自由阻尼梁高频能量流响应的解析模型

doi:10.7527/S1000-6893.2018.22616

Abstract

Abstract: An analytical energy flow model based on wave theory is proposed to predict the vibration of large damping composite structures such as a beam with free layer damping in the high-frequency range. Using the equivalent complex stiffness model, both equivalent flexural stiffness and structural loss factor of a beam with free layer damping are obtained. Then the corresponding energy density equation is derived for a beam with full free layer damping by energy flow analysis. By analyzing the energy transfer char-acteristic at the interface of damping treatment, an analytical model for the energy flow response of a beam with partial free layer damping is developed to predict the vibrating characteristics of the coupled large damping structure. Various numerical analyses show that the energy density obtained by the proposed model is in a good agreement with that by the classic wave model with time-and space-average treatment. Consequently, the present model can be employed to accurately predict the structural energy flow response to high-frequency excitation for large damping composite structures such as a beam with free layer damping.

Key words: beam with free layer damping, energy flow analysis, equivalent complex stiffness model, energy density, high-frequency vibration

CLC Number:

V214.3
TB122

TENG Xiaoyan, FENG Guobao, JIANG Xudong, ZHAO Hetao. Analytical model of high-frequency energy flow response for a beam with free layer damping[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2019, 40(4): 222616-222616.

