基于禁带机理的加筋板减振设计方法

doi:10.7527/S1000-6893.2021.26007

Abstract

Abstract: Aiming at the vibration reduction requirements of engineering periodic structures such as stiffened plates in service conditions, a design method for vibration control using the band gap characteristics in the periodic structure is proposed. Band gap refers to a frequency band where elastic waves in a periodic structure cannot propagate. By constructing the periodic structure, a band gap can be created in a specific frequency band. Hence, the elastic waves can be controlled, so as to achieve the purpose of vibration control. Based on this academic idea, a design method for periodic structure based on the band gap is established, which solves the key technologies including the evaluation of the performance for vibration control based on the band gaps, the selection of the band gaps, and the sparse sampling of the multi-dimensional parameter space. Then, taking the orthogonal stiffened plate as an example, the height and thickness of the ribs are designed to achieve a band gap with a bandwidth of 500 Hz. The forced response analysis shows that boundary conditions and material mistuning have little influences on the performance of vibration reduction. Moreover, based on the structural compliance, the static analysis has been employed to check the static performance of stiffened plate. It is found that the designed stiffened plate also has higher static stiffness, which meets the engineering requirements.

Key words: periodic structure, band gap, design of stiffened plate, vibration reduction, inverse problem

CLC Number:

V214.8

JIANG Zhou, FAN Yu, LI Lin, SHI Jiahui. Design method of stiffened plate for vibration reduction based on band gaps[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(9): 226007-226007.

