Direngenliğin Maksimize Edildiği Topolojilere Sahip Esnek Atalet Artırımı Mekanizmaları ile Düşük Ağırlıklı Periyodik Titreşim Yalıtıcısı Tasarımı

Yıl 2024, Cilt: 10 Sayı: 1, 155 - 171, 30.04.2024

Osman Yuksel , Erol Türkeş

Öz

Periyodik yapıların titreşim yalıtıcısı olarak kullanılması son zamanlarda literatürde karşılaşılan yenilikçi bir yaklaşımdır. Bu makalede, düşük ağırlıklı bir periyodik yapının titreşim yalıtımı performansı çalışılmıştır. Periyodik yapı, direngenliğin maksimize edildiği topolojilere sahip atalet artırımı mekanizmaları kullanılarak oluşturulmuştur. İlk olarak, atalet artırımı kavramı toplu parametreli bir model üzerinde tanıtılmıştır. Ardından, periyodik yapının tekrar eden yapı bloğu (birim hücre) olan esnek bağlantılı bir atalet artırımı mekanizması sunulmuştur. Direngenliğin maksimize edildiği düşük ağırlıklı bir birim hücre elde etmek için, bu esnek bağlantılı mekanizma üzerinde topoloji eniyilemesi gerçekleştirilmiştir. Daha sonrasında, direngenliğin maksimize edildiği topolojilere sahip bu düşük ağırlıklı atalet artırımı birim hücreleri birleştirilerek bir boyutlu periyodik bir yapı elde edilmiştir. Son olarak, titreşim iletkenliği grafikleri vasıtasıyla, oluşturulan periyodik yapının titreşim yalıtımı performansı gösterilmiştir. Tasarlanan topolojik olarak eniyilenmiş düşük ağırlıklı periyodik yapının, aynı direngenlikteki eniyileme yapılmamış orijinal yapıya nazaran, daha düşük bir ağırlık ile çok daha geniş bir bant aralığında yüksek performanslı titreşim yalıtımı sağladığı saptanmıştır.

Anahtar Kelimeler

esneklik minimizasyonu, atalet artırımı, periyodik yapı, topoloji eniyilemesi, titreşim yalıtıcısı

Lightweight Periodic Vibration Isolator Design via Compliant Inertial Amplification Mechanisms with Stiffness Maximized Topologies

Öz

As a novel innovative approach in the literature, periodic structures can be utilized as vibration isolators. In this paper, vibration isolation performance of a lightweight periodic structure is studied. The periodic structure is formed by using inertial amplification mechanisms with stiffness maximized topologies. First of all, inertial amplification concept is introduced on a lumped parameter model. Then, a compliant inertial amplification mechanism, which is the repetitive building block of the periodic structure (i.e., unit cell), is presented. Topology optimization is conducted on this mechanism to attain a stiffness maximized unit cell with reduced weight. After that, a one-dimensional periodic structure is constructed by attaching the lightweight inertial amplification unit cells with stiffness maximized topologies to each other. Finally, vibration isolation performance of the constructed periodic structure is demonstrated via transmissibility plots. It is observed that the designed topologically optimized lightweight periodic structure provides high performance vibration isolation for a wider frequency range with the same stiffness value and less weight, compared to the original structure.

Anahtar Kelimeler

compliance minimization, inertial amplification, periodic structure, topology optimization, vibration isolator

