| 摘要(英) |
This thesis establishes a theoretical analysis method to investigate the vibration characteristics and transient wave propagation behavior of plate structures under the influence of mass effects, including the differences in resonant frequencies and mode shapes of plates with arbitrarily added mass distributions, as well as the transmission paths and energy changes of flexural waves passing through mass arrays, thereby achieving the effect of a mass lens.
The theoretical model first derives an analytical solution for the free vibration of a plate with an attached mass array. After obtaining the vibration characteristics such as resonant frequency and mode shape using the Gorman superposition method, the transient wave propagation theoretical solution is obtained through normal mode method. The theoretical analysis results of vibration characteristics and transient wave propagation are verified by comparison with finite element simulation software. The theoretical analysis of resonant frequency, mode shape, transient displacement, strain, and other physical quantities is highly accurate, confirming that the theoretical method proposed in this study can accurately and effectively analyze the frequency domain and time domain dynamic behavior of plate structures with arbitrarily added mass.
Based on this theoretical model, the influence of the arrangement and distribution of the mass array on the vibration characteristics and transient wave propagation of the plate is investigated. By changing the dynamic behavior of the plate structure through the attached mass array, a wave propagation path analysis method applicable to plate flexural waves is developed. The relationship between the group velocity of flexural waves and the added mass is summarized to control the wave velocity difference to change the wave propagation direction, thereby forming a specific required wave propagation path, and establishing its corresponding mass array.
Finally, based on this design method, the content of the mass array that can form a specific effect, including focusing, divergence, and control of wave propagation direction, is calculated, successfully achieving the purpose of controlling the energy of flexural waves, which can provide significant benefits for energy recovery and vibration reduction. |
| 參考文獻 |
[1] D. J. Gorman, “Free Vibration Analysis of the Completely Free Rectangular Plate by the Method of Superposition.” Journal of Sound and Vibration, Vol 57(3), 1978, pp. 437-447.
[2] S. D. Yu, “Free and Forced Flexural Vibration Analysis of Cantilever Plates with Attached Point Mass.” Journal of sound and vibration, Vol 321(1-2), 2009, pp. 270-285.
[3] S. Abrate, “Transient Response of Beams, Plates, and Shells to Impulsive Loads.” ASME International Mechanical Engineering Congress and Exposition, Vol 43033, January 2007, pp. 107-116.
[4] S. C. S. Lin, T. J. Huang, J. H. Sun, T. T. Wu, “Gradient-Index Phononic Crystals.” Physical Review B—Condensed Matter and Materials Physics, Vol 79(9), 2009, 094302.
[5] Y. Jin, D. Torrent, Y. Pennec, Y. Pan, B. Djafari-Rouhani, “Simultaneous Control of the S and A Lamb Modes by Graded Phononic Crystal Plates.” Journal of Applied Physics, Vol 117(24), 2015.
[6] J. Zhao, B. Bonello, R. Marchal, O. Boyko, “Beam Path and Focusing of Flexural Lamb Waves within Phononic Crystal-Based Acoustic Lenses.” New Journal of Physics, Vol 16(6), 2014, 063031.
[7] Y. Ruan, X. Liang, “Reflective Elastic Metasurface for Flexural Wave Based on Surface Impedance Model.” International Journal of Mechanical Sciences, Vol 212, 2021, 106859.
[8] K. C. Chuang, D. F. Wang, J. J. Liu, C. Y. Liao, “Linking Time-Domain Vibration Behaviors to Spatial-Domain Propagating Waves in a Leaf-like Gradient-Index Phononic Crystal Lens.” Crystals, Vol 11(12), 2021, 1490.
[9] D. F. Wang, K. C. Chuang, J. J. Liu, C. Y. Liao, “Modeling Full-Field Transient Flexural Waves on Damaged Plates with Arbitrary Excitations Using Temporal Vibration Characteristics.” Sensors, Vol 22(16), 2022, 5958.
[10] S. H. Kim, “Analytic Solution of the Generalized Eaton Lens.” Journal of Modern Optics, Vol 68(3), 2021, pp. 143-145.
[11] A. Climente, D. Torrent, J. Sanchez-Dehesa, “Gradient Index Lenses for Flexural Waves Based on Thickness Variations.” Applied Physics Letters, Vol 105(6), 2014.
[12] A. Zareei, A. Darabi, M. J. Leamy, M. R. Alam, “Continuous Profile Flexural GRIN Lens: Focusing and Harvesting Flexural Waves.” Applied Physics Letters, Vol 112(2), 2018.
[13] W. Huang, H. Ji, J. Qiu, L. Cheng, “Analysis of Ray Trajectories of Flexural Waves Propagating over Generalized Acoustic Black Hole Indentations.” Journal of Sound and Vibration, Vol 417, 2018, pp. 216-226.
[14] J. H. Chen, I. C. Chao, T. Chen, “Bandgaps for Flexural Waves in Infinite Beams and Plates with a Periodic Array of Resonators.” Journal of Mechanics, Vol 38, 2022, pp. 376-389.
[15] M. ?arbort, T. Tyc, “Spherical Media and Geodesic Lenses in Geometrical Optics.” Journal of Optics, Vol 14(7), 2012, 075705.
[16] 林沛熹、廖展誼：〈矩形平板施加點質量陣列的振動特性與暫態波傳分析與波源歷時反算應用〉。碩士論文，國立中央大學機械工程研究所，2022年。
[17] D. F. Wang, Y. H. Wang, K. C. Chuang, “Nearly-Isotropic Adjustable Phononic Crystal Lenses Using Concentrated Balls with Hertz Contacts.” Physics Letters A, Vol 396, 2021, 127240.
[18] V. Giurgiutiu, Structural health monitoring: with piezoelectric wafer active sensors. United States: Academic Press, 2007. |
[Endnote RIS 格式]
[相關文章]
[文章引用]
[完整記錄]
[館藏目錄]
至系統瀏覽論文 (2028-1-20以後開放)
plurk
funp
live
udn
HD
myshare
netvibes
friend
youpush
delicious
baidu
Google bookmarks
del.icio.us
hemidemi
facebook
twitter
google
reddit