References

[1] VASILIEV V V, BARYNIN V A, RASIN A F. Anisogrid lattice structures-survey of development and application[J]. Composite Structures, 2001, 54(2-3): 361-370.
[2] GU M K, HE W, TANG K, et al. Research on the development plan of Chinese liquid launch vehicle structure system[J]. Astronautical Systems Engineering Technology, 2021, 5(2): 55-67 (in Chinese). 顾名坤, 何巍, 唐科, 等. 中国液体运载火箭结构系统发展规划研究[J]. 宇航总体技术, 2021, 5(2): 55-67.
[3] HOU A, GRAMOLL K. Design and fabrication of CFRP interstage attach fitting for launch vehicles[J]. Journal of Aerospace Engineering, 1999, 12(3): 83-91.
[4] WEGNER P M, GANLEY J M, HUYNRECHTS S M, et al. Advanced grid stiffened composite payload shroud for the OSP launch vehicle[C]//2000 IEEE Aerospace Conference. Piscataway: IEEE Press, 2000: 359-365.
[5] KONG B, CHEN P H, CHEN Y. Post-buckling failure evaluation method of integrated composite stiffened panels under uniaxial compression[J]. Acta Materiae Compositae Sinica, 2014, 31(3): 765-771 (in Chinese). 孔斌, 陈普会, 陈炎. 复合材料整体加筋板轴压后屈曲失效评估方法[J]. 复合材料学报, 2014, 31(3): 765-771.
[6] MAN L T, YANG C.Optimal design of rectangular stiffened plate structure[J]. China Science and Technology Information, 2018(19): 45-48 (in Chinese). 满林涛, 杨婵. 矩形加筋板结构优化设计[J]. 中国科技信息, 2018(19): 45-48.
[7] ORIFICI A C, THOMSON R S, DEGENHARDT R, et al. Degradation investigation in a postbuckling composite stiffened fuselage panel[J]. Composite Structures, 2008, 82(2): 217-224.
[8] WANG Y, LI S, XU Q Y, et al. Optimization design and analysis of stiffened composite panels in post-buckling under shear[J]. Acta Aeronautica et Astronautica Sinica, 2016, 37(5): 1512-1525 (in Chinese). 王燕, 李书, 许秋怡, 等. 复合材料加筋板剪切后屈曲分析与优化设计[J]. 航空学报, 2016, 37(5): 1512-1525.
[9] TRIPATHI M, DHAKAL R P, DASHTI F, et al. Low-cycle fatigue behaviour of reinforcing bars including the effect of inelastic buckling[J]. Construction and Building Materials, 2018, 190: 1226-1235.
[10] LAHUERTA F, KOORN N, SMISSAERT D. Wind turbine blade trailing edge failure assessment with sub-component test on static and fatigue load conditions[J]. Composite Structures, 2018, 204: 755-766.
[11] DÁVILA C G, BISAGNI C. Fatigue life and damage tolerance of postbuckled composite stiffened structures with initial delamination[J]. Composite Structures, 2017, 161: 73-84.
[12] WILLIAMS P A, KIM H A, BUTLER R. Bimodal buckling ofoptimised truss-lattice shear panels[J]. AIAA Journal, 2008, 46(8): 1937-1943.
[13] ALINIA M M. A study into optimization of stiffeners in plates subjected to shear loading[J]. Thin-Walled Structures, 2005, 43(5): 845-860.
[14] WANG B, TIAN K, HAO P, et al. Hybrid analysis and optimization of hierarchical stiffened plates based on asymptotic homogenization method[J]. Composite Structures, 2015, 132: 136-147.
[15] BAZ A M, RO J J. Vibration control of plates with active constrained-layer damping[C]//Smart Structures and Materials ’95. Proc SPIE 2445, Smart Structures and Materials 1995: Passive Damping, 1995, 2445: 393-409.
[16] HUGHES W, MCNELIS A, HIMELBLAU H. Investigation of acoustic fields for the Cassini spacecraft-Reverberant versus launch environments[C]//5th AIAA/CEAS Aeroacoustics Conference and Exhibit. Reston: AIAA, 1999: 1193-1203.
[17] OSMAN H, JOHNSON M, FULLER C, et al. Interior noise reduction of composite cylinders using distributed vibration absorbers[C]//7th AIAA/CEAS Aeroacoustics Conference and Exhibit.Reston: AIAA, 2001: 2230.
[18] GRIFFIN S, GUSSY J, LANE S, et al. Innovative passive mechanisms for control of sound in a launch vehicle fairing[C]//41 st Structures, Structural Dynamics, and Materials Conference and Exhibit. Reston: AIAA, 2000: 1436.
[19] CAPRACE J D, BAIR F, RIGO P. Scantling multi-objective optimisation of a LNG carrier[J]. Marine Structures, 2010, 23(3): 288-302.
[20] NIKBAKT S, KAMARIAN S, SHAKERI M. A review on optimization of composite structures Part I: Laminated composites[J]. Composite Structures, 2018, 195: 158-185.
[21] XIE C H, WU Y, LIU Z S. Modeling and active vibration control of lattice grid beam with piezoelectric fiber composite using fractional order PDμ algorithm[J]. Composite Structures, 2018, 198: 126-134.
[22] MEAD D J, PARTHAN S. Free wave propagation in two-dimensional periodic plates[J]. Journal of Sound and Vibration, 1979, 64(3): 325-348.
[23] RUZZENE M, BAZ A. Control of wave propagation in periodic composite rods using shape memory inserts[J]. Journal of Vibration and Acoustics, 2000, 122(2): 151-159.
[24] ZHOU C W, LAINÉ J P, ICHCHOU M N, et al. Multi-scale modelling for two-dimensional periodic structures using a combined mode/wave based approach[J]. Computers & Structures, 2015, 154: 145-162.
[25] PENG H, PAI P F, DENG H G. Acoustic multi-stopband metamaterial plates design for broadband elastic wave absorption and vibration suppression[J]. International Journal of Mechanical Sciences, 2015, 103: 104-114.
