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。针对工程中常见的波导结构,基于2.5维有限元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,该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。
Modal density is not only a physical quantity to measure stored energy of vibration system, but also one of main parameters of statistical energy analysis subsystem. Its accuracy can directly affect the accuracy of system response prediction. Group velocity is the propagation velocity of structural wave energy, and is an important parameter to characterize characteristics of structural wave. Here, aiming at common waveguide structures in engineering, dispersion curve of a structure was calculated based on the 2.5 D finite element method, the concept of waveform confidence was used to classify characteristic waves corresponding to the dispersion curve, and deduce the expression of characteristic wave group velocity of a waveguide structure. From the point of view of wave, calculation formulas for total modal density and different characteristic wave modal densities of finite length waveguide structure were derived. The wave characteristics and modal density were analyzed and calculated for a single panel and aluminum profiles for high-speed train. The results showed that with increase in frequency, the modal density calculated using the proposed method agrees well with those obtained using other methods;at the cut-on frequency of the structure, the group velocity is zero and the modal density is infinite, but the average modal density in a finite frequency band is finite;near some cut-off frequencies of the structure, the group velocity and modal density may have negative values to reveal the propagation direction of structural wave being opposite to that of energy;through identification of characteristic waves, the modal density calculation under different characteristic waves can be realized;the relevant results can provide a reference basis for dividing similar modal group subsystems in statistical energy analysis.
作者
张淑敏
圣小珍
杨世均
ZHANG Shumin;SHENG Xiaozhen;YANG Shijun(School of Railway,Shandong Polytechnic,Jinan 250104,China;School of Urban Railway Transportation,Shanghai University of Engineering Sciences,Shanghai 201620,China;State Key Lab of Traction Power,Southwest Jiao Tong University,Chengdu 610031,China)
出处
《振动与冲击》
EI
CSCD
北大核心
2022年第5期90-98,共9页
Journal of Vibration and Shock
基金
国家重点研发计划战略性国际科技创新合作重点专项(2016YFE0205200)。
关键词
模态密度
群速度
频散曲线
波导结构
2.5维有限元法
modal density
group velocity
dispersion curve
waveguide structure
2.5D finite element method