Kaynakça

• [1] S. Daley, F. A. Johnson, J. B. Pearson and R. Dixon, “Active vibration control for marine applications,” Control Engineering Practice, vol. 12, no. 4, pp. 465-474, 2004. doi:10.1016/S0967-0661(03)00135-7
• [2] Y. H. Guan, T. C. Lim and W. S. Shepard, “Experimental study on active vibration control of a gearbox system,” Journal of Sound and Vibration, vol. 282, no. 3-5, pp. 713-733, 2005. doi:10.1016/j.jsv.2004.03.043
• [3] S. M. Kuo, S. Mitra and W. S. Gan, “Active noise control system for headphone applications,” IEEE Transactions on Control Systems Technology, vol. 14, no. 2, pp. 331-335, 2006. doi:10.1109/TCST.2005.863667
• [4] S. M. Khot, P. Y. Nitesh, R. Tomar, S. Desai and S. Vittal, “Active vibration control of cantilever beam by using PID based output feedback controller,” Journal of Vibration and Control, vol. 18, no. 3, pp. 366-372, 2012. doi:10.1177/1077546311406307
• [5] O. Yuksel and C. Yilmaz, “Active noise control in a duct with flow,” Journal of Dynamic Systems, Measurement and Control, vol. 136, no. 3, p. 031014, 2014. doi:10.1115/1.4026410
• [6] A. Zippo, G. Ferrari, M. Amabili, M. Barbieri and F. Pellicano, “Active vibration control of a composite sandwich plate,” Composite Structures, vol. 128, pp. 100-114, 2015. doi:10.1016/j.compstruct.2015.03.037
• [7] M. Moshrefi-Torbati, A. J. Keane, S. J. Elliott, M. J. Brennan and E. Rogers, “Passive vibration control of a satellite boom structure by geometric optimization using genetic algorithm,” Journal of Sound and Vibration, vol. 267, no. 4, pp. 879-892, 2003. doi:10.1016/S0022-460X(03)00192-5
• [8] C. Yilmaz and N. Kikuchi, “Analysis and design of passive low-pass filter-type vibration isolators considering stiffness and mass limitations,” Journal of Sound and Vibration, vol. 293, no. 1-2, pp. 171-195, 2006. doi:10.1016/j.jsv.2005.09.016
• [9] D. Kamesh, R. Pandiyan and A. Ghosal, “Passive vibration isolation of reaction wheel disturbances using a low frequency flexible space platform,” Journal of Sound and Vibration, vol. 331, no. 6, pp. 1310-1330, 2012. doi:10.1016/j.jsv.2011.10.033
• [10] E. A. Ribeiro, J. T. Pereira and C. A. Bavastri, “Passive vibration control in rotor dynamics: Optimization of composed support using viscoelastic materials,” Journal of Sound and Vibration, vol. 351, pp. 43-56, 2015. doi:10.1016/j.jsv.2015.04.007
• [11] Z. Wu, X. Jing, B. Sun and F. Li, “A 6DOF passive vibration isolator using X-shape supporting structures,” Journal of Sound and Vibration, vol. 380, pp. 90-111, 2016. doi:10.1016/j.jsv.2016.06.004
• [12] S. S. Rao, “Vibration Control,” Mechanical Vibrations. Upper Saddle River: Prentice Hall, 2011.
• [13] D. J. Inman, “Design for Vibration Suppression,” Engineering Vibration. Upper Saddle River: Pearson Education, 2014.
• [14] J. Wen, G. Wang, D. Yu, H. Zhao and Y. Liu, “Theoretical and experimental investigation of flexural wave propagation in straight beams with periodic structures: Application to a vibration isolation structure,” Journal of Applied Physics, vol. 97, no. 11, p. 114907, 2005. doi:10.1063/1.1922068
• [15] G. Wang, X. Wen, J. Wen and Y. Liu, “Quasi-one-dimensional periodic structure with locally resonant band gap,” Journal of Applied Mechanics, vol. 73, no. 1, pp. 167-170, 2006. doi:10.1115/1.2061947
• [16] J. H. Oh, S. Qi, Y. Y. Kim and B. Assouar, “Elastic metamaterial insulator for broadband low-frequency flexural vibration shielding,” Physical Review Applied, vol. 8, no. 5, p. 054034, 2017. doi:10.1103/PhysRevApplied.8.054034
• [17] R. Prasad and A. Sarkar, “Broadband vibration isolation for rods and beams using periodic structure theory,” Journal of Applied Mechanics, vol. 86, no. 2, p. 021004, 2019. doi:10.1115/1.4042011
• [18] L. D’Alessandro, R. Ardito, F. Braghin and A. Corigliano, “Low frequency 3D ultra-wide vibration attenuation via elastic metamaterial,” Scientific Reports, vol. 9, p. 8039, 2019. doi:10.1038/s41598-019-44507-6
• [19] M. Sigalas and E. N. Economou, “Elastic and acoustic wave band structure,” Journal of Sound and Vibration, vol. 158, no. 2, pp. 377-382, 1992. doi:10.1016/0022-460X(92)90059-7
• [20] M. Sigalas and E. N. Economou, “Band structure of elastic waves in two dimensional systems,” Solid State Communications, vol. 86, no. 3, pp. 141-143, 1993. doi:10.1016/0038-1098(93)90888-T