References

[1] MACE B R, SHOTER P J. Energy flow models from finite element analysis[J]. Journal of Sound and Vibration, 2003, 233(3):369-389.
[2] 蔡忠云, 唐文勇, 张圣坤. 能量有限元方法在复合材料层合梁耦合结构振动分析中的应用[J]. 振动与冲击, 2010, 29(10):23-27. CAI Z Y, TANG W Y, ZHANG S K. Application of energy finite element method in vibration analysis of composite laminated beam structures[J]. Journal of Vibration and Shock, 2010, 29(10):23-27(in Chinese).
[3] 孔祥杰, 陈花铃, 祝丹晖, 等. 附加自由阻尼梁高频响应的能量有限元模型[J]. 振动与冲击, 2015, 34(17):94-99. KONG X J, CHEN H L, ZHU D H, et al. Energy finite element analysis for high frequency vibration of beams with free layer damping treatment[J]. Journal of Vibration and Shock, 2015, 34(17):94-99(in Chinese).
[4] 王迪, 朱翔, 李天匀, 等. 基于能量有限元法的功能梯度梁振动分析[J]. 振动与冲击, 2018, 37(3):119-124. WANG D, ZHU X, LI T Y, et al. Vibration analysis of a FGM beam based on energy finite element[J]. Journal of Vibration and Shock, 2018, 37(3):119-124(in Chinese).
[5] HAN J B, HONG S Y, SONG J H, et al. Vibrational energy flow models for the 1-D high damping system[J]. Journal of Mechanical Science and Technology, 2013, 27(9):2659-2671.
[6] HAN J B, HONG S Y, SONG J H, et al. Vibrational energy flow models for the Rayleigh-Love and Rayleigh-Bishop rods[J]. Journal of Sound and Vibration, 2014, 333(2), 520-540.
[7] 葛月, 牛军川, 刘知辉. 多种激励形式下任意角度耦合板振动传递特性研究[J]. 机械工程学报, 2017, 53(7):94-103. GE Y, NIU J C, LIU Z H. On energy transmission characteristics of coupled plates with arbitrary coupling angles to multiple types of excitation[J]. Journal of Mechanical Engineering, 2017, 53(7):94-103(in Chinese).
[8] 孙丽萍, 聂武能. 能量有限元法在船舶结构中的应用[J]. 哈尔滨工业大学学报, 2008, 40(9):1491-1494. SUN L P, NIU W N. Application of energy finite element method in ship structures[J]. Journal of Harbin Institute of Technology, 2008, 40(9):1491-1494(in Chinese).
[9] 周红卫, 陈海波, 王用岩. 耦合板结构的非结构零阶能量有限元分析[J]. 振动与冲击, 2015, 34(13):140-145. ZHONG H W, CHEN H B, WANG Y Y. Unstructured zero-order energy finite element method for coupled plate structures[J]. Journal of Vibration and Shock, 2015, 34(13):140-145(in Chinese).
[10] NAVAZI H M, NOKHBATOLFOGHAHAEI A, GHOBAD Y, et al. Experimental measurement of energy density in a vibrating plate and comparison with energy finite element analysis[J]. Journal of Sound and Vibration, 2016, 375:289-307.
[11] SEO S H, HONG S Y, KIL H G. Power flow analysis of reinforced beam-plate coupled structures[J]. Journal of Sound and Vibration, 2003, 267(2):301-334.
[12] 解妙霞, 陈花玲, 吴九汇. 圆柱壳高频弯曲振动的能量有限元分析[J]. 西安交通大学学报, 2008, 42(9):1113-1116. XIE M X, CHEN H L, WU J H. Energy finite element analysis to high frequency bending vibration in cylindrical shell[J]. Journal of Xi'an Jiaotong University, 2008, 42(9):1113-1116(in Chinese).
[13] KWON H W, HONG S Y, SONG J H. Vibrational energy flow analysis of coupled cylindrical thin shell structures[J]. Journal of Mechanical Science and Technology, 2016, 30(9):4049-4062.
[14] 陈书明, 王登峰, 谭刚平, 等. 基于能量有限元方法的声腔内部噪声预测[J]. 吉林大学学报(工学版), 2012, 42(2):303-308. CHEN S M, WANG D F, TAN G P, et al. Prediction of cavity interior noise based on energy finite element method[J]. Journal of Jilin University(Engineering and Technology Edition), 2012, 42(2):303-308(in Chinese).
[15] JANDRON M A, KOCH R M. Effectiveness of energy finite element analysis applied to submerged undersea vehicle noise prediction[J]. Journal of the Acoustical Society of America, 2014, 21(4):2193-2193.
[16] WU K C, VLAHOPOULOS N. Investigation of variance response in energy finite element analysis[J]. Journal of the Acoustical Society of America, 2017, 142(4):2614.
[17] 陈兆林, 杨智春, 王用岩, 等. 基于能量有限元法和虚拟模态综合法的高频冲击响应分析方法[J]. 航空学报, 2018, 39(8):221893. CHEN Z L, YANG Z C, WANG Y Y, et al. A high-frequency shock response analysis method based on energy finite element method and virtual mode synthesis and simulation[J]. Acta Aeronautica et Astronautica Sinica, 2018, 39(8):221893(in Chinese).
[18] KONG X J, CHEN H L, ZHU D H, et al. Study on the validity region of energy finite element analysis[J]. Journal of Sound and Vibration, 2014, 333(9):2588-2660.
[19] LE B A. Derivation of statistical energy analysis from radiative exchanges[J]. Journal of Sound and Vibration, 2007, 300(3):763-779.
[20] LE B A, COTONI V. Validity diagrams of statistical energy analysis[J]. Journal of Sound and Vibration, 2010, 329(2):221-235.
[21] WOHLEVER J, BERNHARD R J. Mechanical energy flow models of rods and beams[J]. Journal of Sound and Vibration, 1992, 153(1):1-19.
[22] LASE Y, ICHCHOU M N, JEZEQUEL L. Energy flow analysis of bars and beams:Theoretical formulations[J]. Journal of Sound and Vibration, 1996, 192(1):282-305.
[23] GOYDER H G D, WHITE R G. Vibrational power flow from machines into build-up structures, part Ι:Introduction and approximate analysis of beam and plate-like foundation[J]. Journal of Sound and Vibration, 1980, 68(1):59-75.

Analytical model of high-frequency energy flow response for a beam with free layer damping

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 3

Recommended Articles

Metrics

Comments

[1]	LIU Zhihui, NIU Junchuan, JIA Ruihao. Energy flow model for high-frequency vibration of beams in thermal-gradient environment [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(5): 425336-425336.
[2]	Feng Jianmin;Wu Fumin;Xiao Shouting. ENERGY METHOD FOR FATIGUE LIFE ESTIMATION UNDER CYCLIC ASYMMETRICAL LOADING [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 1996, 17(6): 107-111.
[3]	Su Bin;Cui Zhenyuan. SOME DISCUSSIONS ABOUT THE FRACTURE CRITERIA OF MIXED-MODE CRACK BASED ON THE STRESS PARAMETER [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 1989, 10(12): 674-677.