基于薄板高频振动时三种波场的能量流控制方程，用三角形网格划分板结构，推导了非结构零阶能量有限元的计算格式。并运用该方法计算了L型耦合板和简化的汽车外壳，得到了各波场在空间上的能量密度结果。将计算结果与统计能量法和能量有限元进行了对比,验证了其正确性。计算结果表明，频率很高时面内波能量往往能达到弯曲波能量水平，高频振动仿真时有必要同时考虑三种波场。
Abstract
Base on the governing equations of Energy Flow Analysis (EFA), meshing plates by triangles, an unstructured zero-order energy finite element method (uEFEM0) is developed. A procedure of calculate the L-shape plates and a simplified vehicle shell was presented, in which both bending and in-plane wave fields were considered. The proposed method was used to predict the distribution of energy response. To confirm its validity, Energy Finite Element Method (EFEM) and Statistical Energy Analysis (SEA) were employed to simulate the same structures, and the results show a good agreement. For simulating plates vibrating in high frequency, it is necessary to considering not only bending wave field but also in-plane wave fields, since the level of in-plane wave energy could be close to that of bending wave energy.
关键词
非结构零阶能量有限元 /
耦合板结构 /
多波场高频振动
{{custom_keyword}} /
Key words
unstructured zero-order finite element /
coupled plates structure /
high frequency vibration with multi-wave fields
{{custom_keyword}} /
{{custom_sec.title}}
{{custom_sec.title}}
{{custom_sec.content}}
参考文献
[1] 伍先俊, 朱石坚, 曹建华. 结构声振研究的功率流方法[J]. 力学进展, 2006, 36(3): 363-372.
WU Xian-jun, ZHU Shi-jian, CAO Jian-hua. Review on structural vibration power flow prediction methods[J]. Advances in Mechanics, 2006, 36(3): 363-372.
[2] Nefske D J, Sung S H. Power flow finite element analysis of dynamic systems: basic theory and application to beams[J]. Journal of Vibration Acoustics Stress and Reliability in Design, 1989, 111(1): 94-100.
[3] Wohlever J C, Bernhard R J. Mechanical energy flow models of rods and beams[J]. Journal of Sound and Vibration, 1992, 153(1): 1-19.
[4] 孙丽萍, 聂武. 杆, 梁结构振动能量密度的简化解法[J]. 哈尔滨工程大学学报, 2004, 25(4): 403-406.
SUN Li-ping, NIE Wu. A simplified method for solving energy density of rods and beams[J]. Journal of Harbin Engineering University, 2004, 25(4):403-406.
[5] Bouthier O M, Bernhard R J. Simple models of the energetics of transversely vibrating plates[J]. Journal of Sound and Vibration, 1995, 182(1): 149-164.
[6] 游进, 李鸿光, 孟光. 耦合板结构随机能量有限元分析[J]. 振动与冲击, 2009, 28(11): 43-46.
YOU Jin, LI Hong-guang, MENG Guang. Random energy finite element analysis of coupled plate structures[J]. Journal of Vibration and Shock, 2009, 28(11):43-46.
[7] Wang Shuo. High frequency energy flow analysis methods: Numerical implementation, applications, and verification[D]. Purdue University: United States, 2000.
[8] Moens I. On the use and the validity of the energy finite element method for high frequency vibrations[M]. Duitsland: Faculteit Toegepaste Wetenschappen, 2001. pp230.
[9] Langley R S, Heron K H. Elastic wave transmission through plate/beam junctions[J]. Journal of Sound and Vibration, 1990, 143(2): 241-253.
[10] Dong J, Choi K K, Wang A, et al. Parametric design sensitivity analysis of high‐frequency structural–acoustic problems using energy finite element method[J]. International Journal for Numerical Methods in Engineering, 2005, 62(1): 83-121.
[11] 刘学哲, 余云龙, 王瑞利, 等. 非结构任意多边形网格辐射扩散方程有限体积格式[J]. 数值计算与计算机应用, 2010 31(4): 259-270.
LIU Xue-zhe, YU Yun-long, WANG Rui-li, et al. A cell-centered finite volume scheme for discretizing diffusion equation on unstructured arbitrary polygonal meshes[J], Journal on Numerical Methods and Computer Applications, 2010, 31(4): 259-270.
[12] Bitsie F. The structural-acoustic energy finite-element method and energy boundary-element method[D]. Purdue University: United States, 1996.
[13] Park D H, Hong S Y, Kil H G, et al. Power flow models and analysis of in-plane waves in finite coupled thin plates[J]. Journal of Sound and Vibration, 2001, 244(4): 651-668.
{{custom_fnGroup.title_cn}}
脚注
{{custom_fn.content}}
PDF(1906 KB)
