Energy Density Analysis of Irregular Shaped Plates Based on Power Flow Finite Element Method
LIU Zhi-hui 1 NIU Jun-chuan 1,2 Zhou Yi-qun 1
1. School of Mechanical Engineering, Shandong University, Jinan 250061, China;
2. Key Laboratory of High Efficiency and Clean Mechanical Manufacture, Shandong University, Jinan 200215, China
It has the important significance to analyze and predict the vibration response of the structures under the different frequency. The power flow finite element method has become a research focus of the vibration analysis due to the advantages of the broad applicable frequency range and the detail information provided. The power flow finite element method is implemented to solve the flexural wave energy density of the thin plate, and the weighted residual method is used to derive the residual of the node points. The linear quadrilateral mesh is used to partition the thin plate and the element’s finite element equation is derived, then the global finite element equation is assembled and solved, and the energy density of the nodes is get. The linear triangular element is introduced to partition the plate with complex shape. The research is meaningful for the implementation of the power flow element method on the thin plate with the arbitrary shape.
刘知辉 1,牛军川 1,2,周一群 1. 基于功率流有限元方法的异形薄板能量密度求解[J]. 振动与冲击, 2017, 36(16): 188-194.
LIU Zhi-hui 1 NIU Jun-chuan 1,2 Zhou Yi-qun 1. Energy Density Analysis of Irregular Shaped Plates Based on Power Flow Finite Element Method. JOURNAL OF VIBRATION AND SHOCK, 2017, 36(16): 188-194.
[1] 宋孔杰,张蔚波,牛军川. 功率流理论在柔性振动控制技术中的应用与发展 [J]. 机械工程学报, 2003, 39(9): 23-28.
Song Kong-jie, Zhang Wei-bo, Niu Jun-chuan. Application and development of power flow theories in the field of the vibration control for flexible system [J]. Chinese Journal of Mechanical Engineering, 2003, 39(9): 23-28
[2] Cho P E. Energy flow analysis of coupled structures [D]. United States: Purdue University, 1993.
[3] 朱继清. 基于能量流有限元的耦合结构振动传递特性分析 [D]. 济南:山东大学, 2011.
Zhu Ji-qing. Vibration transmission characteristic analysis of coupling structure by energy finite element method [D]. Jinan: Shandong University, 2011
[4] 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, 1989, 111(1): 94-100.
[5] 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.
[6] Cho P E, Bernhard R J. Energy flow analysis of coupled beams [J]. Journal of Sound and Vibration, 1998, 211(4): 593-605.
[7] Song J H, Hong S Y, Kang Y, et al. Vibrational energy flow analysis of penetration beam-plate coupled structures [J]. Journal of Mechanical Science and Technology, 2011, 25(3): 567-576.
[8] Bouthier O M, Bernhard R J. Simple models of energy flow in vibrating membranes [J]. Journal of Sound and Vibration. 1995, 182(1): 129-147.
[9] Bouthier O M, Bernhard R J. Simple models of the energetics of transversely vibrating plates [J]. Journal of Sound and Vibration, 1995, 182(1): 149-166.
[10] 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.
[11] 李坤朋. 基于能量有限元法的板耦合结构振动特性分析 [D]. 济南:山东大学, 2013.
Li Kun-peng. Energy finite element method for vibration analysis of coupled-plates structures [D]. Jinan: Shandong University, 2013
[12] Niu Jun-chuan, Li Kun-peng. Energy flow finite element analysis of L-shaped plate including three types of waves [J]. Applied Mechanics and Materials, 2013, 353-356: 3365-3368
[13] Niu Jun-chuan, Li Kun-peng. Energy finite element analysis of n-shaped plate structures with three types of wave [J], Journal of Vibration Engineering and Technologies, 2015, 3(5): 615-625
[14] 江民圣,牛军川,郑建华,等. L 型耦合板结构能量传递系数特性的研究 [J]. 振动与冲击, 2015(17): 131-136.
Jiang Min-sheng, Niu Jun-chuan, Zheng Jian-hua, et al. Energy transfer coefficients features of L-shape coupled plates [J]. Journal of Vibration and Shocks, 2015, (17): 131-136
[15] Seo S, Hong S, Kil H. Power flow analysis of reinforced beam–plate coupled structures [J]. Journal of Sound and Vibration. 2003, 259(5): 1109-1129
[16] Pereira V S, Dos Santos J M C. Coupled plate energy models at mid- and high-frequency vibrations [J]. Computers & Structures, 2014, 134(4): 48-61.