• [21] Z. Liu, X. Zhang, Y. Mao, Y. Y. Zhu, Z. Yang, C. T. Chan and P. Sheng, “Locally resonant sonic materials,” Science, vol. 289, no. 5485, pp. 1734-1736, 2000. doi:10.1126/science.289.5485.1734
• [22] C. Goffaux and J. Sánchez-Dehesa, “Two-dimensional phononic crystals studied using a variational method: application to lattices of locally resonant materials,” Physical Review B, vol. 67, no. 14, p. 144301, 2003. doi:10.1103/PhysRevB.67.144301
• [23] C. Yilmaz, G. M. Hulbert and N. Kikuchi, “Phononic band gaps induced by inertial amplification in periodic media,” Physical Review B, vol. 76, no. 5, p. 054309, 2007. doi:10.1103/PhysRevB.76.054309
• [24] C. Yilmaz and G. M. Hulbert, “Theory of phononic gaps induced by inertial amplification in finite structures,” Physics Letters A, vol. 374, no. 34, pp. 3576-3584, 2010. doi:10.1016/j.physleta.2010.07.001
• [25] G. Acar and C. Yilmaz, “Experimental and numerical evidence for the existence of wide and deep phononic gaps induced by inertial amplification in two-dimensional solid structures,” Journal of Sound and Vibration, vol. 332, no. 24, pp. 6389-6404, 2013. doi:10.1016/j.jsv.2013.06.022
• [26] S. Taniker and C. Yilmaz, “Phononic gaps induced by inertial amplification in BCC and FCC lattices,” Physics Letters A, vol. 377, no. 31-33, pp. 1930-1936, 2013. doi:10.1016/j.physleta.2013.05.022
• [27] O. Yuksel and C. Yilmaz, “Shape optimization of phononic band gap structures incorporating inertial amplification mechanisms,” Journal of Sound and Vibration, vol. 355, pp. 232-245, 2015. doi:10.1016/j.jsv.2015.06.016
• [28] S. Taniker and C. Yilmaz, “Design, analysis and experimental investigation of three-dimensional structures with inertial amplification induced vibration stop bands,” International Journal of Solids and Structures, vol. 72, pp. 88-97, 2015. doi:10.1016/j.ijsolstr.2015.07.013
• [29] N. M. M. Frandsen, O. R. Bilal, J. S. Jensen and M. I. Hussein, “Inertial amplification of continuous structures: Large band gaps from small masses,” Journal of Applied Physics, vol. 119, p. 124902, 2016. doi:10.1063/1.4944429
• [30] S. Taniker and C. Yilmaz, “Generating ultra wide vibration stop bands by a novel inertial amplification mechanism topology with flexure hinges,” International Journal of Solids and Structures, vol. 106, pp. 129-138, 2017. doi:10.1016/j.ijsolstr.2016.11.026
• [31] O. Yuksel and C. Yilmaz, “Size and topology optimization of inertial amplification induced phononic band gap structures,” in Proceedings of the ASME International Mechanical Engineering Congress and Exposition, Tampa, Florida, USA, 2017. p. V013T01A007. doi:10.1115/IMECE2017-71342
• [32] M. Barys, J. S. Jensen and N. M. M. Frandsen, “Efficient attenuation of beam vibrations by inertial amplification,” European Journal of Mechanics-A/Solids, vol. 71, pp. 245-257, 2018. doi:10.1016/j.euromechsol.2018.04.001
• [33] A. H. Orta and C. Yilmaz, “Inertial amplification induced phononic band gaps generated by a compliant axial to rotary motion conversion mechanism,” Journal of Sound and Vibration, vol. 439, pp. 329-343, 2019. doi:10.1016/j.jsv.2018.10.014
• [34] J. Li, P. Yang and S. Li, “Phononic band gaps by inertial amplification mechanisms in periodic composite sandwich beam with lattice truss cores,” Composite Structures, vol. 231, p. 111458, 2020. doi:10.1016/j.compstruct.2019.111458
• [35] O. Yuksel and C. Yilmaz, “Realization of an ultrawide stop band in a 2-D elastic metamaterial with topologically optimized inertial amplification mechanisms,” International Journal of Solids and Structures, vol. 203, pp. 138-150, 2020. doi:10.1016/j.ijsolstr.2020.07.018
• [36] S. Muhammad, S. Wang, F. Li and C. Zhang, “Bandgap enhancement of periodic nonuniform metamaterial beams with inertial amplification mechanisms,” Journal of Vibration and Control, vol. 26, no. 15-16, pp. 1309-1318, 2020. doi:10.1177/1077546319895630
• [37] O. Yuksel and C. Yilmaz, “Design of a broadband elastic metamaterial via topologically optimized inertial amplification mechanisms,” in Proceedings of the 11th International Conference on Structural Dynamics, Athens, Greece, 2020. pp. 4125-4138. doi:10.47964/1120.9337.19454
• [38] K. Mizukami, K. Funaba and K. Ogi, “Design and three-dimensional printing of carbon-fiber-composite elastic metamaterials with inertial amplification mechanisms,” Journal of Sound and Vibration, vol. 513, p. 116412, 2021. doi:10.1016/j.jsv.2021.116412