[26] CAI C X, WANG Z H, CHU Y Y, et al. The phononic band gaps of Bragg scattering and locally resonant pentamode metamaterials[J]. Journal of Physics D: Applied Physics, 2017, 50(41): 415105.
[27] YU K P, CHEN T N, WANG X P. Band gaps in the low-frequency range based on the two-dimensional phononic crystal plates composed of rubber matrix with periodic steel stubs[J]. Physica B: Condensed Matter, 2013, 416: 12-16.
[28] MACE B R, MANCONI E. Wave motion and dispersion phenomena:Veering, locking and strong coupling effects[J]. The Journal of the Acoustical Society of America, 2012, 131(2): 1015-1028.
[29] CHEN S B, WANG G, SONG Y B. Low-frequency vibration isolation in sandwich plates by piezoelectric shunting arrays[J]. Smart Materials and Structures, 2016, 25(12): 125024.
[30] WEN J H, CHEN S B, WANG G, et al. Directionality of wave propagation and attenuation in plates with resonant shunting arrays[J]. Journal of Intelligent Material Systems and Structures, 2016, 27(1): 28-38.
[31] LANGLEY R S, COTONI V. The direct field boundary impedance of two-dimensional periodic structures with application to high frequency vibration prediction[J]. The Journal of the Acoustical Society of America, 2010, 127(4): 2118-2128.
[32] VIGRAN T E. Sound transmission in multilayered structures-Introducing finite structural connections in the transfer matrix method[J]. Applied Acoustics, 2010, 71(1): 39-44.
[33] DOZIO L, RICCIARDI M. Free vibration analysis of ribbed plates by a combined analytical-numerical method[J]. Journal of Sound and Vibration, 2009, 319(1-2): 681-697.
[34] WU J R, LIU W H. Vibration of rectangular plates with edge restraints and intermediate stiffeners[J]. Journal of Sound and Vibration, 1988, 123(1): 103-113.
[35] JIANG S J, SUN M Y, DONG T K, et al. Dynamic characteristics and responses of fused filament fabrication thin plates[J]. Journal of Northeastern University, 2020, 41(5): 673-678 (in Chinese).
[36] LIN T R, ZHANG K. An analytical study of the free and forced vibration response of a ribbed plate with free boundary conditions[J]. Journal of Sound and Vibration, 2018, 422: 15-33.
[37] ZHOU C W, LAINÉ J P, ICHCHOU M N, et al. Numerical and experimental investigation on broadband wave propagation features in perforated plates[J]. Mechanical Systems and Signal Processing, 2016, 75: 556-575.
[38] MANCONI E, MACE B R. Wave characterization of cylindrical and curved panels using a finite element method[J]. The Journal of the Acoustical Society of America, 2009, 125(1): 154-163.
[39] MACE B R, MANCONI E. Modelling wave propagation in two-dimensional structures using finite element analysis[J]. Journal of Sound and Vibration, 2008, 318(4-5): 884-902.
[40] MACE B R, DUHAMEL D, BRENNAN M J, et al. Finite element prediction of wave motion in structural waveguides[J]. The Journal of the Acoustical Society of America, 2005, 117(5): 2835-2843.
[41] WILCOX C H. Theory of bloch waves[J]. Journal d'Analyse Mathématique, 1978, 33(1): 146-167.
[42] MCKAY M D, BECKMAN R J, CONOVER W J. A comparison of three methods for selecting values of input variables in the analysis of output from a computer code[J]. Technometrics, 2000, 42(1): 55-61.
[43] LI L, JIANG Z, FAN Y, et al. Coupled band gaps in the piezoelectric composite plate with interconnected electric impedance[C]//Proceedings of ASME 2018 Conference on Smart Materials, Adaptive Structures and Intelligent Systems.New York:ASME, 2018.
[44] LI L, JIANG Z, FAN Y, et al. Creating thecoupled band gaps in piezoelectric composite plates by interconnected electric impedance[J]. Materials (Basel, Switzerland), 2018, 11(9): 1656.
[45] MEAD D J. Wave propagation and natural modes in periodic systems: Ⅱ. Multi-coupled systems, with and without damping[J]. Journal of Sound and Vibration, 1975, 40(1): 19-39.
[46] BOBROVNITSKII Y I. On the energy flow in evanescent waves[J]. Journal of Sound and Vibration, 1992, 152(1): 175-176.
[47] KURZE U J. Comments on 《On the energy flow in evanescent waves》[J]. Journal of Sound and Vibration, 1993, 161(2): 355-356.
[48] FAN Y, COLLET M, ICHCHOU M, et al. A wave-based design of semi-active piezoelectric composites for broadband vibration control[J]. Smart Materials and Structures, 2016, 25(5): 055032.
[49] PENG X R, XIONG C X, LI W B. Reciprocal criterion of structural compliance topology optimization[J]. Chinese Journal of Applied Mechanics, 2019, 36(2): 334-342, 505 (in Chinese). 彭细荣, 熊创贤, 李文斌. 结构柔顺度拓扑优化的倒变量准则[J]. 应用力学学报, 2019, 36(2): 334-342, 505.
[50] PENG X R, SUI Y K. Adjoint method for stress sensitivity analysis of structural topology optimization[J]. Chinese Journal of Applied Mechanics, 2017, 34(5): 887-893, 1013 (in Chinese). 彭细荣, 隋允康. 结构拓扑优化应力敏度分析的伴随法[J]. 应用力学学报, 2017, 34(5): 887-893, 1013.

