping Plate Based on Iterative Revised Modal Strain Energy Method
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摘要:
忽略约束阻尼结构阻尼层黏弹性材料虚刚度及参数频变特性会对计算该结构模态损耗因子带来误差. 本文在修正模态应变能法（RMSE法）的基础上，结合迭代算法，分析了黏弹性材料虚刚度及参数频变特性对约束阻尼板的振型、固有频率和模态损耗因子的影响，探讨了约束阻尼板阻尼层厚度和约束层厚度对结构模态损耗因子的影响规律. 分析结果表明：本文方法计算的固有频率和模态损耗因子与相关文献中的试验实测值吻合良好；不考虑黏弹性材料参数频变特性，各阶模态振型形状基本不变，但部分振型的相位相反；阻尼层剪切模量直接影响到结构固有频率，忽略其频变特性会导致在低阶时计算结果偏大17.2%，高阶时偏小7.6%；低阶模态时，忽略黏弹性材料频变特性的模态损耗因子误差最大可到56.0%；约束阻尼板模态损耗因子随阻尼层厚度增加而增大，随约束层厚度增加先增大后减小.
Abstract:The neglect of the imaginary stiffness and frequency-dependent characteristic of parameters of viscoelastic materials for the damping layer of the constrained damping structure will result in the error of the modal loss factor of the structure. The influence of the imaginary stiffness and frequency-dependent characteristic of parameters of viscoelastic materials on the modes of vibration, natural frequencies, and modal loss factors of the constrained damping plate was investigated by using the revised modal strain energy (RMSE) method and iterative algorithm. Moreover, the influence of the thickness of the damping layer and that of the constrained layer of the constrained damping plate on the modal loss factor of the structure was discussed. The results show that the natural frequency and modal loss factor calculated by the method in the paper are in good agreement with the experimentally measured values in the related literature. The modal shapes at all orders are not changed, but a reversal of the phase of several modes of vibration occurs if the frequency-dependent characteristic of parameters of viscoelastic materials is ignored. The shear modulus of the damping layer directly affects the natural frequency of the structure. If the frequency-dependent characteristic is ignored, the calculation results will be overestimated by 17.2% at the lower-order modal and underestimated by 7.6% at the higher-order modal. The maximum error of the modal loss factor is up to 56.0% at lower order modal when the frequency-dependent characteristic of the viscoelastic material is ignored. The modal loss factor of the constrained damping plate increases with the damping layer thickness and first goes up and then goes down with the constrained layer thickness.
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Key words:
- constrained damping plate /
- iterative method /
- natural frequency /
- mode of vibration /
- modal loss factor
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图 2 ISD-112阻尼材料频变特性
Figure 2. Frequency-dependent characteristics of damping material ISD-112
图 4 迭代前后各阶固有频率对比
Figure 4. Comparison of intrinsic frequencies before and after iteration
图 6 不同阻尼层厚度下CLD板模态损耗因子
Figure 6. Modal loss factors of CLD plate under various thicknesses of damping layer
图 7 不同约束层厚度下CLD板模态损耗因子
Figure 7. Modal loss factors of CLD plate under various thicknesses of constraint layer
表 1 文献[23]模型参数
Table 1. Model parameters in reference [23]
项目 长度/
mm宽度/
mm厚度/
mm密度/
（kg•m−3）泊松比 基层 260 200 2 2800 0.33 阻尼层 260 200 1 999 0.49 约束层 260 200 1 2800 0.33 
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表 2 试验与计算结果比较
Table 2. Comparison of experimental and calculated results
阶数 固有频率/Hz 模态损耗因子 试验
结果RMSE
迭代MSE
迭代试验
结果RMSE
迭代MSE
迭代1 23.1 24.0 24.0 0.21 0.15 0.15 2 90.6 86.6 80.2 0.28 0.29 0.37 3 191.9 187.4 170.6 0.31 0.31 0.44
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表 3 模型参数
Table 3. Model parameters
项目 长度/
m宽度/
m厚度/
mm密度/
（kg•m−3）泊松比 基层 0.348 0.3048 0.762 2735 0.30 阻尼层 0.348 0.3048 0.254 1300 0.49 约束层 0.348 0.3048 0.762 2735 0.30
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