• [39] C. Xi, L. Dou, Y. Mi and H. Zheng, “Inertial amplification induced band gaps in corrugated-core sandwich panels,” Composite Structures, vol. 267, p. 113918, 2021. doi:10.1016/j.compstruct.2021.113918
• [40] Y. Mi and X. Yu, “Sound transmission of acoustic metamaterial beams with periodic inertial amplification mechanisms,” Journal of Sound and Vibration, vol. 499, p. 116009, 2021. doi:10.1016/j.jsv.2021.116009
• [41] M. Miniaci, M. Mazzotti, A. Amendola and F. Fraternali, “Effect of prestress on phononic band gaps induced by inertial amplification,” International Journal of Solid and Structures, vol. 216, pp. 156-166, 2021. doi:10.1016/j.ijsolstr.2020.12.011
• [42] A. Banerjee, S. Adhikari and M. I. Hussein, “Inertial amplification band-gap generation by coupling a levered mass with a locally resonant mass,” International Journal of Mechanical Sciences, vol. 207, p. 106630, 2021. doi:10.1016/j.ijmecsci.2021.106630
• [43] Y. Li and W. Zhou, “Bandgap and vibration transfer characteristics of scissor-like periodic metamaterials,” Journal of Applied Physics, vol. 130, p. 025103, 2021. doi:10.1063/5.0047119
• [44] E. Er, E. Türkeş and O. Yüksel, “A parametric investigation on various compliant inertial amplification mechanisms for a periodic vibration isolator design,” Gazi Journal of Engineering Sciences, vol. 8, no. 3, pp. 511-523, 2022. doi:10.30855/gmbd.0705039
• [45] Y. Zeng, L. Cao, S. Wan, T. Guo, Y. F. Wang, Q. J. Du, B. Assouar and Y. S. Wang, “Seismic metamaterials: Generating low-frequency bandgaps induced by inertial amplification,” International Journal of Mechanical Sciences, vol. 221, p. 107224, 2022. doi:10.1016/j.ijmecsci.2022.107224
• [46] Y. Li, N. Zhao and S. Yao, “Theoretical analysis of 2D meta-structure with inertia amplification,” International Journal of Mechanical Sciences, vol. 235, p. 107717, 2022. doi:10.1016/j.ijmecsci.2022.107717
• [47] Y. Li, N. Zhao and S. Yao, “Nonlinear dynamics of 1D meta-structure with inertia amplification,” Applied Mathematical Modelling, vol. 118, pp. 728-744, 2023. doi:10.1016/j.apm.2023.01.039
• [48] H. Li, Y. Li and X. Liu, “Double-beam metastructure with inertially amplified resonators for flexural wave attenuation,” European Journal of Mechanics – A / Solids, vol. 97, p. 104794, 2023. doi:10.1016/j.euromechsol.2022.104794
• [49] A. Ni and Z. Shi, “Inertial amplified topological metamaterial beams,” Journal of Applied Physics, vol. 133, p. 065105, 2023. doi:10.1063/5.0140790
• [50] Y. F. Wang, Y. Z. Wang, B. Wu, W. Chen and Y. S. Wang, “Tunable and active phononic crystals and metamaterials,” Applied Mechanics Reviews, vol. 72, no. 4, p. 040801, 2020. doi:10.1115/1.4046222
• [51] C. Yilmaz and G. M. Hulbert, “Dynamics of Locally Resonant and Inertially Amplified Lattice Materials,” Dynamics of Lattice Materials. West Sussex: John Wiley & Sons, 2017.
• [52] H. W. Ma, S. M. Yao, L. Q. Wang and Z. Zhong, “Analysis of the displacement amplification ratio of bridge-type flexure hinge,” Sensors and Actuators A: Physical, vol. 132, no. 2, pp. 730-736, 2006. doi:10.1016/j.sna.2005.12.028
• [53] L. L. Howell, “Introduction to Compliant Mechanisms,” Handbook of Compliant Mechanisms. West Sussex: John Wiley & Sons, 2013.
• [54] O. Yüksel, “An overview on topology optimization methods employed in structural engineering,” Kırklareli University Journal of Engineering and Science, vol. 5, no. 2, pp. 159-175, 2019. doi:10.34186/klujes.606666
• [55] E. Andreassen, A. Clausen, M. Schevenels, B. S. Lazarov and O. Sigmund, “Efficient topology optimization in MATLAB using 88 lines of code,” Structural and Multidisciplinary Optimization, vol. 43, no. 1, pp. 1-16, 2011. doi:10.1007/s00158-010-0594-7 [56] O. Sigmund and K. Maute, “Topology optimization approaches,” Structural and Multidisciplinary Optimization, vol. 48, no. 6, pp. 1031-1055, 2013. doi:10.1007/s00158-013-0978-6
• [57] J. S. Jensen and N. L. Pedersen, “On maximal eigenfrequency separation in two-material structures: the 1d and 2d scalar cases,” Journal of Sound and Vibration, vol. 289, no. 4-5, pp. 967-986, 2006. doi:10.1016/j.jsv.2005.03.028
• [58] O. Yuksel and C. Yilmaz, “Obtaining inertial amplification induced phononic gaps via structural optimization of a compliant mechanism,” in Proceedings of the 11th International Conference on Vibration Problems, Lisbon, Portugal, 2013. pp. 1-10.