基于2.5维有限元的有限长波导结构模态密度计算

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摘要模态密度是衡量振动系统贮存能量大小的物理量，同时也是统计能量分析子系统的主要参数之一，其精度能够直接影响系统响应预测的精度；群速度为结构波能量的传播速度，是表征结构波动特性的重要参数。本文针对工程中常见的波导结构，基于2.5维有限元方法计算结构的频散曲线，利用波形置信度概念对频散曲线对应的特征波进行分类，同时给出波导结构特征波群速度的表达式。从波动角度出发，推导了有限长波导结构总的模态密度和不同特征波模态密度的计算公式。以单板和高速列车用铝型材为例，对其波动特性和模态密度进行分析和计算。研究结果表明，随着频率增加，本文方法计算得到的模态密度和其他方法吻合较好。在结构的截止频率处，群速度为零，模态密度无穷大，但在有限频带内的平均模态密度为有限值；结构的某些截止频率附近，群速度和模态密度可能会存在负值，意味着结构波的传播方向和能量的传播方向相反。通过对特征波的识别，可实现不同特征波下的模态密度计算。相关结果可为统计能量分析中相似模态群子系统的划分提供参考依据。

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	张淑敏1
	圣小珍2
	杨世均3

关键词 ：模态密度, 群速度, 频散曲线, 波导结构, 2.5D有限元法

Abstract：Modal density is one of the main parameters of the statistical energy analysis subsystem, which reflects the energy storage capacity of a vibration system. The accuracy of the modal density can directly influence the prediction accuracy of a subsystem. Group velocity is the speed of the energy of propagation wave, which is an important parameter to study the wave characteristics. In this paper, the dispersion curve of the waveguide structure is firstly calculated based on the two-and-half dimensional finite element method. Different waves are categorized by the concept of wave assurance matrix, and expression of the group velocity of different waves is given. Formulations of the total modal density and different characteristic waves are derived. The wave characteristics and modal density are analyzed and calculated for a single panel and an extruded aluminum panel. Results show that with the increase of frequency, the modal density calculated by the method proposed in this paper agrees well with other methods. At cut-on frequencies, the group velocity is zero and the modal density tends to infinite, but the average modal density in the frequency band is a finite value. The group velocity and modal density may become negative near some cut-on frequencies, which means the propagation direction of the waves and the energy of waves are opposite. The modal density of different waves can be obtained after categorized. Some results can provide reference basis for dividing the subsystems of the statistical energy analysis.

Key words： modal density group velocity dispersion curve waveguide 2.5D finite element method

收稿日期: 2020-10-20 出版日期: 2022-03-15

引用本文:

张淑敏1，圣小珍2，杨世均3. 基于2.5维有限元的有限长波导结构模态密度计算[J]. 振动与冲击, 2022, 41(5): 90-98.
ZHANG Shumin1, SHENG Xiaozhen2, YANG Shijun3. Modal density calculation of finite length waveguide structure based on 2.5D finite element method. JOURNAL OF VIBRATION AND SHOCK, 2022, 41(5): 90-98.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2022/V41/I5/90

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