Design method of stiffened plate for vibration reduction based on band gaps

RichHTML

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 13

Recommended Articles

Metrics

Comments

[1]	WANG Baoguo, HUANG Weiguang, XU Yanji. Professor Naixing Chen's main academic achievements and significant contributions to the development of science and technology: In memory of professor Naixing Chen's one-year anniversary [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2019, 40(10): 23355-023355.
[2]	WEN Zhuoqun, WANG Pengfei, ZHANG Yan, JIANG Yanfen. Vibration reduction technology of mechanical metamaterials presented to large scale structures [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2018, 39(S1): 721651-721651.
[3]	YU Weigang, CHEN Guo, LIU Binbin, CUN Wenyuan, ZHANG Maolin, ZHAO Zhengda, CHEN Xuemei, HOU Minli. Design of a particle damping absorber and experimental study on vibration damping of the pipe [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2018, 39(12): 422264-422264.
[4]	BAI Junqiang, QIU Yasong, HUA Jun. Improved Airfoil Inverse Design Method Based on Gappy POD [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2013, 34(4): 762-771.
[5]	QI Wen-kai;GAO De-ping. Microslip Study on Friction Damping and Its Application in Design of Vibration Reduction [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2006, 27(5): 805-809.
[6]	LI Feng-ming;WANG Yue-sheng. Study on Wave Localization in Disordered Periodic Piezoelectric Composite Structures [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2006, 27(1): 38-43.
[7]	ZHANG Xiao-wei;YANG Jia-ling. Inverse Problem of Elastica in the Design of Flexible-walled Wind Tunnel [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2005, 26(6): 696-700.
[8]	YU Chao;LI Xiao-dong. Feedforward Control Study on Gust/Cascade Interaction Noise [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2003, 24(3): 237-241.
[9]	Hua Jun;Zhang Zhongyin;Fu Dawei;G. Redeker. CFD SOFTWARE FOR TRANSONIC AIRFOIL AND WING DESIGN—AN UPDATE Hua Jun, Zhang Zhongyin [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 1997, 18(5): 519-522.
[10]	Dai Hua. STIFFNESS MATRIX CORRECTIONUSING TEST DATA [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 1994, 15(9): 1091-1094.
[11]	Feng Lin;Lei Ping;Ruan Ying-zheng. A POLARIZATION-SELECTIVE REFLECTOR ANTENNA WITH SMALL RCS [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 1993, 14(11): 649-652.
[12]	Yao Qi-hang;Huang Wen-chao;Ma Xiao-jun. INVESTIGATION OF CABIN NOISE REDUCTION IN THE Yl2 [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 1992, 13(9): 543-547.
[13]	Qi Piqian. AN INVERSE PROBLEM OF THE BRANCH MODE SYNTHESIS [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 1991, 12(6): 238-244.